diff --git a/.github/workflows/python-package.yml b/.github/workflows/python-package.yml
index 276827e4..744e9d54 100644
--- a/.github/workflows/python-package.yml
+++ b/.github/workflows/python-package.yml
@@ -15,7 +15,7 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: [3.8]
+        python-version: ["3.10", "3.11", "3.12"]
 
     steps:
     - uses: actions/checkout@v2
diff --git a/docs/notebooks/active_inference_from_scratch.ipynb b/docs/notebooks/active_inference_from_scratch.ipynb
index 53ca2f56..da06de66 100644
--- a/docs/notebooks/active_inference_from_scratch.ipynb
+++ b/docs/notebooks/active_inference_from_scratch.ipynb
@@ -165,9 +165,9 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "[[0.42309635]\n",
-            " [0.50568896]\n",
-            " [0.07121468]]\n",
+            "[[0.16880278]\n",
+            " [0.51728256]\n",
+            " [0.31391466]]\n",
             "Integral of the distribution: 1.0\n"
           ]
         }
@@ -232,7 +232,7 @@
       "outputs": [
         {
           "data": {
-            "image/png": "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",
+            "image/png": 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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -281,9 +281,9 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "[[0.322 0.726 0.772 0.126]\n",
-            " [0.52  0.812 0.567 0.608]\n",
-            " [0.452 0.44  0.201 0.441]]\n"
+            "[[0.089 0.739 0.145 0.399]\n",
+            " [0.772 0.201 0.026 0.578]\n",
+            " [0.181 0.253 0.788 0.844]]\n"
           ]
         }
       ],
@@ -308,9 +308,9 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "[[0.249 0.367 0.501 0.107]\n",
-            " [0.402 0.41  0.368 0.518]\n",
-            " [0.349 0.223 0.131 0.375]]\n"
+            "[[0.086 0.619 0.151 0.219]\n",
+            " [0.741 0.168 0.027 0.318]\n",
+            " [0.174 0.212 0.821 0.463]]\n"
           ]
         }
       ],
@@ -340,10 +340,10 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "[[0.2488664 ]\n",
-            " [0.40202984]\n",
-            " [0.34910376]]\n",
-            "Integral of P(X|Y=0): 1.0\n"
+            "[[0.08555937]\n",
+            " [0.74093812]\n",
+            " [0.1735025 ]]\n",
+            "Integral of P(X|Y=0): 0.9999999999999999\n"
           ]
         }
       ],
@@ -2028,12 +2028,12 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Time 2: Agent observes itself in location: (0, 1)\n"
+            "Time 2: Agent observes itself in location: (0, 0)\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -2045,12 +2045,12 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Time 3: Agent observes itself in location: (0, 1)\n"
+            "Time 3: Agent observes itself in location: (0, 0)\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -2062,12 +2062,12 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Time 4: Agent observes itself in location: (0, 2)\n"
+            "Time 4: Agent observes itself in location: (0, 0)\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -2353,12 +2353,12 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Time 3: Agent observes itself in location: (0, 0)\n"
+            "Time 3: Agent observes itself in location: (0, 1)\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -2370,12 +2370,12 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Time 4: Agent observes itself in location: (0, 0)\n"
+            "Time 4: Agent observes itself in location: (0, 2)\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -2387,12 +2387,12 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Time 5: Agent observes itself in location: (0, 1)\n"
+            "Time 5: Agent observes itself in location: (1, 2)\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -2404,12 +2404,12 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Time 6: Agent observes itself in location: (0, 2)\n"
+            "Time 6: Agent observes itself in location: (2, 2)\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -2421,12 +2421,12 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Time 7: Agent observes itself in location: (1, 2)\n"
+            "Time 7: Agent observes itself in location: (2, 2)\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
diff --git a/docs/notebooks/cue_chaining_demo.ipynb b/docs/notebooks/cue_chaining_demo.ipynb
index e01e2d68..b00a28f9 100644
--- a/docs/notebooks/cue_chaining_demo.ipynb
+++ b/docs/notebooks/cue_chaining_demo.ipynb
@@ -118,7 +118,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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AAAQTDMHzzz+Xqy/+ZN520p8MexQABiCYYAhuveqLmbfH/PzKW08f9igADEAwwQx75qnHcsN3/1N+43f+PLWbb0GAUeCnNcywa7/1mRzy+ndl0ZLjhj0KAAMSTDCDHn3g+tx36yU57pQ/G/YoAEzAvGEPALuSqy/+VI469kPZ8+X7ZsPPn/jF9k3PPZsNzz6ZPefvN8TpAHgpgglm0M/W3ZvH1t6UW6/6q222X/utz+R7/7AyZ3zhiZf4kwAMk2CCGXTy8q+nbX5+m20X/ZdleeNvfCSHv+HkIU0FQI9ggmmwedNzufeWS3bYvmjJsdlrwYE7bF944OFZfISbwAFmK8EE02DjhvVZff6O77H0ux9b/aLBBMDsJphgih2zbEWOWbZi4P3PPGf9NE4DwFTwtgIAAB2CCQCgQzABAHQIJgCADsEEANAhmAAAOgQTAECHYAIA6BBMAAAdggkAoEMwAQB0CCYAgA7BBADQIZgAADoEEwBAh2ACAOgQTAAAHYIJAKBDMAEAdAgmAIAOwQQA0DFvkJ2q6sEk65M8n2RTa23pdA4FADCbDBRMY36rtfb4tE0CADBLVWutv9OWM0xLBw2mquofFABgdljTu3o26D1MLcn/rKo1VbV88nMBAIyOQS/JHddae6SqXpXksqq6u7X2T1vvMBZSL8TUhiS3T+Gcu5IDkrj0ufOs3+RYv51n7SbH+k2O9ZucI3s7DHRJbps/ULUyydOttf88zj43uTF851i7ybF+k2P9dp61mxzrNznWb3IGWb/uJbmq2ruqFrzweZJ3x9kjAGAXMsgluVcn+WZVvbD/Ba21f5zWqQAAZpFuMLXW7k/yqxM87qqdG4dYu8myfpNj/XaetZsc6zc51m9yuus34XuYAAB2NX41CgBAx5QGU1WdWFX3VNV9VfWpqTz2XFdV51XVuqpyQ/1OqKqDq+rKqrqzqu6oqjOHPdOoqKqXV9UNVXXb2Np9btgzjaKq2r2qbqmqS4c9y6ipqger6p+r6taqumnY84ySqlpYVX9fVXdX1V1V9bZhzzQqqurIsefcCx9PVdXHX3L/qbokV1W7J/lhkhOSPJzkxiSnttbunJK/YI6rqnckeTrJ37TWjhr2PKOmqg5KclBr7eaxV3WuSXKK519fbXlFx96ttaerao8k1yY5s7V23ZBHGylV9YkkS5Ps21o7adjzjJKJ/jYJ/r+q+kqSa1prX6qqlyXZq7X2xLDnGjVjDfNIkre21ta+2D5TeYbpLUnua63d31rbmOTCJO+dwuPPaWNvBPrTYc8xqlprj7bWbh77fH2Su5IsGu5Uo6Ft8fTYwz3GPtzcOAFVtTjJbyf50rBnYddRVfsleUeSLydJa22jWNpp70ryo5eKpWRqg2lRkoe2evxw/IPFEFTVoUmOTnL9cCcZHWOXk25Nsi7JZa01azcxX0jyySSbhz3IiPLrt3bOYUl+kuT8scvBXxp7v0Qm7v1JvjbeDm76Zk6pqn2SXJTk4621p4Y9z6horT3fWntjksVJ3lJVLgsPqKpOSrKutbZm2LOMsONaa29K8p4kHx27RYG+eUnelOSvW2tHJ3kmifuHJ2jsUubJSb4x3n5TGUyPJDl4q8eLx7bBjBi7/+aiJF9trV087HlG0djp/CuTnDjsWUbIsUlOHrsP58Ik76yqvxvuSKOltfbI2H/XJflmttziQd/DSR7e6ozw32dLQDEx70lyc2vtsfF2mspgujHJEVV12FitvT/Jt6fw+PCSxm5c/nKSu1prfzHseUZJVR1YVQvHPp+fLS/cuHu4U42O1tqnW2uLW2uHZsvPvStaax8Y8lgjw6/f2nmttR8neaiqXvjFse9K4oUuE3dqOpfjksF+NcpAWmubquoPk3w3ye5Jzmut3TFVx5/rquprSX4zyQFV9XCSz7bWvjzcqUbKsUlOT/LPY/fiJMmK1trqIc40Kg5K8pWxV4nsluTrrTUvjWem+PVbk/OxJF8dO1Fxf5IPDnmekTIW6Sck+XB3X+/0DQAwPjd9AwB0CCYAgA7BBADQIZgAADoEEwBAh2ACAOgQTAAAHYIJAKDj/wE8oHqSk954pgAAAABJRU5ErkJggg==",
+      "image/png": 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",
       "text/plain": [
        "<Figure size 720x432 with 1 Axes>"
       ]
@@ -698,7 +698,7 @@
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 720x432 with 1 Axes>"
       ]
@@ -977,7 +977,7 @@
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 720x432 with 1 Axes>"
       ]
@@ -1059,7 +1059,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.10"
+   "version": "3.8.8"
   },
   "orig_nbformat": 4
  },
diff --git a/docs/notebooks/free_energy_calculation.ipynb b/docs/notebooks/free_energy_calculation.ipynb
index 3f78419b..f80f7826 100644
--- a/docs/notebooks/free_energy_calculation.ipynb
+++ b/docs/notebooks/free_energy_calculation.ipynb
@@ -26,7 +26,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -44,7 +44,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -78,7 +78,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -93,7 +93,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -167,7 +167,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -216,7 +216,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
@@ -267,7 +267,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -285,7 +285,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -327,7 +327,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -388,7 +388,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -447,7 +447,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -501,7 +501,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -546,7 +546,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -566,7 +566,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -620,7 +620,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -653,7 +653,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
@@ -662,13 +662,13 @@
        "Text(0.5, 1.0, 'Gradient descent on VFE')"
       ]
      },
-     "execution_count": 54,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 576x432 with 1 Axes>"
       ]
@@ -691,7 +691,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
@@ -751,7 +751,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.10"
+   "version": "3.8.8"
   },
   "vscode": {
    "interpreter": {
diff --git a/docs/notebooks/pymdp_fundamentals.ipynb b/docs/notebooks/pymdp_fundamentals.ipynb
index fb43573c..329c96bf 100644
--- a/docs/notebooks/pymdp_fundamentals.ipynb
+++ b/docs/notebooks/pymdp_fundamentals.ipynb
@@ -171,7 +171,7 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "[0.53712305 0.46287695]\n"
+            "[0.13370366 0.86629634]\n"
           ]
         }
       ],
@@ -533,7 +533,7 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "[0, 1, 6]\n"
+            "[2, 2, 0]\n"
           ]
         }
       ],
@@ -630,7 +630,7 @@
       "name": "python",
       "nbconvert_exporter": "python",
       "pygments_lexer": "ipython3",
-      "version": "3.7.10"
+      "version": "3.8.8"
     },
     "vscode": {
       "interpreter": {
diff --git a/docs/notebooks/tmaze_demo.ipynb b/docs/notebooks/tmaze_demo.ipynb
index 5f8c9e3d..2d791396 100644
--- a/docs/notebooks/tmaze_demo.ipynb
+++ b/docs/notebooks/tmaze_demo.ipynb
@@ -628,7 +628,7 @@
      "output_type": "stream",
      "text": [
       " === Starting experiment === \n",
-      " Reward condition: Right, Observation: [CENTER, No reward, Cue Right]\n",
+      " Reward condition: Right, Observation: [CENTER, No reward, Cue Left]\n",
       "[Step 0] Action: [Move to CUE LOCATION]\n",
       "[Step 0] Observation: [CUE LOCATION,  No reward, Cue Right]\n",
       "[Step 1] Action: [Move to RIGHT ARM]\n",
@@ -636,9 +636,9 @@
       "[Step 2] Action: [Move to RIGHT ARM]\n",
       "[Step 2] Observation: [RIGHT ARM,  Reward!, Cue Left]\n",
       "[Step 3] Action: [Move to RIGHT ARM]\n",
-      "[Step 3] Observation: [RIGHT ARM,  Reward!, Cue Left]\n",
+      "[Step 3] Observation: [RIGHT ARM,  Reward!, Cue Right]\n",
       "[Step 4] Action: [Move to RIGHT ARM]\n",
-      "[Step 4] Observation: [RIGHT ARM,  Reward!, Cue Left]\n"
+      "[Step 4] Observation: [RIGHT ARM,  Reward!, Cue Right]\n"
      ]
     }
    ],
diff --git a/docs/notebooks/using_the_agent_class.ipynb b/docs/notebooks/using_the_agent_class.ipynb
index 200392da..c1251a43 100644
--- a/docs/notebooks/using_the_agent_class.ipynb
+++ b/docs/notebooks/using_the_agent_class.ipynb
@@ -290,7 +290,7 @@
       "outputs": [
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x432 with 1 Axes>"
             ]
@@ -359,7 +359,7 @@
       "outputs": [
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x432 with 1 Axes>"
             ]
@@ -411,7 +411,7 @@
       "outputs": [
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x432 with 1 Axes>"
             ]
@@ -532,7 +532,7 @@
       "outputs": [
         {
           "data": {
-            "image/png": 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",
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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -754,12 +754,12 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Context: Left-Better\n"
+            "Context: Right-Better\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEICAYAAABPgw/pAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAATeUlEQVR4nO3df7BcZ33f8ffHErKDMSbFRI1lRXKxhkaOXZxcrGQmDTfEDTIkFhmgsdNkMCVVmFYNifOjTkI8HichgbaB/NAUHOJxGsDGpG2iFDOeaeEmk6FQycFNEK5S4Rgk8ysYm2BjMArf/nGOyNFq772rq5VWevR+zezcPec8e853zz772bPP7t6TqkKSdPo7a9YFSJKmw0CXpEYY6JLUCANdkhphoEtSIwx0SWqEgX6aSTKf5OBgem+S+Qlv+wNJDiR5LMkVU6pnY5JKsnoa6zteo/tH05fk55O8ddZ16GgG+gwkeTDJE32wPpLk3UnWr2RdVXVpVS1M2Pw/ADuq6mlV9aGVbO9kSnJ7kl9epk0lueRk1TQN06z5eNfV98Wrllh+1AtkVb2uqn50pds8Fkmem+TeJF/s/z73ZGz3dGWgz873V9XTgG8EPg381knY5gZg70nYjnTckqwB/gh4G/D1wO8Bf9TP1zhV5eUkX4AHgasG0y8C/mowfTbd0fTH6cL+zcDX9cvmgYPj1kX3An0j8FHgYeAu4B/063sMKOBx4KN9+38HPAR8AdgHfM8i9b4Y+BDwt8AB4ObBso39ercDnwA+Cfz0yH15U7/sE/31s/tl1wN/NrKtAi7p1/cV4Mm+9j8eU9efDu7TY8APHt4/wE8Bn+nreeUk+3aR+/6vgPv7ffQR4Fv7+d8MLACP0r1IXjO4ze3ATuDd/e0+CDx7sZr7+d8H3Nev7/3A5f38HwT+Gnh6P3018CngWYuta6T+ZwPv7fvDZ4G3A8/ol/0+8FXgif72Pzty23P7ZV/tlz8GXAjcDLxt5PF/Zd83HgFeDTwP+Iv+/vz2yHr/Zb9PHwHuATYssu+/l65/ZjDv48DWWT+HT9XLzAs4Ey8cGcJPpTvy+M+D5W8EdtGF8XnAHwO/2i+bZ/FAfw3wAeAiuuB6C3DHoG0Bl/TXn9M/AS/spzceDp0x9c4Dl9G9YFxOF4QvGdyugDv6ALgM+JtBTbf0NX1DH0LvB36pX3Y9iwR6f/124JeX2Zdfaz+o9VC/3afQvVh+Efj65fbtmHW/vA+U5wGhe6HZ0K93P/DzwBrgBXTB/ZxB3Q8DVwKr6UL0ziVqvoLuxWcLsAp4Rf+4Hn7he3u/zmfSvSh+32LrGnMfLgH+Wd8fDr8IvGlc/1nisT84Mu9mjg70NwPn0IXwl4A/7B/zdf19e37fflu/77653zevBd6/yLZ/EnjPyLz/DvzUrJ/Dp+pl5gWciZf+SfQY3dHLV/on6WX9stAdcT170P47gL/urx/xBOPIQL+fwVE23XDOV4DV/fQwLC/pn2hXAU85xvrfBLyxv374Cf2PB8vfAPxuf/2jwIsGy14IPNhfv54TE+hPHL7P/bzPAN++3L4ds+57gNeMmf9P6Y6SzxrMu4P+nUtf91sHy14E/N8lav5P9C9yg3n7BiH4DLoj078E3rLU/Z/gsXsJ8KFx/WeR9kf0t37ezRwd6OsGyx9m8G4B+C/AT/TX3wO8arDsLLoX3A1jtv2LDF4I+3lvZ/AO0cuRl1PimwlnqJdU1f9IsoruqOVPkmyme3v7VODeJIfbhu7IbTkbgP+W5KuDeX8HrKU70vyaqtqf5CfonpyXJrkHuKGqPjG60iRbgF8DvoXuiPRs4F0jzQ4Mrn+M7kgdurfoHxtZduEE9+V4PFxVhwbTXwSeRneEeiz7dj3dC9KoC4EDVTXczx+jOxo97FNjtr+YDcArkvzbwbw1/XaoqkeTvAu4AXjpEus5SpK1wG/QvQidRxegjxzLOib06cH1J8ZMH77/G4DfSPIfh2XS7bthP4HuoOfpI/OeTvduSGP4oeiMVdXfVdV/pQve76Qb53wCuLSqntFfzq/uA9TlHACuHtzuGVV1TlU9NK5xVb2jqr6T7klWwOsXWe876IYp1lfV+XRvrzPSZvgtnW+ie9dB/3fDIssepwtYAJL8w9ESF6lnpY513x6gG4Me9QlgfZLh8+ebGHnRPAYHgF8ZedyeWlV3QPdND7px5zuA3zzGdb+Obj9eVlVPB36YIx+75fbxtB+DA8CPjdzXr6uq949puxe4PINXX7ohPz/YX4SBPmPpbKP7FP/+/qjvd4A3JvmGvs26JC+cYHVvBn4lyYb+ds/q1z1uu89J8oIkZ9ONeR7+8Guc84DPVdWXklwJ/NCYNr+Y5KlJLqX7gOyd/fw7gNf2tVwA3ET3rQWA/0P37uC5Sc6he7cw9GngHy1znydpA8AK9u1bgZ9O8m3943RJv28/SHfU/bNJntL/DuD7gTsnqWNMzb8DvDrJln475yZ5cZLz+v3yNrrx+lcC65L86yXWNeo8uiPdzydZB/zMMrWMq/WZSc6f6J4t783Az/X9hCTnJ3n5Im0X6A50fjzJ2Ul29PPfO6Va2jPrMZ8z8UI3bnn4mwVfAD4M/IvB8nPojqweoPtmyf3Aj/fL5ln6Wy430I2/foFuuOB1g7bD8enLgf/dt/sc3YdNFy5S78vo3g5/oW/32xw9hnr4Wy6fYvBtif6+/Cbdt00+2V8/Z7D8F+iOnA/QHT0Oa9zE33/z4w8Xqe3V/XofBf756P4Zs48W3bdLrH9f/1h9GLiin38p8CfA5+m+/fIDg9vczmDsf8xjdkTN/bytwO5+3ifphrTOo/sQ9z2D2/6T/vHatNi6Ruq/FLi3r/8+um//DGvZRjc+/yiDbyeNrOM2unHxR1n8Wy7DzywOAvOD6bcBrx1M/wjd5wGHvzV12xL7/4q+/ieAPz+8/72Mv6TfaZKk05xDLpLUCANdkhphoEtSIwx0SWrEzH5YdMEFF9TGjRtntfmmPP7445x77rmzLkNalH10eu69997PVtWzxi2bWaBv3LiRPXv2zGrzTVlYWGB+fn7WZUiLso9OT5LRX9R+jUMuktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqRETBXqSrUn2Jdmf5MYxy69P8jdJ7usvJ+WM4JKkv7fs99D7M+rspDsv4UFgd5JdVfWRkabvrKodR61AknRSTHKEfiWwv6oeqKon6f6J/9iTJkiSZmeSX4qu48jzRR6kOzv5qJcm+S7gr4CfrKoDow2SbKc7EQJr165lYWHhmAsGmP/u717R7Vo1P+sCTjEL73vfrEuwj46Yn3UBp5gT1UeXPcFFkpcBW6vqR/vpHwG2DIdXkjwTeKyqvpzkx+jO+P2CpdY7NzdXK/7pf0ZPZykNnAonbbGPainH0UeT3FtVc+OWTTLk8hBHngD4Io4+g/zDVfXlfvKtwLetpFBJ0spNEui7gU1JLk6yBriW7gzwX5PkGweT19Cdp1GSdBItO4ZeVYf6s23fA6yiO6Hr3iS3AHuqahfdWbmvAQ7RncD2+hNYsyRpjJmdJNoxdJ0wjqHrVDfDMXRJ0mnAQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqRETBXqSrUn2Jdmf5MYl2r00SSWZm16JkqRJLBvoSVYBO4Grgc3AdUk2j2l3HvAa4IPTLlKStLxJjtCvBPZX1QNV9SRwJ7BtTLtfAl4PfGmK9UmSJrR6gjbrgAOD6YPAlmGDJN8KrK+qdyf5mcVWlGQ7sB1g7dq1LCwsHHPBAPMrupXOFCvtV9M0P+sCdEo7UX10kkBfUpKzgF8Hrl+ubVXdCtwKMDc3V/Pz88e7eeko9iud6k5UH51kyOUhYP1g+qJ+3mHnAd8CLCR5EPh2YJcfjErSyTVJoO8GNiW5OMka4Fpg1+GFVfX5qrqgqjZW1UbgA8A1VbXnhFQsSRpr2UCvqkPADuAe4H7grqram+SWJNec6AIlSZOZaAy9qu4G7h6Zd9MibeePvyxJ0rHyl6KS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRkwU6Em2JtmXZH+SG8csf3WSv0xyX5I/S7J5+qVKkpaybKAnWQXsBK4GNgPXjQnsd1TVZVX1XOANwK9Pu1BJ0tImOUK/EthfVQ9U1ZPAncC2YYOq+tvB5LlATa9ESdIkVk/QZh1wYDB9ENgy2ijJvwFuANYAL5hKdZKkiU0S6BOpqp3AziQ/BLwWeMVomyTbge0Aa9euZWFhYUXbml9xlToTrLRfTdP8rAvQKe1E9dFULT06kuQ7gJur6oX99M8BVNWvLtL+LOCRqjp/qfXOzc3Vnj17VlQ0ycpupzPDMn36pLCPainH0UeT3FtVc+OWTTKGvhvYlOTiJGuAa4FdIxvYNJh8MfD/VlqsJGlllh1yqapDSXYA9wCrgNuqam+SW4A9VbUL2JHkKuArwCOMGW6RJJ1YE42hV9XdwN0j824aXH/NlOuSJB0jfykqSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNmCjQk2xNsi/J/iQ3jll+Q5KPJPmLJP8zyYbplypJWsqygZ5kFbATuBrYDFyXZPNIsw8Bc1V1OfAHwBumXagkaWmTHKFfCeyvqgeq6kngTmDbsEFVva+qvthPfgC4aLplSpKWs3qCNuuAA4Ppg8CWJdq/CnjPuAVJtgPbAdauXcvCwsJkVY6YX9GtdKZYab+apvlZF6BT2onqo5ME+sSS/DAwBzx/3PKquhW4FWBubq7m5+enuXkJAPuVTnUnqo9OEugPAesH0xf1846Q5CrgF4DnV9WXp1OeJGlSk4yh7wY2Jbk4yRrgWmDXsEGSK4C3ANdU1WemX6YkaTnLBnpVHQJ2APcA9wN3VdXeJLckuaZv9u+BpwHvSnJfkl2LrE6SdIJMNIZeVXcDd4/Mu2lw/aop1yVJOkb+UlSSGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUiIkCPcnWJPuS7E9y45jl35Xkz5McSvKy6ZcpSVrOsoGeZBWwE7ga2Axcl2TzSLOPA9cD75h2gZKkyayeoM2VwP6qegAgyZ3ANuAjhxtU1YP9sq+egBolSROYJNDXAQcG0weBLSvZWJLtwHaAtWvXsrCwsJLVML+iW+lMsdJ+NU3zsy5Ap7QT1UcnCfSpqapbgVsB5ubman5+/mRuXmcI+5VOdSeqj07yoehDwPrB9EX9PEnSKWSSQN8NbEpycZI1wLXArhNbliTpWC0b6FV1CNgB3APcD9xVVXuT3JLkGoAkz0tyEHg58JYke09k0ZKko000hl5VdwN3j8y7aXB9N91QjCRpRvylqCQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNWKiQE+yNcm+JPuT3Dhm+dlJ3tkv/2CSjVOvVJK0pGUDPckqYCdwNbAZuC7J5pFmrwIeqapLgDcCr592oZKkpU1yhH4lsL+qHqiqJ4E7gW0jbbYBv9df/wPge5JkemVKkpazeoI264ADg+mDwJbF2lTVoSSfB54JfHbYKMl2YHs/+ViSfSspWke5gJF9fUbzWOJUZB8dOr4+umGxBZME+tRU1a3ArSdzm2eCJHuqam7WdUiLsY+eHJMMuTwErB9MX9TPG9smyWrgfODhaRQoSZrMJIG+G9iU5OIka4BrgV0jbXYBr+ivvwx4b1XV9MqUJC1n2SGXfkx8B3APsAq4rar2JrkF2FNVu4DfBX4/yX7gc3Shr5PHYSyd6uyjJ0E8kJakNvhLUUlqhIEuSY0w0E9jy/1LBmnWktyW5DNJPjzrWs4EBvppasJ/ySDN2u3A1lkXcaYw0E9fk/xLBmmmqupP6b75ppPAQD99jfuXDOtmVIukU4CBLkmNMNBPX5P8SwZJZxAD/fQ1yb9kkHQGMdBPU1V1CDj8LxnuB+6qqr2zrUo6UpI7gP8FPCfJwSSvmnVNLfOn/5LUCI/QJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqxP8H5w0AOaQW0uwAAAAASUVORK5CYII=",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -779,7 +779,7 @@
         },
         {
           "data": {
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",
+            "image/png": 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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -799,7 +799,7 @@
         },
         {
           "data": {
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+            "image/png": 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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -813,13 +813,13 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Action at time 2: Play-left\n",
+            "Action at time 2: Play-right\n",
             "Reward at time 2: Reward\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -833,13 +833,13 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Action at time 3: Play-left\n",
+            "Action at time 3: Play-right\n",
             "Reward at time 3: Reward\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -853,13 +853,13 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Action at time 4: Play-left\n",
-            "Reward at time 4: Reward\n"
+            "Action at time 4: Play-right\n",
+            "Reward at time 4: Loss\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -873,13 +873,13 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Action at time 5: Play-left\n",
-            "Reward at time 5: Reward\n"
+            "Action at time 5: Play-right\n",
+            "Reward at time 5: Loss\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -893,13 +893,13 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Action at time 6: Play-left\n",
-            "Reward at time 6: Loss\n"
+            "Action at time 6: Play-right\n",
+            "Reward at time 6: Reward\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -913,13 +913,13 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Action at time 7: Play-left\n",
-            "Reward at time 7: Reward\n"
+            "Action at time 7: Play-right\n",
+            "Reward at time 7: Loss\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -933,13 +933,13 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Action at time 8: Play-left\n",
+            "Action at time 8: Play-right\n",
             "Reward at time 8: Reward\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -953,8 +953,8 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Action at time 9: Play-left\n",
-            "Reward at time 9: Loss\n"
+            "Action at time 9: Play-right\n",
+            "Reward at time 9: Reward\n"
           ]
         }
       ],
@@ -996,7 +996,7 @@
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -1011,12 +1011,12 @@
           "output_type": "stream",
           "text": [
             "Action at time 0: Play-left\n",
-            "Reward at time 0: Loss\n"
+            "Reward at time 0: Reward\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -1030,13 +1030,13 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Action at time 1: Play-right\n",
-            "Reward at time 1: Reward\n"
+            "Action at time 1: Play-left\n",
+            "Reward at time 1: Loss\n"
           ]
         },
         {
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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -1050,13 +1050,13 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Action at time 2: Play-right\n",
-            "Reward at time 2: Reward\n"
+            "Action at time 2: Play-left\n",
+            "Reward at time 2: Loss\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -1076,7 +1076,7 @@
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -1091,12 +1091,12 @@
           "output_type": "stream",
           "text": [
             "Action at time 4: Play-right\n",
-            "Reward at time 4: Loss\n"
+            "Reward at time 4: Reward\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": 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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -1116,7 +1116,7 @@
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": 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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -1136,7 +1136,7 @@
         },
         {
           "data": {
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+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -1151,12 +1151,12 @@
           "output_type": "stream",
           "text": [
             "Action at time 7: Play-right\n",
-            "Reward at time 7: Loss\n"
+            "Reward at time 7: Reward\n"
           ]
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": 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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -1176,7 +1176,7 @@
         },
         {
           "data": {
-            "image/png": 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",
+            "image/png": "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",
             "text/plain": [
               "<Figure size 432x288 with 1 Axes>"
             ]
@@ -1231,7 +1231,7 @@
       "name": "python",
       "nbconvert_exporter": "python",
       "pygments_lexer": "ipython3",
-      "version": "3.7.10"
+      "version": "3.8.8"
     },
     "vscode": {
       "interpreter": {
diff --git a/examples/building_up_agent_loop.ipynb b/examples/building_up_agent_loop.ipynb
new file mode 100644
index 00000000..cdb45e55
--- /dev/null
+++ b/examples/building_up_agent_loop.ipynb
@@ -0,0 +1,182 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import jax.numpy as jnp\n",
+    "import jax.tree_util as jtu\n",
+    "from jax import random as jr\n",
+    "from pymdp.jax.agent import Agent as AIFAgent\n",
+    "from pymdp.utils import random_A_matrix, random_B_matrix"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(2, 10, 5, 4)\n",
+      "[1 1]\n",
+      "(10, 3, 3, 3)\n",
+      "(10, 3, 3, 2)\n"
+     ]
+    }
+   ],
+   "source": [
+    "def scan(f, init, xs, length=None, axis=0):\n",
+    "  if xs is None:\n",
+    "    xs = [None] * length\n",
+    "  carry = init\n",
+    "  ys = []\n",
+    "  for x in xs:\n",
+    "    carry, y = f(carry, x)\n",
+    "    if y is not None:\n",
+    "       ys.append(y)\n",
+    "  \n",
+    "  ys = None if len(ys) < 1 else jtu.tree_map(lambda *x: jnp.stack(x,axis=axis), *ys)\n",
+    "\n",
+    "  return carry, ys\n",
+    "\n",
+    "def evolve_trials(agent, env, block_idx, num_timesteps, prng_key=jr.PRNGKey(0)):\n",
+    "\n",
+    "    batch_keys = jr.split(prng_key, batch_size)\n",
+    "    def step_fn(carry, xs):\n",
+    "        actions = carry['actions']\n",
+    "        outcomes = carry['outcomes']\n",
+    "        beliefs = agent.infer_states(outcomes, actions, *carry['args'])\n",
+    "        q_pi, _ = agent.infer_policies(beliefs)\n",
+    "        actions_t = agent.sample_action(q_pi, rng_key=batch_keys)\n",
+    "\n",
+    "        outcome_t = env.step(actions_t)\n",
+    "        outcomes = jtu.tree_map(\n",
+    "           lambda prev_o, new_o: jnp.concatenate([prev_o, jnp.expand_dims(new_o, -1)], -1), outcomes, outcome_t\n",
+    "          )\n",
+    "\n",
+    "        if actions is not None:\n",
+    "          actions = jnp.concatenate([actions, jnp.expand_dims(actions_t, -2)], -2)\n",
+    "        else:\n",
+    "          actions = jnp.expand_dims(actions_t, -2)\n",
+    "\n",
+    "        args = agent.update_empirical_prior(actions_t, beliefs)\n",
+    "\n",
+    "        ### @ NOTE !!!!: Shape of policy_probs = (num_blocks, num_trials, batch_size, num_policies) if scan axis = 0, but size of `actions` will \n",
+    "        ### be (num_blocks, batch_size, num_trials, num_controls) -- so we need to 1) swap axes to both to have the same first three dimensiosn aligned,\n",
+    "        # 2) use the action indices (the integers stored in the last dimension of `actions`) to index into the policy_probs array\n",
+    "        \n",
+    "        # args = (pred_{t+1}, [post_1, post_{2}, ..., post_{t}])\n",
+    "        # beliefs =  [post_1, post_{2}, ..., post_{t}]\n",
+    "        return {'args': args, 'outcomes': outcomes, 'beliefs': beliefs, 'actions': actions}, {'policy_probs': q_pi}\n",
+    "\n",
+    "   \n",
+    "    outcome_0  = jtu.tree_map(lambda x: jnp.expand_dims(x, -1), env.step())\n",
+    "    # qs_hist = jtu.tree_map(lambda x: jnp.expand_dims(x, -2), agent.D) # add a time dimension to the initial state prior\n",
+    "    init = {\n",
+    "       'args': (agent.D, None,),\n",
+    "       'outcomes': outcome_0, \n",
+    "       'beliefs': [],\n",
+    "       'actions': None\n",
+    "    }\n",
+    "    last, q_pis_ = scan(step_fn, init, range(num_timesteps), axis=1)\n",
+    "\n",
+    "    return last, q_pis_, env\n",
+    "\n",
+    "def step_fn(carry, block_idx):\n",
+    "    agent, env = carry\n",
+    "    output, q_pis_, env = evolve_trials(agent, env, block_idx, num_timesteps)\n",
+    "    args = output.pop('args')\n",
+    "    output['beliefs'] = agent.infer_states(output['outcomes'], output['actions'], *args)\n",
+    "    output.update(q_pis_)\n",
+    "\n",
+    "    # How to deal with contiguous blocks of trials? Two options we can imagine: \n",
+    "    # A) you use final posterior (over current and past timesteps) to compute the smoothing distribution over qs_{t=0} and update pD, and then pass pD as the initial state prior ($D = \\mathbb{E}_{pD}[qs_{t=0}]$);\n",
+    "    # B) we don't assume that blocks 'reset time', and are really just adjacent chunks of one long sequence, so you set the initial state prior to be the final output (`output['beliefs']`) passed through\n",
+    "    # the transition model entailed by the action taken at the last timestep of the previous block.\n",
+    "    # print(output['beliefs'].shape)\n",
+    "    agent = agent.learning(**output)\n",
+    "    \n",
+    "    return (agent, env), output\n",
+    "\n",
+    "# define an agent and environment here\n",
+    "batch_size = 10\n",
+    "num_obs = [3, 3]\n",
+    "num_states = [3, 3]\n",
+    "num_controls = [2, 2]\n",
+    "num_blocks = 2\n",
+    "num_timesteps = 5\n",
+    "\n",
+    "A_np = random_A_matrix(num_obs=num_obs, num_states=num_states)\n",
+    "B_np = random_B_matrix(num_states=num_states, num_controls=num_controls)\n",
+    "A = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_size,) + x.shape), list(A_np))\n",
+    "B = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_size,) + x.shape), list(B_np))\n",
+    "C = [jnp.zeros((batch_size, no)) for no in num_obs]\n",
+    "D = [jnp.ones((batch_size, ns)) / ns for ns in num_states]\n",
+    "E = jnp.ones((batch_size, 4 )) / 4 \n",
+    "\n",
+    "pA = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_size,) + x.shape), list(A_np))\n",
+    "pB = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_size,) + x.shape), list(B_np))\n",
+    "\n",
+    "class TestEnv:\n",
+    "    def __init__(self, num_obs, prng_key=jr.PRNGKey(0)):\n",
+    "      self.num_obs=num_obs\n",
+    "      self.key = prng_key\n",
+    "    def step(self, actions=None):\n",
+    "      # return a list of random observations for each agent or parallel realization (each entry in batch_dim)\n",
+    "      obs = [jr.randint(self.key, (batch_size,), 0, no) for no in self.num_obs]\n",
+    "      self.key, _ = jr.split(self.key)\n",
+    "      return obs\n",
+    "\n",
+    "agents = AIFAgent(A, B, C, D, E, pA, pB, use_param_info_gain=True, use_inductive=False, inference_algo='fpi', sampling_mode='marginal', action_selection='stochastic')\n",
+    "env = TestEnv(num_obs)\n",
+    "init = (agents, env)\n",
+    "(agents, env), sequences = scan(step_fn, init, range(num_blocks) )\n",
+    "print(sequences['policy_probs'].shape)\n",
+    "print(sequences['actions'][0][0][0])\n",
+    "print(agents.A[0].shape)\n",
+    "print(agents.B[0].shape)\n",
+    "# def loss_fn(agents):\n",
+    "#     env = TestEnv(num_obs)\n",
+    "#     init = (agents, env)\n",
+    "#     (agents, env), sequences = scan(step_fn, init, range(num_blocks)) \n",
+    "\n",
+    "#     return jnp.sum(jnp.log(sequences['policy_probs']))\n",
+    "\n",
+    "# dLoss_dAgents = jax.grad(loss_fn)(agents)\n",
+    "# print(dLoss_dAgents.A[0].shape)\n",
+    "\n",
+    "\n",
+    "# sequences = jtu.tree_map(lambda x: x.swapaxes(1, 2), sequences)\n",
+    "\n",
+    "# NOTE: all elements of sequences will have dimensionality blocks, trials, batch_size, ...\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "jax_pymdp_test",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.6"
+  },
+  "orig_nbformat": 4
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/examples/inductive_inference_example.ipynb b/examples/inductive_inference_example.ipynb
new file mode 100644
index 00000000..d4745fb4
--- /dev/null
+++ b/examples/inductive_inference_example.ipynb
@@ -0,0 +1,146 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Imports"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pymdp.jax import control\n",
+    "import jax.numpy as jnp\n",
+    "import jax.tree_util as jtu\n",
+    "from jax import nn, vmap, random, lax\n",
+    "\n",
+    "from typing import List, Optional\n",
+    "from jaxtyping import Array\n",
+    "from jax import random as jr"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Set up generative model (random one with trivial observation model)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Set up a generative model\n",
+    "num_states = [5, 3]\n",
+    "num_controls = [2, 2]\n",
+    "\n",
+    "# make some arbitrary policies (policy depth 3, 2 control factors)\n",
+    "policy_1 = jnp.array([[0, 1],\n",
+    "                         [1, 1],\n",
+    "                         [0, 0]])\n",
+    "policy_2 = jnp.array([[1, 0],\n",
+    "                        [0, 0],\n",
+    "                        [1, 1]])\n",
+    "policy_matrix = jnp.stack([policy_1, policy_2]) \n",
+    "\n",
+    "# observation modalities (isomorphic/identical to hidden states, just need to include for the need to include likleihood model)\n",
+    "num_obs = [5, 3]\n",
+    "num_factors = len(num_states)\n",
+    "num_modalities = len(num_obs)\n",
+    "\n",
+    "# sample parameters of the model (A, B, C)\n",
+    "key = jr.PRNGKey(1)\n",
+    "factor_keys = jr.split(key, num_factors)\n",
+    "\n",
+    "d = [0.1* jr.uniform(factor_key, (ns,)) for factor_key, ns in zip(factor_keys, num_states)]\n",
+    "qs_init = [jr.dirichlet(factor_key, d_f) for factor_key, d_f  in zip(factor_keys, d)]\n",
+    "A = [jnp.eye(no) for no in num_obs]\n",
+    "\n",
+    "factor_keys = jr.split(factor_keys[-1], num_factors)\n",
+    "b = [jr.uniform(factor_keys[f], shape=(num_controls[f], num_states[f], num_states[f])) for f in range(num_factors)]\n",
+    "b_sparse = [jnp.where(b_f < 0.75, 1e-5, b_f) for b_f in b]\n",
+    "B = [jnp.swapaxes(jr.dirichlet(factor_keys[f], b_sparse[f]), 2, 0) for f in range(num_factors)]\n",
+    "\n",
+    "modality_keys = jr.split(factor_keys[-1], num_modalities)\n",
+    "C = [nn.one_hot(jr.randint(modality_keys[m], shape=(1,), minval=0, maxval=num_obs[m]), num_obs[m]) for m in range(num_modalities)]\n",
+    "\n",
+    "# trivial dependencies -- factor 1 drives modality 1, etc.\n",
+    "A_dependencies = [[0], [1]]\n",
+    "B_dependencies = [[0], [1]]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Generate sparse constraints vectors `H` and inductive matrix `I`, using inductive parameters like depth and threshold "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# generate random constraints (H vector)\n",
+    "factor_keys = jr.split(key, num_factors)\n",
+    "H = [jr.uniform(factor_key, (ns,)) for factor_key, ns in zip(factor_keys, num_states)]\n",
+    "H = [jnp.where(h < 0.75, 0., 1.) for h in H]\n",
+    "\n",
+    "# depth and threshold for inductive planning algorithm. I made policy-depth equal to inductive planning depth, out of ignorance -- need to ask Tim or Tommaso about this\n",
+    "inductive_depth, inductive_threshold = 3, 0.5\n",
+    "I = control.generate_I_matrix(H, B, inductive_threshold, inductive_depth)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Evaluate posterior probability of policies and negative EFE using new version of `update_posterior_policies`\n",
+    "#### This function no longer computes info gain (for both states and parameters) since deterministic model is assumed, and includes new inductive matrix `I` and `inductive_epsilon` parameter"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# evaluate Q(pi) and negative EFE using the inductive planning algorithm\n",
+    "\n",
+    "E = jnp.ones(policy_matrix.shape[0])\n",
+    "pA = jtu.tree_map(lambda a: jnp.ones_like(a), A)\n",
+    "pB = jtu.tree_map(lambda b: jnp.ones_like(b), B)\n",
+    "\n",
+    "q_pi, neg_efe = control.update_posterior_policies_inductive(policy_matrix, qs_init, A, B, C, E, pA, pB, A_dependencies, B_dependencies, I, gamma=16.0, use_utility=True, use_inductive=True, inductive_epsilon=1e-3)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "atari_env",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/examples/inductive_inference_gridworld.ipynb b/examples/inductive_inference_gridworld.ipynb
new file mode 100644
index 00000000..99fb2f27
--- /dev/null
+++ b/examples/inductive_inference_gridworld.ipynb
@@ -0,0 +1,202 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Imports"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import jax.numpy as jnp\n",
+    "import jax.tree_util as jtu\n",
+    "from jax import nn, vmap, random, lax\n",
+    "from typing import List, Optional\n",
+    "from jaxtyping import Array\n",
+    "from jax import random as jr\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "\n",
+    "from pymdp.envs import GridWorldEnv\n",
+    "from pymdp.jax import control as j_control\n",
+    "from pymdp.jax.agent import Agent as AIFAgent\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Grid world generative model"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "num_rows, num_columns = 7, 7\n",
+    "num_states = [num_rows*num_columns] # number of states equals the number of grid locations\n",
+    "num_obs = [num_rows*num_columns]    # number of observations equals the number of grid locations (fully observable)\n",
+    "\n",
+    "# number of agents\n",
+    "n_batches = 5\n",
+    "\n",
+    "# construct A arrays\n",
+    "A = [jnp.broadcast_to(jnp.eye(num_states[0]), (n_batches,) + (num_obs[0], num_states[0]))] # fully observable (identity observation matrix\n",
+    "\n",
+    "# construct B arrays\n",
+    "grid_world = GridWorldEnv(shape=[num_rows, num_columns])\n",
+    "B = [jnp.broadcast_to(jnp.array(grid_world.get_transition_dist()), (n_batches,) + (num_states[0], num_states[0], grid_world.n_control))]  # easy way to get the generative model parameters is to extract them from one of pre-made GridWorldEnv classes\n",
+    "num_controls = [grid_world.n_control] # number of control states equals the number of actions\n",
+    " \n",
+    "# create mapping from gridworld coordinates to linearly-index states\n",
+    "grid = np.arange(grid_world.n_states).reshape(grid_world.shape)\n",
+    "it = np.nditer(grid, flags=[\"multi_index\"])\n",
+    "coord_to_idx_map = {}\n",
+    "while not it.finished:\n",
+    "    coord_to_idx_map[it.multi_index] = it.iterindex\n",
+    "    it.iternext()\n",
+    "\n",
+    "# construct C arrays\n",
+    "desired_position = (6,6) # lower corner\n",
+    "desired_state_id = coord_to_idx_map[desired_position]\n",
+    "desired_obs_id = jnp.argmax(A[0][:, desired_state_id]) # throw this in there, in case there is some indeterminism between states and observations\n",
+    "C = [jnp.broadcast_to(nn.one_hot(desired_obs_id, num_obs[0]), (n_batches, num_obs[0]))]\n",
+    "\n",
+    "# construct D arrays\n",
+    "starting_position = (3, 3) # middle\n",
+    "# starting_position = (0, 0) # upper left corner\n",
+    "starting_state_id = coord_to_idx_map[starting_position]\n",
+    "starting_obs_id = jnp.argmax(A[0][:, starting_state_id]) # throw this in there, in case there is some indeterminism between states and observations\n",
+    "D = [jnp.broadcast_to(nn.one_hot(starting_state_id, num_states[0]), (n_batches, num_states[0]))]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Planning parameters"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "planning_horizon, inductive_threshold = 1, 0.1\n",
+    "inductive_depth = 7\n",
+    "policy_matrix = j_control.construct_policies(num_states, num_controls, policy_len=planning_horizon)\n",
+    "\n",
+    "# inductive planning goal states\n",
+    "H = [jnp.broadcast_to(nn.one_hot(desired_state_id, num_states[0]), (n_batches, num_states[0]))] # list of factor-specific goal vectors (shape of each is (n_batches, num_states[f]))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Initialize an `Agent()`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# create agent\n",
+    "agent = AIFAgent(A, B, C, D, E=None, pA=None, pB=None, policies=policy_matrix, policy_len=planning_horizon, \n",
+    "                inductive_depth=inductive_depth, inductive_threshold=inductive_threshold,\n",
+    "                H=H, use_utility=True, use_states_info_gain=False, use_param_info_gain=False, use_inductive=True)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Run active inference"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Grid position for agent 2 at time 0: (3, 3)\n",
+      "Grid position for agent 2 at time 1: (3, 4)\n",
+      "Grid position for agent 2 at time 2: (3, 5)\n",
+      "Grid position for agent 2 at time 3: (3, 6)\n",
+      "Grid position for agent 2 at time 4: (4, 6)\n",
+      "Grid position for agent 2 at time 5: (5, 6)\n",
+      "Grid position for agent 2 at time 6: (6, 6)\n"
+     ]
+    }
+   ],
+   "source": [
+    "# T = 14 # needed if you start further away from the goal (e.g. in upper left corner)\n",
+    "T = 7 # can get away with fewer timesteps if you start closer to the goal (e.g. in the middle)\n",
+    "\n",
+    "qs_init = [jnp.broadcast_to(nn.one_hot(starting_state_id, num_states[0]), (n_batches, num_states[0]))] # same as D\n",
+    "obs_idx = [jnp.broadcast_to(starting_obs_id, (n_batches,))] # list of len (num_modalities), each list element of shape (n_batches,)\n",
+    "obs_idx  = jtu.tree_map(lambda x: jnp.expand_dims(x, -1), obs_idx) #  list of len (num_modalities), elements each of shape (n_batches,1), this adds a trivial \"time dimension\"\n",
+    "\n",
+    "state = jnp.broadcast_to(starting_state_id, (n_batches,))\n",
+    "infer_args = (agent.D, None,)\n",
+    "batch_keys = jr.split(jr.PRNGKey(0), n_batches)\n",
+    "batch_to_track = 1\n",
+    "\n",
+    "for t in range(T):\n",
+    "\n",
+    "    print('Grid position for agent {} at time {}: {}'.format(batch_to_track+1, t, np.unravel_index(state[batch_to_track], grid_world.shape)))\n",
+    "\n",
+    "    if t == 0:\n",
+    "        actions = None\n",
+    "    else:\n",
+    "        actions = actions_t\n",
+    "    beliefs = agent.infer_states(obs_idx, actions, *infer_args)\n",
+    "    q_pi, _ = agent.infer_policies(beliefs)\n",
+    "    actions_t = agent.sample_action(q_pi, rng_key=batch_keys)\n",
+    "    infer_args = agent.update_empirical_prior(actions_t, beliefs)\n",
+    "\n",
+    "    # get next state and observation from the grid world (need to vmap everything over batches)\n",
+    "    state = vmap(lambda b, s, a: jnp.argmax(b[:, s, a]), in_axes=(0,0,0))(B[0], state, actions_t)\n",
+    "    next_obs = vmap(lambda a, s: jnp.argmax(a[:, s]), in_axes=(0,0))(A[0], state)\n",
+    "    obs_idx = [next_obs]\n",
+    "    obs_idx  = jtu.tree_map(lambda x: jnp.expand_dims(x, -1), obs_idx) # add a trivial time dimension to the observation to enable indexing during agent.infer_states\n",
+    "\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "atari_env",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/examples/model_inversion.ipynb b/examples/model_inversion.ipynb
new file mode 100644
index 00000000..563f3501
--- /dev/null
+++ b/examples/model_inversion.ipynb
@@ -0,0 +1,939 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Active Inference model inversion: T-Maze Environment"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import jax\n",
+    "import jax.numpy as jnp\n",
+    "\n",
+    "import seaborn as sns\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "from pymdp.jax.agent import Agent as AIFAgent\n",
+    "from pymdp.envs import TMazeEnv"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pybefit import ModelInference\n",
+    "\n",
+    "def param_transform(z):\n",
+    "    init = {}  # define some initial values of random variables that should be infered\n",
+    "    params = {}  # define parameters that should be infered\n",
+    "    return init, params\n",
+    "\n",
+    "\n",
+    "# we could simplify the interface so that AIFAgent class is constructed as \n",
+    "# aif_agent = AIFAgent(init_variables, params, options)\n",
+    "\n",
+    "# define some static options for the AIFAgent class\n",
+    "agent_options = {\n",
+    "\n",
+    "}\n",
+    "\n",
+    "# define properties of inference\n",
+    "inference_options = {\n",
+    "    # e.g. method can be svi or nuts\n",
+    "    'method': 'SVI',\n",
+    "    # different forms of the parameteric prior, such as, NormalGamma, NormalHorseshoe, NormalRegularizedHorseshoe\n",
+    "    'prior': 'NormalGamma',\n",
+    "    # hierachical inference with group level \n",
+    "    'type': 'Hierarchical',\n",
+    "\n",
+    "}\n",
+    "\n",
+    "inference = ModelInference(AIFAgent, agent_options, inference_options)\n",
+    "\n",
+    "num_samples = 1000\n",
+    "max_iterations = 1000\n",
+    "tolerance = 1e-3\n",
+    "# optimizer options\n",
+    "opts = {\n",
+    "    'learning_rate': 1e-3\n",
+    "}\n",
+    "\n",
+    "inference.fit(behavioural_data, num_samples, max_iterations, tolerance, opts)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Auxiliary Functions\n",
+    "\n",
+    "Define some utility functions that will be helpful for plotting."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_beliefs(belief_dist, title=\"\"):\n",
+    "    plt.grid(zorder=0)\n",
+    "    plt.bar(range(belief_dist.shape[0]), belief_dist, color='r', zorder=3)\n",
+    "    plt.xticks(range(belief_dist.shape[0]))\n",
+    "    plt.title(title)\n",
+    "    plt.show()\n",
+    "    \n",
+    "def plot_likelihood(A, title=\"\"):\n",
+    "    ax = sns.heatmap(A, cmap=\"OrRd\", linewidth=2.5)\n",
+    "    plt.xticks(range(A.shape[1]))\n",
+    "    plt.yticks(range(A.shape[0]))\n",
+    "    plt.title(title)\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Environment\n",
+    "\n",
+    "Here we consider an agent navigating a three-armed 'T-maze,' with the agent starting in a central location of the maze. The bottom arm of the maze contains an informative cue, which signals in which of the two top arms ('Left' or 'Right', the ends of the 'T') a reward is likely to be found. \n",
+    "\n",
+    "At each timestep, the environment is described by the joint occurrence of two qualitatively-different 'kinds' of states (hereafter referred to as _hidden state factors_). These hidden state factors are independent of one another.\n",
+    "\n",
+    "We represent the first hidden state factor (`Location`) as a $ 1 \\ x \\ 4 $ vector that encodes the current position of the agent, and can take the following values: {`CENTER`, `RIGHT ARM`, `LEFT ARM`, or `CUE LOCATION`}. For example, if the agent is in the `CUE LOCATION`, the current state of this factor would be $s_1 = [0 \\ 0 \\ 0 \\ 1]$.\n",
+    "\n",
+    "We represent the second hidden state factor (`Reward Condition`) as a $ 1 \\ x \\ 2 $ vector that encodes the reward condition of the trial: {`Reward on Right`, or `Reward on Left`}.  A trial where the condition is reward is `Reward on Left` is thus encoded as the state $s_2 = [0 \\ 1]$.\n",
+    "\n",
+    "The environment is designed such that when the agent is located in the `RIGHT ARM` and the reward condition is `Reward on Right`, the agent has a specified probability $a$ (where $a > 0.5$) of receiving a reward, and a low probability $b = 1 - a$ of receiving a 'loss' (we can think of this as an aversive or unpreferred stimulus). If the agent is in the `LEFT ARM` for the same reward condition, the reward probabilities are swapped, and the agent experiences loss with probability $a$, and reward with lower probability $b = 1 - a$. These reward contingencies are intuitively swapped for the `Reward on Left` condition. \n",
+    "\n",
+    "For instance, we can encode the state of the environment at the first time step in a `Reward on Right` trial with the following pair of hidden state vectors: $s_1 = [1 \\ 0 \\ 0 \\ 0]$, $s_2 = [1 \\ 0]$, where we assume the agent starts sitting in the central location. If the agent moved to the right arm, then the corresponding hidden state vectors would now be $s_1 = [0 \\ 1 \\ 0 \\ 0]$, $s_2 = [1 \\ 0]$. This highlights the _independence_ of the two hidden state factors -- the location of the agent ($s_1$) can change without affecting the identity of the reward condition ($s_2$).\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 1. Initialize environment\n",
+    "Now we can initialize the T-maze environment using the built-in `TMazeEnv` class from the `pymdp.envs` module."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Choose reward probabilities $a$ and $b$, where $a$ and $b$ are the probabilities of reward / loss in the 'correct' arm, and the probabilities of loss / reward in the 'incorrect' arm. Which arm counts as 'correct' vs. 'incorrect' depends on the reward condition (state of the 2nd hidden state factor)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "reward_probabilities = [0.98, 0.02] # probabilities used in the original SPM T-maze demo"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Initialize an instance of the T-maze environment"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "env = TMazeEnv(reward_probs = reward_probabilities)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Structure of the state --> outcome mapping\n",
+    "We can 'peer into' the rules encoded by the environment (also known as the _generative process_ ) by looking at the probability distributions that map from hidden states to observations. Following the SPM version of active inference, we refer to this collection of probabilistic relationships as the `A` array. In the case of the true rules of the environment, we refer to this array as `A_gp` (where the suffix `_gp` denotes the generative process). \n",
+    "\n",
+    "It is worth outlining what constitute the agent's observations in this task. In this T-maze demo, we have three sensory channels or observation modalities: `Location`, `Reward`, and `Cue`. \n",
+    "\n",
+    ">The `Location` observation values are identical to the `Location` hidden state values. In this case, the agent always unambiguously observes its own state - if the agent is in `RIGHT ARM`, it receives a `RIGHT ARM` observation in the corresponding modality. This might be analogized to a 'proprioceptive' sense of one's own place.\n",
+    "\n",
+    ">The `Reward` observation modality assumes the values `No Reward`, `Reward` or `Loss`. The `No Reward` (index 0) observation is  observed whenever the agent isn't occupying one of the two T-maze arms (the right or left arms). The `Reward` (index 1) and `Loss` (index 2) observations are observed in the right and left arms of the T-maze, with associated probabilities that depend on the reward condition (i.e. on the value of the second hidden state factor).\n",
+    "\n",
+    "> The `Cue` observation modality assumes the values `Cue Right`, `Cue Left`. This observation unambiguously signals the reward condition of the trial, and therefore in which arm the `Reward` observation is more probable. When the agent occupies the other arms, the `Cue` observation will be `Cue Right` or `Cue Left` with equal probability. However (as we'll see below when we intialise the agent), the agent's beliefs about the likelihood mapping render these observations uninformative and irrelevant to state inference.\n",
+    "\n",
+    "In `pymdp`, we store the set of probability distributions encoding the conditional probabilities of observations, under different configurations of hidden states, as a set of matrices referred to as the likelihood mapping or `A` array (this is a convention borrowed from SPM). The likelihood mapping _for a single modality_ is stored as a single matrix `A[i]` with the larger likelihood array, where `i` is the index of the corresponding modality. Each modality-specific A matrix has `n_observations[i]` rows, and as many lagging dimensions (e.g. columns, 'slices' and higher-order dimensions) as there are hidden state factors. `n_observations[i]` tells you the number of observation values for observation modality `i`, and is usually stored as a property of the `Env` class (e.g. `env.n_observations`).\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A_gp = env.get_likelihood_dist()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_likelihood(A_gp[1][:, :, 0],'Reward Right')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_likelihood(A_gp[1][:, :, 1],'Reward Left')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_likelihood(A_gp[2][:, 3, :],'Cue Mapping')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Transition Dynamics\n",
+    "\n",
+    "We represent the dynamics of the environment (e.g. changes in the location of the agent and changes to the reward condition) as conditional probability distributions that encode the likelihood of transitions between the states of a given hidden state factor. These distributions are collected into the so-called `B` array, also known as _transition likelihoods_ or _transition distribution_ . As with the `A` array, we denote the true probabilities describing the environmental dynamics as `B_gp`. Each sub-matrix `B_gp[f]` of the larger array encodes the transition probabilities between state-values of a given hidden state factor with index `f`. These matrices encode dynamics as Markovian transition probabilities, such that the entry $i,j$ of a given matrix encodes the probability of transition to state $i$ at time $t+1$, given state $j$ at $t$. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "B_gp = env.get_transition_dist()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "For example, we can inspect the 'dynamics' of the `Reward Condition` factor by indexing into the appropriate sub-matrix of `B_gp`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_likelihood(B_gp[1][:, :, 0],'Reward Condition Transitions')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The above transition array is the 'trivial' identity matrix, meaning that the reward condition doesn't change over time (it's mapped from whatever it's current value is to the same value at the next timestep)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### (Controllable-) Transition Dynamics\n",
+    "\n",
+    "Importantly, some hidden state factors are _controllable_ by the agent, meaning that the probability of being in state $i$ at $t+1$ isn't merely a function of the state at $t$, but also of actions (or from the agent's perspective, _control states_ ). So now each transition likelihood encodes conditional probability distributions over states at $t+1$, where the conditioning variables are both the states at $t-1$ _and_ the actions at $t-1$. This extra conditioning on actions is encoded via an optional third dimension to each factor-specific `B` matrix.\n",
+    "\n",
+    "For example, in our case the first hidden state factor (`Location`) is under the control of the agent, which means the corresponding transition likelihoods `B[0]` are index-able by both previous state and action."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_likelihood(B_gp[0][:,:,0],'Transition likelihood for \"Move to Center\"')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_likelihood(B_gp[0][:,:,1],'Transition likelihood for \"Move to Right Arm\"')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_likelihood(B_gp[0][:,:,2],'Transition likelihood for \"Move to Left Arm\"')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_likelihood(B_gp[0][:,:,3],'Transition likelihood for \"Move to Cue Location\"')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## The generative model\n",
+    "Now we can move onto setting up the generative model of the agent - namely, the agent's beliefs about how hidden states give rise to observations, and how hidden states transition among eachother.\n",
+    "\n",
+    "In almost all MDPs, the critical building blocks of this generative model are the agent's representation of the observation likelihood, which we'll refer to as `A_gm`, and its representation of the transition likelihood, or `B_gm`. \n",
+    "\n",
+    "Here, we assume the agent has a veridical representation of the rules of the T-maze (namely, how hidden states cause observations) as well as its ability to control its own movements with certain consequences (i.e. 'noiseless' transitions)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "num_agents = 50  # number of different agents \n",
+    "A_gm = [jnp.broadcast_to(jnp.array(a), (num_agents,) + a.shape) for a in A_gp]  # map the true observation likelihood to jax arrays\n",
+    "B_gm = [jnp.broadcast_to(jnp.array(b), (num_agents,) + b.shape) for b in B_gp]  # map the true transition likelihood to jax arrays\n",
+    "D_gm = [jnp.broadcast_to(jnp.array([1., 0., 0., 0.]), (num_agents, 4)), jnp.broadcast_to(jnp.array([.5, .5]), (num_agents, 2))]\n",
+    "C_gm = [jnp.zeros((num_agents, 4)), jnp.broadcast_to(jnp.array([0., -3., 3.]), (num_agents, 3)),jnp.zeros((num_agents, 2))]\n",
+    "E_gm = jnp.ones((num_agents, 4))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "###  Note !\n",
+    "It is not necessary, or even in many cases _important_ , that the generative model is a veridical representation of the generative process. This distinction between generative model (essentially, beliefs entertained by the agent and its interaction with the world) and the generative process (the actual dynamical system 'out there' generating sensations) is of crucial importance to the active inference formalism and (in our experience) often overlooked in code.\n",
+    "\n",
+    "It is for notational and computational convenience that we encode the generative process using `A` and `B` matrices. By doing so, it simply puts the rules of the environment in a data structure that can easily be converted into the Markovian-style conditional distributions useful for encoding the agent's generative model.\n",
+    "\n",
+    "Strictly speaking, however, all the generative process needs to do is generate observations and be 'perturbable' by actions. The way in which it does so can be arbitrarily complex, non-linear, and unaccessible by the agent."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Introducing the `Agent()` class\n",
+    "\n",
+    "In `pymdp`, we have abstracted much of the computations required for active inference into the `Agent()` class, a flexible object that can be used to store necessary aspects of the generative model, the agent's instantaneous observations and actions, and perform action / perception using functions like `Agent.infer_states` and `Agent.infer_policies`. \n",
+    "\n",
+    "An instance of `Agent` is straightforwardly initialized with a call to `Agent()` with a list of optional arguments.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In our call to `Agent()`, we need to constrain the default behavior with some of our T-Maze-specific needs. For example, we want to make sure that the agent's beliefs about transitions are constrained by the fact that it can only control the `Location` factor - _not_ the `Reward Condition` (which we assumed stationary across an epoch of time). Therefore we specify this using a list of indices that will be passed as the `control_fac_idx` argument of the `Agent()` constructor. \n",
+    "\n",
+    "Each element in the list specifies a hidden state factor (in terms of its index) that is controllable by the agent. Hidden state factors whose indices are _not_ in this list are assumed to be uncontrollable."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "controllable_indices = [0] # this is a list of the indices of the hidden state factors that are controllable"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now we can construct our agent..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "agent = Agent(A_gm, B_gm, C_gm, D_gm, E_gm, control_fac_idx=controllable_indices)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(4, 1, 2)\n",
+      "int32\n"
+     ]
+    }
+   ],
+   "source": [
+    "policies = jnp.stack(agent.policies)\n",
+    "print(policies.shape)\n",
+    "print(policies.dtype)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "PyTreeDef(CustomNode(Agent[(('A', 'B', 'C', 'D', 'E', 'gamma', 'qs', 'q_pi'), ('num_obs', 'num_modalities', 'num_states', 'num_factors', 'num_controls', 'inference_algo', 'control_fac_idx', 'policy_len', 'policies', 'use_utility', 'use_states_info_gain', 'use_param_info_gain', 'action_selection'), ([4, 3, 2], 3, [4, 2], 2, [4, 1], 'VANILLA', [0], 1, DeviceArray([[[0, 0]],\n",
+      "\n",
+      "             [[1, 0]],\n",
+      "\n",
+      "             [[2, 0]],\n",
+      "\n",
+      "             [[3, 0]]], dtype=int32), True, True, False, 'deterministic'))], [[*, *, *], [*, *], [*, *, *], [*, *], *, *, None, None]))\n"
+     ]
+    }
+   ],
+   "source": [
+    "import jax.tree_util as jtu\n",
+    "\n",
+    "vals, tree = jtu.tree_flatten(agent)\n",
+    "\n",
+    "print(tree)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Active Inference\n",
+    "Now we can start off the T-maze with an initial observation and run active inference via a loop over a desired time interval."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      " === Starting experiment === \n",
+      " Reward condition: Right, Observation: [CENTER, No reward, Cue Left]\n",
+      "[Step 0] Action: [Move to RIGHT ARM]\n",
+      "[Step 0] Observation: [RIGHT ARM,  Reward!, Cue Right]\n",
+      "[Step 1] Action: [Move to CUE LOCATION]\n",
+      "[Step 1] Observation: [CUE LOCATION,  No reward, Cue Right]\n",
+      "[Step 2] Action: [Move to LEFT ARM]\n",
+      "[Step 2] Observation: [LEFT ARM,  Loss!, Cue Left]\n",
+      "[Step 3] Action: [Move to CUE LOCATION]\n",
+      "[Step 3] Observation: [CUE LOCATION,  No reward, Cue Right]\n",
+      "[Step 4] Action: [Move to LEFT ARM]\n",
+      "[Step 4] Observation: [LEFT ARM,  Reward!, Cue Right]\n"
+     ]
+    }
+   ],
+   "source": [
+    "T = 5 # number of timesteps\n",
+    "\n",
+    "emp_prior = D_gm\n",
+    "_obs = env.reset() # reset the environment and get an initial observation\n",
+    "obs = jnp.broadcast_to(jnp.array(_obs), (num_agents, len(_obs)))\n",
+    "\n",
+    "# these are useful for displaying read-outs during the loop over time\n",
+    "reward_conditions = [\"Right\", \"Left\"]\n",
+    "location_observations = ['CENTER','RIGHT ARM','LEFT ARM','CUE LOCATION']\n",
+    "reward_observations = ['No reward','Reward!','Loss!']\n",
+    "cue_observations = ['Cue Right','Cue Left']\n",
+    "msg = \"\"\" === Starting experiment === \\n Reward condition: {}, Observation: [{}, {}, {}]\"\"\"\n",
+    "print(msg.format(reward_conditions[env.reward_condition], location_observations[_obs[0]], reward_observations[_obs[1]], cue_observations[_obs[2]]))\n",
+    "\n",
+    "measurements = {'actions': [], 'outcomes': [obs]}\n",
+    "for t in range(T):\n",
+    "    qs = agent.infer_states(obs, emp_prior)\n",
+    "\n",
+    "    q_pi, efe = agent.infer_policies(qs)\n",
+    "\n",
+    "    actions = agent.sample_action(q_pi)\n",
+    "    emp_prior = agent.update_empirical_prior(actions, qs)\n",
+    "\n",
+    "    measurements[\"actions\"].append( actions )\n",
+    "    msg = \"\"\"[Step {}] Action: [Move to {}]\"\"\"\n",
+    "    print(msg.format(t, location_observations[int(actions[0, 0])]))\n",
+    "\n",
+    "    obs = []\n",
+    "    for a in actions:\n",
+    "        obs.append( jnp.array(env.step(list(a))) )\n",
+    "    obs = jnp.stack(obs)\n",
+    "    measurements[\"outcomes\"].append(obs)\n",
+    "\n",
+    "    msg = \"\"\"[Step {}] Observation: [{},  {}, {}]\"\"\"\n",
+    "    print(msg.format(t, location_observations[obs[0, 0]], reward_observations[obs[0, 1]], cue_observations[obs[0, 2]]))\n",
+    "    \n",
+    "measurements['actions'] = jnp.stack(measurements['actions']).astype(jnp.int32)\n",
+    "measurements['outcomes'] = jnp.stack(measurements['outcomes'])\n",
+    "\n",
+    "measurements['outcomes'] = measurements['outcomes'][None, :T]\n",
+    "measurements['actions'] = measurements['actions'][None]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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CAgI0e/Zs52t+fn4KDw93jn/o0CFNmzZNH3zwQaX9PD8/32X4uuuuq3T/0sGDB+Xh4eHy5i9VvZ9WZf/+/Wrfvv0Fnzw7ePCgWrRo4RK2pf9eGqk4NlQ4O2BUOPs4dvToUZ06darKbaN9+/YuH2wu1cGDB9WuXTuXp3GkmtdesT+eu27wX4SROqgmn8S3bNmioUOHqk+fPlqwYIGaN28uLy8vLVmyREuXLv0Nqqze3XffrZiYGP3zn//U2rVrNWvWLL3wwgv6xz/+oUGDBl1w3PLycnXp0kVz586t8vXQ0FCX4bM/Wdam2p5uxVmPWbNmKSIioso+FffN1HR67iyncwUGBiorK0tr1qzRxx9/rI8//lhLlixRUlJSpZv7zmZy+ztf2D73Bu+Lde46r1hnjz766Hk/sbdt21aS1KJFC7Vu3VqbN29WWFiYLMtSdHS0AgICNGnSJB08eFBbtmxRz549nW+MZWVlGjhwoI4fP64nnnhCHTp0UIMGDXTkyBGNHj260pkyu91e6U31SnS+45h1zs2uV6KruXZTCCPXqPfee08+Pj5as2aNyyNvS5YsuaTpVnxyP9t3333nvCG0VatWkuQ8DX22vXv3yt/f3+Uxw+bNm2vChAmaMGGCcnNzdcstt+i5555zhpHzvbG0adNGX375pW699dZLOtNztoCAANWvX/+8tXt4eFT75l2dc5efZVnat2+fbr75ZklyfnL18/NTbGzsJc2rYnqXupy8vb01ZMgQDRkyROXl5ZowYYIWLVqkqVOnOt9kz+Xu9ne+7ap+/frOszo1XTcVn1JPnDjh8qjyuZ9upUs7S1ih4kyel5dXjdZZTEyMNm/erNatWysiIkINGzZUeHi4GjVqpNWrV2vnzp2aMWOGs/9XX32l7777Tm+//baSkpKc7e5cOmvVqpXKy8udZzgqVLU8q9KmTRt99tlncjgc571Bs1WrVlq3bp0KCwtdzo7s3bvX+bo7AgICVK9evSq3jZrU7c66bdWqlf7973+rvLzcJchdbO2o7MqPx7gsPD09ZbPZXD4NHjhwoNJTJu5atWqV8/q3JG3fvl2fffaZMzw0b95cERERevvtt3XixAlnv6+//lpr165VQkKCpDOf9s49vRwYGKgWLVq4nNJv0KBBpX7SmbMqR44c0RtvvFHptVOnTtXoyZZzeXp6Ki4uTu+//77Ltzbm5ORo6dKl6t27t/z8/Nye7tkqnkaqsHLlSv3yyy/O5RcZGak2bdpo9uzZOnnyZKXxKy5Z1NSlLqdjx465DHt4eDiD07mPUJ/N3e1v27ZtLveSHD58WO+//77i4uLk6enp1rqpCHRnPxpcVFRU5ZmcBg0auGynFyMwMFD9+vXTokWL9Msvv1R6/dx1FhMTowMHDmjZsmXOyzYeHh7q2bOn5s6dK4fD4XK/SMWn8LM/dVuWVaPHqytUbF9nP1YsqcbfbnznnXcqLy9P8+bNq/RaRV0JCQkqKyur1Oell16SzWar9mznuTw9PRUfH69Vq1bp0KFDzvY9e/ZozZo11Y5f8aGnJus3ISFB2dnZWrZsmbPt9OnTevXVV+Xr66u+ffu6VTsq48zINWrw4MGaO3eubrvtNo0cOVK5ubmaP3++2rZtq3//+98XPd22bduqd+/eGj9+vEpKSpSWlqZmzZrp8ccfd/aZNWuWBg0apOjoaI0dO9b5aG+jRo2c3+lRWFio66+/XsOGDVN4eLh8fX21bt06ff7555ozZ45zWpGRkVq2bJmSk5PVvXt3+fr6asiQIbr33nu1fPlyPfDAA9qwYYN69eqlsrIy7d27V8uXL9eaNWvcug+nwrPPPquMjAz17t1bEyZM0HXXXadFixappKREL7744kUvtwpNmzZV7969NWbMGOXk5CgtLU1t27bVuHHjJJ15U/rLX/6iQYMGqVOnThozZoxCQkJ05MgRbdiwQX5+fvrXv/5V4/ld6nK67777dPz4cQ0YMEDXX3+9Dh48qFdffVURERHnfUxScn/769y5s+Lj410e7ZXkcoagpusmLi5OLVu21NixY/XYY4/J09NTixcvVkBAgMubmnRm+3rttdf07LPPqm3btgoMDHTe3OuO+fPnq3fv3urSpYvGjRunG264QTk5Odq2bZt++uknffnll86+FUHj22+/1fPPP+9s79Onjz7++GPn91ZU6NChg9q0aaNHH31UR44ckZ+fn9577z237k+IiIjQiBEjtGDBAuXn56tnz57KzMzUvn37ajR+UlKS/vrXvyo5OVnbt29XTEyMioqKtG7dOk2YMEG33367hgwZov79++upp57SgQMHFB4errVr1+r999/XI488Uul+lZqYMWOGVq9erZiYGE2YMMEZEDp16lTtcSwiIkKenp564YUXlJ+fL7vdrgEDBigwMLBS3/vvv1+LFi3S6NGjtWPHDoWFhWnlypX65JNPlJaWVuk+GFwEQ0/xoAYqHjX8/PPPq3z9fI/2NmjQoFLfqh5nfPPNN6127dpZdrvd6tChg7VkyZIq+7nzaO+sWbOsOXPmWKGhoZbdbrdiYmKsL7/8slL/devWWb169bLq1atn+fn5WUOGDLF2797tfL2kpMR67LHHrPDwcKthw4ZWgwYNrPDwcGvBggUu0zl58qQ1cuRIq3HjxpYkl8d8S0tLrRdeeMHq1KmTZbfbrSZNmliRkZHWjBkzrPz8fGc/Sed9hFhVPNa4c+dOKz4+3vL19bXq169v9e/f3/r0009d+lS37s5V8Wjv//7v/1opKSlWYGCgVa9ePWvw4MEujy1W2LVrl3XHHXdYzZo1s+x2u9WqVSvr7rvvtjIzMyvVcKFHe91ZTlU92rty5UorLi7OCgwMtLy9va2WLVtaf/jDH6xffvml2r+5pttfxfp55513nP27du1a5SOZNVk3lmVZO3bssKKiopw1z507t8rllZ2dbQ0ePNhq2LChJemCj/mevQ9UZf/+/VZSUpIVHBxseXl5WSEhIdbvfvc7a+XKlZX6BgYGWpKsnJwcZ9vWrVstSVZMTEyl/rt377ZiY2MtX19fy9/f3xo3bpzzUdiaHB8sy7JOnTplPfzww1azZs2sBg0aWEOGDLEOHz5co0d7LevM48VPPfWU1bp1a8vLy8sKDg62hg0b5vKodWFhoTV58mSrRYsWlpeXl9WuXTtr1qxZLo+pW9b598mqjkWbNm2yIiMjLW9vb+uGG26wFi5cWOPj2BtvvGHdcMMNzkeBK7apqvaTnJwca8yYMZa/v7/l7e1tdenSxWXZWtaFt4GaLsdrlc2yuKMGl+7AgQNq3bq1Zs2apUcffdR0OQCAqwj3jAAAAKMIIwAAwCjCCAAAMIp7RgAAgFGcGQEAAEYRRgAAgFFXxZeelZeX6+eff1bDhg1r7au9AQDA5WVZlgoLC9WiRYsL/ibSVRFGfv7550v+zQ8AAGDG4cOHK/1a9NmuijBS8VW7hw8fvuTf/sCVy+FwaO3atYqLizvvj20BuPqxr187CgoKFBoaWu1X5l8VYaTi0oyfnx9hpA5zOByqX7++/Pz8OEABdRj7+rWnulssuIEVAAAYRRgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGEEQAAYBRhBAAAGEUYAQAARrkdRjZv3qwhQ4aoRYsWstlsWrVqVbXjbNy4Ubfccovsdrvatm2rt9566yJKBQAAdZHbYaSoqEjh4eGaP39+jfr/+OOPGjx4sPr376+srCw98sgjuu+++7RmzRq3iwUAAHWP2z+UN2jQIA0aNKjG/RcuXKjWrVtrzpw5kqSOHTtq69ateumllxQfH+/u7AEAQB1z2X+1d9u2bYqNjXVpi4+P1yOPPHLecUpKSlRSUuIcLigokHTmlx4dDsdlqRPmVaxb1jFQt7GvXztquo4vexjJzs5WUFCQS1tQUJAKCgp06tQp1atXr9I4M2fO1IwZMyq1r127VvXr16/V+m5PTKzV6eHieUm63XQRqOT9GtwXBlyMjIwM0yXgMisuLq5Rv8seRi5GSkqKkpOTncMFBQUKDQ1VXFyc/Pz8DFYGXHsSEhJMl4A6xuFwKCMjQwMHDpSXl5fpcnAZVVzZqM5lDyPBwcHKyclxacvJyZGfn1+VZ0UkyW63y263V2r38vJiwwV+Y+xzuFw4ptd9NV2/l/17RqKjo5WZmenSlpGRoejo6Ms9awAAcBVwO4ycPHlSWVlZysrKknTm0d2srCwdOnRI0plLLElJSc7+DzzwgH744Qc9/vjj2rt3rxYsWKDly5dr8uTJtfMXAACAq5rbYeSLL75Q165d1bVrV0lScnKyunbtqmnTpkmSfvnlF2cwkaTWrVvro48+UkZGhsLDwzVnzhz95S9/4bFeAAAg6SLuGenXr58syzrv61V9u2q/fv20a9cud2cFAACuAfw2DQAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwKiLCiPz589XWFiYfHx8FBUVpe3bt1+wf1pamtq3b6969eopNDRUkydP1q+//npRBQMAgLrF7TCybNkyJScnKzU1VTt37lR4eLji4+OVm5tbZf+lS5dqypQpSk1N1Z49e/Tmm29q2bJlevLJJy+5eAAAcPVzO4zMnTtX48aN05gxY3TTTTdp4cKFql+/vhYvXlxl/08//VS9evXSyJEjFRYWpri4OI0YMaLasykAAODacJ07nUtLS7Vjxw6lpKQ42zw8PBQbG6tt27ZVOU7Pnj31zjvvaPv27erRo4d++OEHpaen69577z3vfEpKSlRSUuIcLigokCQ5HA45HA53Sq6WV61ODah7anufAyq2Kbatuq+m69itMJKXl6eysjIFBQW5tAcFBWnv3r1VjjNy5Ejl5eWpd+/esixLp0+f1gMPPHDByzQzZ87UjBkzKrWvXbtW9evXd6fkat1eq1MD6p709HTTJaCOysjIMF0CLrPi4uIa9XMrjFyMjRs36vnnn9eCBQsUFRWlffv2adKkSfrTn/6kqVOnVjlOSkqKkpOTncMFBQUKDQ1VXFyc/Pz8LnfJAM6SkJBgugTUMQ6HQxkZGRo4cKC8vDg/XZdVXNmojlthxN/fX56ensrJyXFpz8nJUXBwcJXjTJ06Vffee6/uu+8+SVKXLl1UVFSk+++/X0899ZQ8PCrftmK322W32yu1e3l5seECvzH2OVwuHNPrvpquX7duYPX29lZkZKQyMzOdbeXl5crMzFR0dHSV4xQXF1cKHJ6enpIky7LcmT0AAKiD3L5Mk5ycrFGjRqlbt27q0aOH0tLSVFRUpDFjxkiSkpKSFBISopkzZ0qShgwZorlz56pr167OyzRTp07VkCFDnKEEAABcu9wOI8OHD9fRo0c1bdo0ZWdnKyIiQqtXr3be1Hro0CGXMyFPP/20bDabnn76aR05ckQBAQEaMmSInnvuudr7KwAAwFXLZl0F10oKCgrUqFEj5efn1/4NrDZb7U4PqGuu/EMErjIOh0Pp6elKSEjgnpE6rqbv3/w2DQAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMuKozMnz9fYWFh8vHxUVRUlLZv337B/idOnNDEiRPVvHlz2e123XjjjUpPT7+oggEAQN1ynbsjLFu2TMnJyVq4cKGioqKUlpam+Ph4ffvttwoMDKzUv7S0VAMHDlRgYKBWrlypkJAQHTx4UI0bN66N+gEAwFXO7TAyd+5cjRs3TmPGjJEkLVy4UB999JEWL16sKVOmVOq/ePFiHT9+XJ9++qm8vLwkSWFhYZdWNQAAqDPcCiOlpaXasWOHUlJSnG0eHh6KjY3Vtm3bqhzngw8+UHR0tCZOnKj3339fAQEBGjlypJ544gl5enpWOU5JSYlKSkqcwwUFBZIkh8Mhh8PhTsnV8qrVqQF1T23vc0DFNsW2VffVdB27FUby8vJUVlamoKAgl/agoCDt3bu3ynF++OEHrV+/Xvfcc4/S09O1b98+TZgwQQ6HQ6mpqVWOM3PmTM2YMaNS+9q1a1W/fn13Sq7W7bU6NaDu4f4uXC4ZGRmmS8BlVlxcXKN+bl+mcVd5ebkCAwP1+uuvy9PTU5GRkTpy5IhmzZp13jCSkpKi5ORk53BBQYFCQ0MVFxcnPz+/y10ygLMkJCSYLgF1jMPhUEZGhgYOHOi8fI+6qeLKRnXcCiP+/v7y9PRUTk6OS3tOTo6Cg4OrHKd58+by8vJyuSTTsWNHZWdnq7S0VN7e3pXGsdvtstvtldq9vLzYcIHfGPscLheO6XVfTdevW4/2ent7KzIyUpmZmc628vJyZWZmKjo6uspxevXqpX379qm8vNzZ9t1336l58+ZVBhEAAHBtcft7RpKTk/XGG2/o7bff1p49ezR+/HgVFRU5n65JSkpyucF1/PjxOn78uCZNmqTvvvtOH330kZ5//nlNnDix9v4KAABw1XL7npHhw4fr6NGjmjZtmrKzsxUREaHVq1c7b2o9dOiQPDz+m3FCQ0O1Zs0aTZ48WTfffLNCQkI0adIkPfHEE7X3VwAAgKuWzbIsy3QR1SkoKFCjRo2Un59f+zew2my1Oz2grrnyDxG4yjgcDqWnpyshIYF7Ruq4mr5/89s0AADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAoy4qjMyfP19hYWHy8fFRVFSUtm/fXqPx3n33XdlsNiUmJl7MbAEAQB3kdhhZtmyZkpOTlZqaqp07dyo8PFzx8fHKzc294HgHDhzQo48+qpiYmIsuFgAA1D3XuTvC3LlzNW7cOI0ZM0aStHDhQn300UdavHixpkyZUuU4ZWVluueeezRjxgxt2bJFJ06cuOA8SkpKVFJS4hwuKCiQJDkcDjkcDndLviCvWp0aUPfU9j4HVGxTbFt1X03XsVthpLS0VDt27FBKSoqzzcPDQ7Gxsdq2bdt5x3vmmWcUGBiosWPHasuWLdXOZ+bMmZoxY0al9rVr16p+/frulFyt22t1akDdk56ebroE1FEZGRmmS8BlVlxcXKN+boWRvLw8lZWVKSgoyKU9KChIe/furXKcrVu36s0331RWVlaN55OSkqLk5GTncEFBgUJDQxUXFyc/Pz93SgZwiRISEkyXgDrG4XAoIyNDAwcOlJcX56frsoorG9Vx+zKNOwoLC3XvvffqjTfekL+/f43Hs9vtstvtldq9vLzYcIHfGPscLheO6XVfTdevW2HE399fnp6eysnJcWnPyclRcHBwpf779+/XgQMHNGTIEGdbeXn5mRlfd52+/fZbtWnTxp0SAABAHePW0zTe3t6KjIxUZmams628vFyZmZmKjo6u1L9Dhw766quvlJWV5fw3dOhQ9e/fX1lZWQoNDb30vwAAAFzV3L5Mk5ycrFGjRqlbt27q0aOH0tLSVFRU5Hy6JikpSSEhIZo5c6Z8fHzUuXNnl/EbN24sSZXaAQDAtcntMDJ8+HAdPXpU06ZNU3Z2tiIiIrR69WrnTa2HDh2Shwdf7AoAAGrGZlmWZbqI6hQUFKhRo0bKz8+v/adpbLbanR5Q11z5hwhcZRwOh9LT05WQkMANrHVcTd+/OYUBAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAqIsKI/Pnz1dYWJh8fHwUFRWl7du3n7fvG2+8oZiYGDVp0kRNmjRRbGzsBfsDAIBri9thZNmyZUpOTlZqaqp27typ8PBwxcfHKzc3t8r+Gzdu1IgRI7RhwwZt27ZNoaGhiouL05EjRy65eAAAcPWzWZZluTNCVFSUunfvrnnz5kmSysvLFRoaqoceekhTpkypdvyysjI1adJE8+bNU1JSUo3mWVBQoEaNGik/P19+fn7ulFs9m612pwfUNe4dIoBqORwOpaenKyEhQV5eXqbLwWVU0/fv69yZaGlpqXbs2KGUlBRnm4eHh2JjY7Vt27YaTaO4uFgOh0NNmzY9b5+SkhKVlJQ4hwsKCiSd2YAdDoc7JVeL3QC4sNre54CKbYptq+6r6Tp2K4zk5eWprKxMQUFBLu1BQUHau3dvjabxxBNPqEWLFoqNjT1vn5kzZ2rGjBmV2teuXav69eu7U3K1bq/VqQF1T3p6uukSUEdlZGSYLgGXWXFxcY36uRVGLtWf//xnvfvuu9q4caN8fHzO2y8lJUXJycnO4YKCAue9JrV+mQbABSUkJJguAXWMw+FQRkaGBg4cyGWaOq7iykZ13Aoj/v7+8vT0VE5Ojkt7Tk6OgoODLzju7Nmz9ec//1nr1q3TzTfffMG+drtddru9UruXlxcbLvAbY5/D5cIxve6r6fp162kab29vRUZGKjMz09lWXl6uzMxMRUdHn3e8F198UX/605+0evVqdevWzZ1ZAgCAOs7tyzTJyckaNWqUunXrph49eigtLU1FRUUaM2aMJCkpKUkhISGaOXOmJOmFF17QtGnTtHTpUoWFhSk7O1uS5OvrK19f31r8UwAAwNXI7TAyfPhwHT16VNOmTVN2drYiIiK0evVq502thw4dkofHf0+4vPbaayotLdWwYcNcppOamqrp06dfWvUAAOCq5/b3jJjA94wABl35hwhcZfiekWtHTd+/+W0aAABgFGEEAAAYRRgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGEEQAAYBRhBAAAGEUYAQAARhFGAACAUYQRAABgFGEEAAAYRRgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGEEQAAYBRhBAAAGEUYAQAARhFGAACAUYQRAABgFGEEAAAYRRgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGEEQAAYBRhBAAAGEUYAQAARhFGAACAUYQRAABgFGEEAAAYRRgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGEEQAAYBRhBAAAGEUYAQAARhFGAACAUYQRAABgFGEEAAAYRRgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGEEQAAYBRhBAAAGEUYAQAARl1UGJk/f77CwsLk4+OjqKgobd++/YL9V6xYoQ4dOsjHx0ddunRRenr6RRULAADqHrfDyLJly5ScnKzU1FTt3LlT4eHhio+PV25ubpX9P/30U40YMUJjx47Vrl27lJiYqMTERH399deXXDwAALj62SzLstwZISoqSt27d9e8efMkSeXl5QoNDdVDDz2kKVOmVOo/fPhwFRUV6cMPP3S2/b//9/8UERGhhQsX1mieBQUFatSokfLz8+Xn5+dOudWz2Wp3ekBd494hAqiWw+FQenq6EhIS5OXlZbocXEY1ff++zp2JlpaWaseOHUpJSXG2eXh4KDY2Vtu2batynG3btik5OdmlLT4+XqtWrTrvfEpKSlRSUuIczs/PlyQdP35cDofDnZKr1axWpwbUPceOHTNdAuoYh8Oh4uJiHTt2jDBSxxUWFkqSqjvv4VYYycvLU1lZmYKCglzag4KCtHfv3irHyc7OrrJ/dnb2eeczc+ZMzZgxo1J769at3SkXQG3w9zddAYCrXGFhoRo1anTe190KI7+VlJQUl7Mp5eXlOn78uJo1ayYbl1XqrIKCAoWGhurw4cO1fzkOwBWDff3aYVmWCgsL1aJFiwv2cyuM+Pv7y9PTUzk5OS7tOTk5Cg4OrnKc4OBgt/pLkt1ul91ud2lr3LixO6XiKubn58cBCrgGsK9fGy50RqSCW0/TeHt7KzIyUpmZmc628vJyZWZmKjo6uspxoqOjXfpLUkZGxnn7AwCAa4vbl2mSk5M1atQodevWTT169FBaWpqKioo0ZswYSVJSUpJCQkI0c+ZMSdKkSZPUt29fzZkzR4MHD9a7776rL774Qq+//nrt/iUAAOCq5HYYGT58uI4ePapp06YpOztbERERWr16tfMm1UOHDsnD478nXHr27KmlS5fq6aef1pNPPql27dpp1apV6ty5c+39FagT7Ha7UlNTK12iA1C3sK/jXG5/zwgAAEBt4rdpAACAUYQRAABgFGEEAAAYRRgBAABGEUYAAIBRhBFcMebPn6+wsDD5+PgoKipK27dvN10SgFq0efNmDRkyRC1atJDNZrvgD6bi2kIYwRVh2bJlSk5OVmpqqnbu3Knw8HDFx8crNzfXdGkAaklRUZHCw8M1f/5806XgCsP3jOCKEBUVpe7du2vevHmSzvzMQGhoqB566CFNmTLFcHUAapvNZtM///lPJSYmmi4FVwDOjMC40tJS7dixQ7Gxsc42Dw8PxcbGatu2bQYrAwD8FggjMC4vL09lZWXOnxSoEBQUpOzsbENVAQB+K4QRAABgFGEExvn7+8vT01M5OTku7Tk5OQoODjZUFQDgt0IYgXHe3t6KjIxUZmams628vFyZmZmKjo42WBkA4LdwnekCAElKTk7WqFGj1K1bN/Xo0UNpaWkqKirSmDFjTJcGoJacPHlS+/btcw7/+OOPysrKUtOmTdWyZUuDlcE0Hu3FFWPevHmaNWuWsrOzFRERoVdeeUVRUVGmywJQSzZu3Kj+/ftXah81apTeeuut374gXDEIIwAAwCjuGQEAAEYRRgAAgFGEEQAAYBRhBAAAGEUYAQAARhFGAACAUYQRAABgFGEEAAAYRRgBAABGEUYAAIBRhBEAAGDU/wf4Hucgx9rGqwAAAABJRU5ErkJggg==",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_beliefs(qs[1][0],\"Final posterior beliefs about reward condition\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Model inversion\n",
+    "Define model likelihood given the observed sequence of actions and outcomes"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(1, 5, 50, 3)\n",
+      "(1, 5, 50, 2)\n",
+      "494 ms ± 6.2 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
+      "172 ms ± 412 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
+      "dict_keys(['actions', 'outcomes'])\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpyro as npyro\n",
+    "from jax import random\n",
+    "from numpyro.infer import Predictive\n",
+    "from pymdp.jax.likelihoods import aif_likelihood, evolve_trials\n",
+    "\n",
+    "print(measurements['outcomes'].shape)\n",
+    "print(measurements['actions'].shape)\n",
+    "\n",
+    "Nb, Nt, Na, _ = measurements['actions'].shape\n",
+    "\n",
+    "xs = {'outcomes': measurements['outcomes'][0], 'actions': measurements['actions'][0]}\n",
+    "evolve_trials(agent, xs)\n",
+    "%timeit evolve_trials(agent, xs)\n",
+    "\n",
+    "rng_key = random.PRNGKey(0)\n",
+    "\n",
+    "with npyro.handlers.seed(rng_seed=0):\n",
+    "    aif_likelihood(Nb, Nt, Na, measurements, agent)\n",
+    "\n",
+    "%timeit pred_samples = Predictive(aif_likelihood, num_samples=11)(rng_key, Nb, Nt, Na, measurements, agent)\n",
+    "print(pred_samples.keys())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 59,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpyro as npyro\n",
+    "import numpyro.distributions as dist\n",
+    "from jax import nn, lax, vmap\n",
+    "\n",
+    "@vmap\n",
+    "def trans_params(z):\n",
+    "\n",
+    "    a = nn.sigmoid(z[0])\n",
+    "    lam = nn.softplus(z[1])\n",
+    "    d = nn.sigmoid(z[2])\n",
+    "\n",
+    "    A = lax.stop_gradient([jnp.array(x) for x in list(A_gp)])\n",
+    "\n",
+    "    middle_matrix1 = jnp.array([[0., 0.], [a, 1-a], [1-a, a]])\n",
+    "    middle_matrix2 = jnp.array([[0., 0.], [1-a, a], [a, 1-a]])\n",
+    "\n",
+    "    side_vector = jnp.stack([jnp.array([1.0, 0., 0.]), jnp.array([1.0, 0., 0.])], -1)\n",
+    "\n",
+    "    A[1] = jnp.stack([side_vector, middle_matrix1, middle_matrix2, side_vector], -2)\n",
+    "    \n",
+    "    C = [\n",
+    "        jnp.zeros(4),\n",
+    "        lam * jnp.array([0., 1., -1.]),\n",
+    "        jnp.zeros(2)\n",
+    "    ]\n",
+    "\n",
+    "    D = [nn.one_hot(0, 4), jnp.array([d, 1-d])]\n",
+    "\n",
+    "    E = jnp.ones(4)/4\n",
+    "\n",
+    "    params = {\n",
+    "        'A': A,\n",
+    "        'B': lax.stop_gradient([jnp.array(x) for x in list(B_gp)]),\n",
+    "        'C': C,\n",
+    "        'D': D,\n",
+    "        'E': E\n",
+    "    }\n",
+    "\n",
+    "    return  params, a, lam, d"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 61,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "357 ms ± 3.31 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
+      "dict_keys(['a', 'actions', 'd', 'lambda', 'outcomes', 'z'])\n"
+     ]
+    }
+   ],
+   "source": [
+    "def model(data, num_blocks, num_steps, num_agents, num_params=3):\n",
+    "    with npyro.plate('agents', num_agents):\n",
+    "        z = npyro.sample('z', dist.Normal(0., 1.).expand([num_params]).to_event(1))\n",
+    "        params, a, lmbd, d = trans_params(z)\n",
+    "        # register parameter values\n",
+    "        npyro.deterministic('a', a)\n",
+    "        npyro.deterministic('lambda', lmbd)\n",
+    "        npyro.deterministic('d', d)\n",
+    "\n",
+    "    agents = Agent(\n",
+    "        params['A'], \n",
+    "        params['B'], \n",
+    "        params['C'], \n",
+    "        params['D'], \n",
+    "        params['E'], \n",
+    "        control_fac_idx=controllable_indices\n",
+    "    )\n",
+    "\n",
+    "    aif_likelihood(num_blocks, num_steps, num_agents, data, agents)\n",
+    "    \n",
+    "with npyro.handlers.seed(rng_seed=101111):\n",
+    "    model(measurements, Nb, Nt, Na)\n",
+    "\n",
+    "%timeit pred_samples = Predictive(model, num_samples=11)(rng_key, measurements, Nb, Nt, Na)\n",
+    "print(pred_samples.keys())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 62,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# inference with NUTS and MCMC\n",
+    "from numpyro.infer import NUTS, MCMC\n",
+    "from numpyro.infer import init_to_feasible, init_to_sample\n",
+    "\n",
+    "rng_key = random.PRNGKey(0)\n",
+    "kernel = NUTS(model, init_strategy=init_to_feasible)\n",
+    "\n",
+    "mcmc = MCMC(kernel, num_warmup=1000, num_samples=1000, progress_bar=False)\n",
+    "\n",
+    "rng_key, _rng_key = random.split(rng_key)\n",
+    "mcmc.run(_rng_key, measurements, Nb, Nt, Na)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 83,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1200x600 with 6 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import arviz as az\n",
+    "az.style.use('arviz-darkgrid')\n",
+    "\n",
+    "coords = {\n",
+    "    'idx': jnp.arange(num_agents),\n",
+    "    'vars': jnp.arange(3), \n",
+    "}\n",
+    "dims = {'z': [\"idx\", \"vars\"], 'd': [\"idx\"], 'lambda': [\"idx\"], 'a': [\"idx\"]}\n",
+    "data_kwargs = {\n",
+    "    \"dims\": dims,\n",
+    "    \"coords\": coords,\n",
+    "}\n",
+    "data_mcmc = az.from_numpyro(posterior=mcmc, **data_kwargs)\n",
+    "az.plot_trace(data_mcmc, kind=\"rank_bars\", var_names=['d', 'lambda', 'a']);\n",
+    "\n",
+    "#TODO: maybe plot real values on top of samples from the posterior"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 69,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# inferenace with SVI and autoguides\n",
+    "import optax\n",
+    "from numpyro.infer import SVI, Trace_ELBO, Predictive\n",
+    "from numpyro.infer.autoguide import AutoMultivariateNormal\n",
+    "\n",
+    "num_iters = 1000\n",
+    "guide = AutoMultivariateNormal(model)\n",
+    "optimizer = npyro.optim.optax_to_numpyro(optax.chain(optax.adabelief(1e-3)))\n",
+    "svi = SVI(model, guide, optimizer, Trace_ELBO(num_particles=10))\n",
+    "rng_key, _rng_key = random.split(rng_key)\n",
+    "svi_res = svi.run(_rng_key, num_iters, measurements, Nb, Nt, Na, progress_bar=False)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 70,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1600x500 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.figure(figsize=(16,5))\n",
+    "plt.plot(svi_res.losses)\n",
+    "plt.ylabel('Variational free energy');\n",
+    "plt.xlabel('iter step');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 81,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "rng_key, _rng_key = random.split(rng_key)\n",
+    "pred = Predictive(\n",
+    "    model, \n",
+    "    guide=guide, \n",
+    "    params=svi_res.params, \n",
+    "    num_samples=1000, \n",
+    "    return_sites=[\"d\", \"a\", \"lambda\"]\n",
+    ")\n",
+    "post_sample = pred(_rng_key, measurements, Nb, Nt, Na)\n",
+    "\n",
+    "for key in post_sample:\n",
+    "    post_sample[key] = jnp.expand_dims(post_sample[key], 0)\n",
+    "\n",
+    "data_svi = az.convert_to_inference_data(post_sample, group=\"posterior\", **data_kwargs)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 85,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 2000x600 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "axes = az.plot_forest(\n",
+    "    [data_mcmc, data_svi],\n",
+    "    model_names = [\"nuts\", \"svi\"],\n",
+    "    kind='forestplot',\n",
+    "    var_names=['d', 'lambda', 'a'],\n",
+    "    coords={\"idx\": 0},\n",
+    "    combined=True,\n",
+    "    figsize=(20, 6)\n",
+    ")"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "pymdp",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.0 | packaged by conda-forge | (main, Oct 25 2022, 06:18:27) [GCC 10.4.0]"
+  },
+  "vscode": {
+   "interpreter": {
+    "hash": "ee9ec9b0986c80b528a0decd8a099ef790c4bc969bd74a31889dfc8308eb58a2"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/examples/testing_large_latent_spaces.ipynb b/examples/testing_large_latent_spaces.ipynb
new file mode 100644
index 00000000..7dffa920
--- /dev/null
+++ b/examples/testing_large_latent_spaces.ipynb
@@ -0,0 +1,473 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import os\n",
+    "# Set cuda device to use\n",
+    "os.environ[\"CUDA_DEVICE_ORDER\"] = \"PCI_BUS_ID\"\n",
+    "os.environ[\"CUDA_VISIBLE_DEVICES\"] = \"0\"\n",
+    "\n",
+    "# do not prealocate memory\n",
+    "os.environ[\"XLA_PYTHON_CLIENT_PREALLOCATE\"] = \"false\"\n",
+    "os.environ[\"XLA_PYTHON_CLIENT_ALLOCATOR\"] = \"platform\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import jax.numpy as jnp\n",
+    "import jax.tree_util as jtu\n",
+    "import equinox as eqx\n",
+    "import numpy as np\n",
+    "from functools import partial\n",
+    "from jax import vmap, lax, nn, jit, remat\n",
+    "from jax import random as jr\n",
+    "from pymdp.jax.agent import Agent as AIFAgent\n",
+    "from pymdp.utils import random_A_matrix, random_B_matrix\n",
+    "from opt_einsum import contract"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# @partial(jit, static_argnames=['dims', 'keep_dims'])\n",
+    "def factor_dot(M, xs, dims, keep_dims = None):\n",
+    "    \"\"\" Dot product of a multidimensional array with `x`.\n",
+    "    \n",
+    "    Parameters\n",
+    "    ----------\n",
+    "    - `qs` [list of 1D numpy.ndarray] - list of jnp.ndarrays\n",
+    "    \n",
+    "    Returns \n",
+    "    -------\n",
+    "    - `Y` [1D numpy.ndarray] - the result of the dot product\n",
+    "    \"\"\"\n",
+    "    all_dims = list(range(M.ndim))\n",
+    "    matrix = [[xs[f], dims[f]] for f in range(len(xs))]\n",
+    "    args = [M, all_dims]\n",
+    "    for row in matrix:\n",
+    "        args.extend(row)\n",
+    "\n",
+    "    args += [keep_dims]\n",
+    "    return contract(*args, backend='jax', optimize='auto')\n",
+    "\n",
+    "@vmap\n",
+    "def get_marginals(posterior):\n",
+    "  d = posterior.ndim - 1\n",
+    "  marginals = []\n",
+    "  for i in range(d):\n",
+    "     marginals.append( jnp.sum(posterior, axis=(j + 1 for j in range(d) if j != i)) )\n",
+    "\n",
+    "  return marginals\n",
+    "\n",
+    "@vmap\n",
+    "def merge_marginals(marginals):\n",
+    "  q = marginals[0]\n",
+    "  for m in marginals[1:]:\n",
+    "    q = jnp.expand_dims(q, -1) * m\n",
+    "  \n",
+    "  return q"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(0, 2, 3)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def make_tuple(i, d, ext):\n",
+    "    l = [i,]\n",
+    "    l.extend(d + i for i in ext)\n",
+    "    return tuple(l)\n",
+    "\n",
+    "make_tuple(0, 1, (1, 2))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "@partial(vmap, in_axes=(0, 0, None, None))\n",
+    "def delta_A(beliefs, outcomes, deps, num_obs):\n",
+    "  def merge(beliefs, outcomes):\n",
+    "    y = nn.one_hot(outcomes, num_obs)\n",
+    "    d = beliefs.ndim\n",
+    "    marg_beliefs = jnp.sum(beliefs, axis=(i for i in range(d) if i not in deps))\n",
+    "    axis = ( - (i+1) for i in range(len(deps)))\n",
+    "    return jnp.expand_dims(y, axis) * marg_beliefs\n",
+    "  \n",
+    "  return vmap(merge, in_axes=(0, None))(beliefs, outcomes)\n",
+    "  \n",
+    "@partial(vmap, in_axes=(0, 0, 0, None))\n",
+    "def delta_B(post_b, cond_b, action, num_actions):\n",
+    "   a = nn.one_hot(action, num_actions)\n",
+    "   all_dims = tuple(range(cond_b.ndim - 1))\n",
+    "   fd = lambda x, y: factor_dot(x, [y], ((0,),), keep_dims=all_dims)\n",
+    "   b = vmap(fd)(cond_b, post_b)\n",
+    "   return b * a\n",
+    "\n",
+    "@partial(vmap, in_axes=(None, 0))\n",
+    "def get_reverse_conditionals(B, beliefs):\n",
+    "  all_dims = tuple(range(B.ndim - 1))\n",
+    "  dims = tuple((i,) for i in all_dims[1:-1])\n",
+    "  fd = lambda x, y: factor_dot(x, y, dims, keep_dims=all_dims)\n",
+    "  joint = vmap(fd)(B, beliefs)\n",
+    "  pred = joint.sum(axis=all_dims[2:], keepdims=True)\n",
+    "  return joint / pred\n",
+    "\n",
+    "@partial(vmap, in_axes=(0, 0, None))\n",
+    "def get_reverse_predictive(post, cond, deps):\n",
+    "  def pred(post, cond, deps):\n",
+    "    d = post.ndim\n",
+    "    dims = tuple(make_tuple(i, d, deps[i]) for i in range(len(deps)))\n",
+    "    keep_dims = list(dims[0][1:])\n",
+    "    for row in dims[1:]:\n",
+    "      keep_dims.extend(list(row[1:]))\n",
+    "    \n",
+    "    unique_dims = tuple(set(keep_dims))\n",
+    "\n",
+    "    return factor_dot(post, cond, dims, keep_dims=unique_dims)\n",
+    "  \n",
+    "  out = vmap(pred, in_axes=(0, 0, None))(post, cond, deps)\n",
+    "  return out\n",
+    "\n",
+    "def learning(agent, beliefs, actions, outcomes, lag=1):\n",
+    "  A_deps = agent.A_dependencies\n",
+    "  B_deps = agent.B_dependencies\n",
+    "  num_obs = agent.num_obs\n",
+    "  posterior_beliefs = merge_marginals( jtu.tree_map(lambda x: x[..., -1, :], beliefs) )\n",
+    "  qA = agent.pA\n",
+    "  qB = agent.pB\n",
+    "\n",
+    "  def step_fn(carry, xs):\n",
+    "    posterior_beliefs, qA, qB = carry\n",
+    "    obs, acts, filter_beliefs = xs\n",
+    "    # learn A matrix\n",
+    "    if agent.learn_A:\n",
+    "      qA = jtu.tree_map(\n",
+    "        lambda qa, o, m: qa + delta_A(posterior_beliefs, o, A_deps[m], num_obs[m]).sum(0), \n",
+    "        qA, \n",
+    "        obs, \n",
+    "        list(range(len(num_obs)))\n",
+    "        )\n",
+    "\n",
+    "    # learn B matrix\n",
+    "    conditional_beliefs = jtu.tree_map(\n",
+    "       lambda b, f: get_reverse_conditionals(b, [filter_beliefs[i] for i in B_deps[f]]),\n",
+    "       agent.B, \n",
+    "       list(range(len(agent.B))) \n",
+    "    )\n",
+    "    post_marg = get_marginals(posterior_beliefs)\n",
+    "    acts =  [acts[..., i] for i in range(acts.shape[-1])]\n",
+    "\n",
+    "    qB = jtu.tree_map(\n",
+    "       lambda qb, pb, cb, a, nc: qb + delta_B(pb, cb, a, nc).sum(0),\n",
+    "       qB,\n",
+    "       post_marg,\n",
+    "       conditional_beliefs,\n",
+    "       acts,\n",
+    "       agent.num_controls  \n",
+    "    )\n",
+    "\n",
+    "    # compute posterior beliefs for the next time step\n",
+    "    get_transition = lambda cb, a: cb[..., a]\n",
+    "    conditional_beliefs = jtu.tree_map(\n",
+    "      lambda cb, a: vmap(get_transition)(cb, a), conditional_beliefs, acts\n",
+    "    )\n",
+    "    posterior_beliefs = get_reverse_predictive(posterior_beliefs, conditional_beliefs, B_deps)\n",
+    "\n",
+    "    return (posterior_beliefs, qA, qB), None\n",
+    "\n",
+    "  first_outcomes = jtu.tree_map(lambda x: x[..., 0], outcomes)\n",
+    "  outcomes = jtu.tree_map(lambda x: jnp.flipud(x.swapaxes(0, 1))[1:lag+1], outcomes)\n",
+    "  actions = jnp.flipud(actions.swapaxes(0, 1))[:lag]\n",
+    "  beliefs = jtu.tree_map(lambda x: jnp.flipud(jnp.moveaxis(x, 2, 0))[1:lag+1], beliefs)\n",
+    "  iters = (outcomes, actions, beliefs)\n",
+    "  (last_beliefs, qA, qB), _ = lax.scan(step_fn, (posterior_beliefs, qA, qB), iters)\n",
+    "\n",
+    "  # update A with the first outcome \n",
+    "  if agent.learn_A:\n",
+    "    qA = jtu.tree_map(\n",
+    "      lambda qa, o, m: qa + delta_A(last_beliefs, o, A_deps[m], num_obs[m]).sum(0), \n",
+    "      qA, \n",
+    "      first_outcomes, \n",
+    "      list(range(len(num_obs)))\n",
+    "    )\n",
+    "\n",
+    "  if qA is not None:\n",
+    "    E_qA = jtu.tree_map(lambda qa: qa / qa.sum(0), qA)\n",
+    "  else:\n",
+    "    E_qA = agent.A\n",
+    "  E_qB =jtu.tree_map(lambda qb: qb / qb.sum(0), qB)\n",
+    "  agent = eqx.tree_at(\n",
+    "    lambda x: (x.A, x.pA, x.B, x.pB), agent, (E_qA, qA, E_qB, qB), is_leaf=lambda x: x is None\n",
+    "  )\n",
+    "\n",
+    "  return agent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "class TestEnv:\n",
+    "    def __init__(self, num_agents, num_obs, prng_key=jr.PRNGKey(0)):\n",
+    "      self.num_obs = num_obs\n",
+    "      self.num_agents = num_agents\n",
+    "      self.key = prng_key\n",
+    "    \n",
+    "    def step(self, actions=None):\n",
+    "      # return a list of random observations for each agent or parallel realization (each entry in batch_dim)\n",
+    "      obs = [jr.randint(self.key, (self.num_agents,), 0, no) for no in self.num_obs]\n",
+    "      self.key, _ = jr.split(self.key)\n",
+    "      return obs"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def update_agent_state(agent, env, args, key, outcomes, actions):\n",
+    "    beliefs = agent.infer_states(outcomes, actions, *args)\n",
+    "    # q_pi, _ = agent.infer_policies(beliefs)\n",
+    "    q_pi = jnp.ones((agent.batch_size, 6)) / 6\n",
+    "    batch_keys = jr.split(key, agent.batch_size)\n",
+    "    actions = agent.sample_action(q_pi, rng_key=batch_keys)\n",
+    "\n",
+    "    outcomes = env.step(actions)\n",
+    "    outcomes = jtu.tree_map(lambda x: jnp.expand_dims(x, -1), outcomes)\n",
+    "    args = agent.update_empirical_prior(actions, beliefs)\n",
+    "    args = (args[0], None)  # remove belief history from args\n",
+    "    latest_belief = jtu.tree_map(lambda x: x[:, 0], beliefs)\n",
+    "\n",
+    "    return args, latest_belief, outcomes, actions\n",
+    "\n",
+    "def evolve_trials(agent, env, batch_size, num_timesteps, prng_key=jr.PRNGKey(0)):\n",
+    "\n",
+    "    def step_fn(carry, xs):\n",
+    "        actions = carry['actions']\n",
+    "        outcomes = carry['outcomes']\n",
+    "        key = carry['key']\n",
+    "        key, _key = jr.split(key)\n",
+    "        vect_uas = vmap(partial(update_agent_state, agent, env))\n",
+    "        keys = jr.split(_key, batch_size)\n",
+    "        args, beliefs, outcomes, actions = vect_uas(carry['args'], keys, outcomes, actions)\n",
+    "        output = {\n",
+    "           'args': args, \n",
+    "           'outcomes': outcomes, \n",
+    "           'actions': actions,\n",
+    "           'key': key\n",
+    "        }\n",
+    "\n",
+    "        return output, {'beliefs': beliefs, 'actions': actions[..., 0, :], 'outcomes': outcomes}\n",
+    "\n",
+    "   \n",
+    "    outcome_0  = jtu.tree_map(lambda x: jnp.expand_dims(x, -1), env.step())\n",
+    "    outcome_0 = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_size,) + x.shape), outcome_0)\n",
+    "    prior = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_size,) + x.shape), agent.D)\n",
+    "    init = {\n",
+    "      'args': (prior, None),\n",
+    "      'outcomes': outcome_0,\n",
+    "      'actions': - jnp.ones((batch_size, 1, agent.policies.shape[-1]), dtype=jnp.int32),\n",
+    "      'key': prng_key\n",
+    "    }\n",
+    "\n",
+    "    last, sequences = lax.scan(step_fn, init, jnp.arange(num_timesteps))\n",
+    "    sequences['outcomes'] = jtu.tree_map(\n",
+    "        lambda x, y: jnp.concatenate([jnp.expand_dims(x.squeeze(), 0), y.squeeze()]), \n",
+    "        outcome_0, \n",
+    "        sequences['outcomes']\n",
+    "      )\n",
+    "\n",
+    "    return last, sequences\n",
+    "\n",
+    "@partial(jit, static_argnums=(1, 2, 3, 4))\n",
+    "def training_step(agent, env, batch_size, num_timesteps, lag=1):\n",
+    "    output, sequences = evolve_trials(agent, env, batch_size, num_timesteps)\n",
+    "    args = output.pop('args')\n",
+    "    \n",
+    "    outcomes = jtu.tree_map(lambda x: x.swapaxes(0, 1), sequences['outcomes'])\n",
+    "    actions = sequences['actions'].swapaxes(0, 1)\n",
+    "    beliefs = jtu.tree_map(lambda x: jnp.moveaxis(x, [0, 2], [1, 1]), sequences['beliefs'])\n",
+    "\n",
+    "    def update_beliefs(outcomes, actions, args):\n",
+    "        return agent.infer_states(outcomes, actions, *args)\n",
+    "\n",
+    "    # update beliefs with the last action-outcome pair\n",
+    "    last_belief = vmap(update_beliefs)(\n",
+    "       output['outcomes'], \n",
+    "       output['actions'],\n",
+    "       args\n",
+    "      )\n",
+    "\n",
+    "    beliefs = jtu.tree_map(lambda x, y: jnp.concatenate([x, y], -2), beliefs, last_belief)\n",
+    "    # agent, beliefs, actions, outcomes = lax.stop_gradient((agent, beliefs, actions, outcomes))\n",
+    "    agent = learning(agent, beliefs, actions, outcomes, lag=lag)\n",
+    "\n",
+    "    return agent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# define an agent and environment here\n",
+    "batch_size = 16\n",
+    "num_agents = 1\n",
+    "\n",
+    "num_pixels = 32\n",
+    "# y_pos paddle 1, y_pos paddle 2, (x_pos, y_pos) ball\n",
+    "num_obs = [num_pixels, num_pixels, num_pixels, num_pixels]\n",
+    "num_states = [num_pixels, num_pixels, num_pixels, num_pixels, 96]\n",
+    "num_controls = [1, 1, 1, 1, 6]\n",
+    "num_blocks = 1\n",
+    "num_timesteps = 25\n",
+    "\n",
+    "action_lists = [jnp.zeros(6, dtype=jnp.int32)] * 4\n",
+    "action_lists += [jnp.arange(6, dtype=jnp.int32)]\n",
+    "\n",
+    "policies = jnp.expand_dims(jnp.stack(action_lists, -1), -2)\n",
+    "num_policies = len(policies)\n",
+    "\n",
+    "A_dependencies = [[0], [1], [2], [3]]\n",
+    "B_dependencies = [[0, 4], [1, 4], [2, 4], [3, 4], [4]]\n",
+    "\n",
+    "A_np = [np.eye(o) for o in num_obs]\n",
+    "B_np = list(random_B_matrix(num_states=num_states, num_controls=num_controls, B_factor_list=B_dependencies))\n",
+    "A = jtu.tree_map(lambda x: jnp.broadcast_to(x, (num_agents,) + x.shape), A_np)\n",
+    "B = jtu.tree_map(lambda x: jnp.broadcast_to(x, (num_agents,) + x.shape), B_np)\n",
+    "C = [jnp.zeros((num_agents, no)) for no in num_obs]\n",
+    "D = [jnp.ones((num_agents, ns)) / ns for ns in num_states]\n",
+    "E = jnp.ones((num_agents, num_policies )) / num_policies\n",
+    "\n",
+    "pA = None # jtu.tree_map(lambda x: jnp.broadcast_to(jnp.ones_like(x), (num_agents,) + x.shape), A_np)\n",
+    "pB = jtu.tree_map(lambda x: jnp.broadcast_to(jnp.ones_like(x), (num_agents,) + x.shape), B_np)\n",
+    "\n",
+    "agents = AIFAgent(A, B, C, D, E, pA, pB, learn_A=False, policies=policies, A_dependencies=A_dependencies, B_dependencies=B_dependencies, use_param_info_gain=True, inference_algo='fpi', sampling_mode='marginal', action_selection='deterministic', num_iter=8)\n",
+    "env = TestEnv(num_agents, num_obs)\n",
+    "agents = training_step(agents, env, batch_size, num_timesteps, lag=25)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# agents = lax.stop_gradient(agents)\n",
+    "%timeit training_step(agents, env, batch_size, num_timesteps, lag=25).A[0].block_until_ready()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# define an agent and environment here\n",
+    "batch_size = 16\n",
+    "num_agents = 1\n",
+    "\n",
+    "num_pixels = 32\n",
+    "# y_pos paddle 1, y_pos paddle 2, (x_pos, y_pos) ball\n",
+    "num_obs = [num_pixels, num_pixels, num_pixels, num_pixels]\n",
+    "num_states = [num_pixels, 2, num_pixels, 2, num_pixels, num_pixels, 24]\n",
+    "num_controls = [1, 6, 1, 6, 1, 1, 6]\n",
+    "num_blocks = 1\n",
+    "num_timesteps = 25\n",
+    "\n",
+    "action_lists = [jnp.zeros(6, dtype=jnp.int32), jnp.arange(6, dtype=jnp.int32)] * 2\n",
+    "action_lists += [jnp.zeros(6, dtype=jnp.int32), jnp.zeros(6, dtype=jnp.int32), jnp.arange(6, dtype=jnp.int32)]\n",
+    "\n",
+    "policies = jnp.expand_dims(jnp.stack(action_lists, -1), -2)\n",
+    "num_policies = len(policies)\n",
+    "\n",
+    "A_dependencies = [[0], [2], [4], [5]]\n",
+    "B_dependencies = [[0, 1], [1], [2, 3], [3], [4, 6], [5, 6], [6]]\n",
+    "\n",
+    "A_np = [np.eye(o) for o in num_obs]\n",
+    "B_np = list(random_B_matrix(num_states=num_states, num_controls=num_controls, B_factor_list=B_dependencies))\n",
+    "A = jtu.tree_map(lambda x: jnp.broadcast_to(x, (num_agents,) + x.shape), A_np)\n",
+    "B = jtu.tree_map(lambda x: jnp.broadcast_to(x, (num_agents,) + x.shape), B_np)\n",
+    "C = [jnp.zeros((num_agents, no)) for no in num_obs]\n",
+    "D = [jnp.ones((num_agents, ns)) / ns for ns in num_states]\n",
+    "E = jnp.ones((num_agents, num_policies )) / num_policies\n",
+    "\n",
+    "pA = None # jtu.tree_map(lambda x: jnp.broadcast_to(jnp.ones_like(x), (num_agents,) + x.shape), A_np)\n",
+    "pB = jtu.tree_map(lambda x: jnp.broadcast_to(jnp.ones_like(x), (num_agents,) + x.shape), B_np)\n",
+    "\n",
+    "agents = AIFAgent(A, B, C, D, E, pA, pB, learn_A=False, policies=policies, A_dependencies=A_dependencies, B_dependencies=B_dependencies, use_param_info_gain=True, inference_algo='fpi', sampling_mode='marginal', action_selection='deterministic', num_iter=8)\n",
+    "env = TestEnv(num_agents, num_obs)\n",
+    "agents = training_step(agents, env, batch_size, num_timesteps, lag=25)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "31.4 s ± 15.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%timeit training_step(agents, env, batch_size, num_timesteps, lag=25).A[0].block_until_ready()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "jax_pymdp_test",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.7"
+  },
+  "orig_nbformat": 4
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/pymdp/__init__.py b/pymdp/__init__.py
index 52606d70..8692e691 100644
--- a/pymdp/__init__.py
+++ b/pymdp/__init__.py
@@ -7,3 +7,4 @@
 from . import learning
 from . import algos
 from . import default_models
+from . import jax
diff --git a/pymdp/agent.py b/pymdp/agent.py
index d63b2566..de8363c8 100644
--- a/pymdp/agent.py
+++ b/pymdp/agent.py
@@ -36,10 +36,11 @@ def __init__(
         B,
         C=None,
         D=None,
-        E = None,
+        E=None,
+        H=None,
         pA=None,
-        pB = None,
-        pD = None,
+        pB=None,
+        pD=None,
         num_controls=None,
         policy_len=1,
         inference_horizon=1,
@@ -59,9 +60,18 @@ def __init__(
         factors_to_learn="all",
         lr_pB=1.0,
         lr_pD=1.0,
-        use_BMA = True,
-        policy_sep_prior = False,
-        save_belief_hist = False
+        use_BMA=True,
+        policy_sep_prior=False,
+        save_belief_hist=False,
+        A_factor_list=None,
+        B_factor_list=None,
+        sophisticated=False,
+        si_horizon=3,
+        si_policy_prune_threshold=1/16,
+        si_state_prune_threshold=1/16,
+        si_prune_penalty=512,
+        ii_depth=10,
+        ii_threshold=1/16,
     ):
 
         ### Constant parameters ###
@@ -83,6 +93,15 @@ def __init__(
         self.lr_pB = lr_pB
         self.lr_pD = lr_pD
 
+        # sophisticated inference parameters
+        self.sophisticated = sophisticated
+        if self.sophisticated:
+            assert self.policy_len == 1, "Sophisticated inference only works with policy_len = 1"
+        self.si_horizon = si_horizon
+        self.si_policy_prune_threshold = si_policy_prune_threshold
+        self.si_state_prune_threshold = si_state_prune_threshold
+        self.si_prune_penalty = si_prune_penalty
+
         # Initialise observation model (A matrices)
         if not isinstance(A, np.ndarray):
             raise TypeError(
@@ -91,7 +110,7 @@ def __init__(
 
         self.A = utils.to_obj_array(A)
 
-        assert utils.is_normalized(self.A), "A matrix is not normalized (i.e. A.sum(axis = 0) must all equal 1.0)"
+        assert utils.is_normalized(self.A), "A matrix is not normalized (i.e. A[m].sum(axis = 0) must all equal 1.0 for all modalities)"
 
         # Determine number of observation modalities and their respective dimensions
         self.num_obs = [self.A[m].shape[0] for m in range(len(self.A))]
@@ -108,7 +127,7 @@ def __init__(
 
         self.B = utils.to_obj_array(B)
 
-        assert utils.is_normalized(self.B), "B matrix is not normalized (i.e. B.sum(axis = 0) must all equal 1.0)"
+        assert utils.is_normalized(self.B), "B matrix is not normalized (i.e. B[f].sum(axis = 0) must all equal 1.0 for all factors)"
 
         # Determine number of hidden state factors and their dimensionalities
         self.num_states = [self.B[f].shape[0] for f in range(len(self.B))]
@@ -119,13 +138,61 @@ def __init__(
 
         # If no `num_controls` are given, then this is inferred from the shapes of the input B matrices
         if num_controls == None:
-            self.num_controls = [self.B[f].shape[2] for f in range(self.num_factors)]
+            self.num_controls = [self.B[f].shape[-1] for f in range(self.num_factors)]
         else:
+            inferred_num_controls = [self.B[f].shape[-1] for f in range(self.num_factors)]
+            assert num_controls == inferred_num_controls, "num_controls must be consistent with the shapes of the input B matrices"
             self.num_controls = num_controls
-        
+
+        # checking that `A_factor_list` and `B_factor_list` are consistent with `num_factors`, `num_states`, and lagging dimensions of `A` and `B` tensors
+        self.factorized = False
+        if A_factor_list == None:
+            self.A_factor_list = self.num_modalities * [list(range(self.num_factors))] # defaults to having all modalities depend on all factors
+            for m in range(self.num_modalities):
+                factor_dims = tuple([self.num_states[f] for f in self.A_factor_list[m]])
+                assert self.A[m].shape[1:] == factor_dims, f"Please input an `A_factor_list` whose {m}-th indices pick out the hidden state factors that line up with lagging dimensions of A{m}..." 
+                if self.pA is not None:
+                    assert self.pA[m].shape[1:] == factor_dims, f"Please input an `A_factor_list` whose {m}-th indices pick out the hidden state factors that line up with lagging dimensions of pA{m}..." 
+        else:
+            self.factorized = True
+            for m in range(self.num_modalities):
+                assert max(A_factor_list[m]) <= (self.num_factors - 1), f"Check modality {m} of A_factor_list - must be consistent with `num_states` and `num_factors`..."
+                factor_dims = tuple([self.num_states[f] for f in A_factor_list[m]])
+                assert self.A[m].shape[1:] == factor_dims, f"Check modality {m} of A_factor_list. It must coincide with lagging dimensions of A{m}..." 
+                if self.pA is not None:
+                    assert self.pA[m].shape[1:] == factor_dims, f"Check modality {m} of A_factor_list. It must coincide with lagging dimensions of pA{m}..."
+            self.A_factor_list = A_factor_list
+
+        # generate a list of the modalities that depend on each factor 
+        A_modality_list = []
+        for f in range(self.num_factors):
+            A_modality_list.append( [m for m in range(self.num_modalities) if f in self.A_factor_list[m]] )
+
+        # Store thee `A_factor_list` and the `A_modality_list` in a Markov blanket dictionary
+        self.mb_dict = {
+                        'A_factor_list': self.A_factor_list,
+                        'A_modality_list': A_modality_list
+                        }
+
+        if B_factor_list == None:
+            self.B_factor_list = [[f] for f in range(self.num_factors)] # defaults to having all factors depend only on themselves
+            for f in range(self.num_factors):
+                factor_dims = tuple([self.num_states[f] for f in self.B_factor_list[f]])
+                assert self.B[f].shape[1:-1] == factor_dims, f"Please input a `B_factor_list` whose {f}-th indices pick out the hidden state factors that line up with the all-but-final lagging dimensions of B{f}..." 
+                if self.pB is not None:
+                    assert self.pB[f].shape[1:-1] == factor_dims, f"Please input a `B_factor_list` whose {f}-th indices pick out the hidden state factors that line up with the all-but-final lagging dimensions of pB{f}..." 
+        else:
+            self.factorized = True
+            for f in range(self.num_factors):
+                assert max(B_factor_list[f]) <= (self.num_factors - 1), f"Check factor {f} of B_factor_list - must be consistent with `num_states` and `num_factors`..."
+                factor_dims = tuple([self.num_states[f] for f in B_factor_list[f]])
+                assert self.B[f].shape[1:-1] == factor_dims, f"Check factor {f} of B_factor_list. It must coincide with all-but-final lagging dimensions of B{f}..." 
+                if self.pB is not None:
+                    assert self.pB[f].shape[1:-1] == factor_dims, f"Check factor {f} of B_factor_list. It must coincide with all-but-final lagging dimensions of pB{f}..."
+            self.B_factor_list = B_factor_list
+
         # Users have the option to make only certain factors controllable.
-        # default behaviour is to make all hidden state factors controllable
-        # (i.e. self.num_states == self.num_controls)
+        # default behaviour is to make all hidden state factors controllable, i.e. `self.num_factors == len(self.num_controls)`
         if control_fac_idx == None:
             self.control_fac_idx = [f for f in range(self.num_factors) if self.num_controls[f] > 1]
         else:
@@ -138,7 +205,7 @@ def __init__(
 
         # Again, the use can specify a set of possible policies, or
         # all possible combinations of actions and timesteps will be considered
-        if policies == None:
+        if policies is None:
             policies = self._construct_policies()
         self.policies = policies
 
@@ -183,7 +250,7 @@ def __init__(
             else:
                 self.D = self._construct_D_prior()
 
-        assert utils.is_normalized(self.D), "A matrix is not normalized (i.e. A.sum(axis = 0) must all equal 1.0"
+        assert utils.is_normalized(self.D), "D vector is not normalized (i.e. D[f].sum() must all equal 1.0 for all factors)"
 
         # Assigning prior parameters on initial hidden states (pD vectors)
         self.pD = pD
@@ -201,6 +268,14 @@ def __init__(
         else:
             self.E = self._construct_E_prior()
         
+        # Construct I for backwards induction (if H specified)
+        if H is not None:
+            self.H = H
+            self.I = control.backwards_induction(H, B, B_factor_list, threshold=ii_threshold, depth=ii_depth)
+        else:
+            self.H = None
+            self.I = None
+
         self.edge_handling_params = {}
         self.edge_handling_params['use_BMA'] = use_BMA # creates a 'D-like' moving prior
         self.edge_handling_params['policy_sep_prior'] = policy_sep_prior # carries forward last timesteps posterior, in a policy-conditioned way
@@ -309,6 +384,12 @@ def reset(self, init_qs=None):
             
         else:
             self.qs = init_qs
+        
+        if self.pA is not None:
+            self.A = utils.norm_dist_obj_arr(self.pA)
+        
+        if self.pB is not None:
+            self.B = utils.norm_dist_obj_arr(self.pB)
 
         return self.qs
 
@@ -394,7 +475,7 @@ def get_future_qs(self):
         return future_qs_seq
 
 
-    def infer_states(self, observation, distr_obs = False):
+    def infer_states(self, observation, distr_obs=False):
         """
         Update approximate posterior over hidden states by solving variational inference problem, given an observation.
 
@@ -403,6 +484,8 @@ def infer_states(self, observation, distr_obs = False):
         observation: ``list`` or ``tuple`` of ints
             The observation input. Each entry ``observation[m]`` stores the index of the discrete
             observation for modality ``m``.
+        distr_obs: ``bool``
+            Whether the observation is a distribution over possible observations, rather than a single observation.
 
         Returns
         ---------
@@ -421,16 +504,19 @@ def infer_states(self, observation, distr_obs = False):
 
         if self.inference_algo == "VANILLA":
             if self.action is not None:
-                empirical_prior = control.get_expected_states(
-                    self.qs, self.B, self.action.reshape(1, -1) #type: ignore
+                empirical_prior = control.get_expected_states_interactions(
+                    self.qs, self.B, self.B_factor_list, self.action.reshape(1, -1) 
                 )[0]
             else:
                 empirical_prior = self.D
-            qs = inference.update_posterior_states(
-            self.A,
-            observation,
-            empirical_prior,
-            **self.inference_params
+            qs = inference.update_posterior_states_factorized(
+                self.A,
+                observation,
+                self.num_obs,
+                self.num_states,
+                self.mb_dict,
+                empirical_prior,
+                **self.inference_params
             )
         elif self.inference_algo == "MMP":
 
@@ -442,9 +528,11 @@ def infer_states(self, observation, distr_obs = False):
                 latest_obs = self.prev_obs
                 latest_actions = self.prev_actions
 
-            qs, F = inference.update_posterior_states_full(
+            qs, F = inference.update_posterior_states_full_factorized(
                 self.A,
+                self.mb_dict,
                 self.B,
+                self.B_factor_list,
                 latest_obs,
                 self.policies, 
                 latest_actions, 
@@ -461,12 +549,12 @@ def infer_states(self, observation, distr_obs = False):
 
         return qs
 
-    def _infer_states_test(self, observation):
+    def _infer_states_test(self, observation, distr_obs=False):
         """
         Test version of ``infer_states()`` that additionally returns intermediate variables of MMP, such as
         the prediction errors and intermediate beliefs from the optimization. Used for benchmarking against SPM outputs.
         """
-        observation = tuple(observation)
+        observation = tuple(observation) if not distr_obs else observation
 
         if not hasattr(self, "qs"):
             self.reset()
@@ -474,15 +562,15 @@ def _infer_states_test(self, observation):
         if self.inference_algo == "VANILLA":
             if self.action is not None:
                 empirical_prior = control.get_expected_states(
-                    self.qs, self.B, self.action.reshape(1, -1) #type: ignore
-                )
+                    self.qs, self.B, self.action.reshape(1, -1) 
+                )[0]
             else:
                 empirical_prior = self.D
             qs = inference.update_posterior_states(
-            self.A,
-            observation,
-            empirical_prior,
-            **self.inference_params
+                self.A,
+                observation,
+                empirical_prior,
+                **self.inference_params
             )
         elif self.inference_algo == "MMP":
 
@@ -512,14 +600,19 @@ def _infer_states_test(self, observation):
 
         self.qs = qs
 
-        return qs, xn, vn
-
+        if self.inference_algo == "MMP":
+            return qs, xn, vn
+        else:
+            return qs
+    
     def infer_policies(self):
         """
         Perform policy inference by optimizing a posterior (categorical) distribution over policies.
         This distribution is computed as the softmax of ``G * gamma + lnE`` where ``G`` is the negative expected
         free energy of policies, ``gamma`` is a policy precision and ``lnE`` is the (log) prior probability of policies.
         This function returns the posterior over policies as well as the negative expected free energy of each policy.
+        In this version of the function, the expected free energy of policies is computed using known factorized structure 
+        in the model, which speeds up computation (particular the state information gain calculations).
 
         Returns
         ----------
@@ -530,29 +623,53 @@ def infer_policies(self):
         """
 
         if self.inference_algo == "VANILLA":
-            q_pi, G = control.update_posterior_policies(
-                self.qs,
-                self.A,
-                self.B,
-                self.C,
-                self.policies,
-                self.use_utility,
-                self.use_states_info_gain,
-                self.use_param_info_gain,
-                self.pA,
-                self.pB,
-                E = self.E,
-                gamma = self.gamma
-            )
+            if self.sophisticated:
+                q_pi, G = control.sophisticated_inference_search(
+                    self.qs, 
+                    self.policies, 
+                    self.A, 
+                    self.B, 
+                    self.C, 
+                    self.A_factor_list, 
+                    self.B_factor_list, 
+                    self.I,
+                    self.si_horizon,
+                    self.si_policy_prune_threshold, 
+                    self.si_state_prune_threshold, 
+                    self.si_prune_penalty,
+                    1.0,
+                    self.inference_params,
+                    n=0
+                )
+            else:
+                q_pi, G = control.update_posterior_policies_factorized(
+                    self.qs,
+                    self.A,
+                    self.B,
+                    self.C,
+                    self.A_factor_list,
+                    self.B_factor_list,
+                    self.policies,
+                    self.use_utility,
+                    self.use_states_info_gain,
+                    self.use_param_info_gain,
+                    self.pA,
+                    self.pB,
+                    E = self.E,
+                    I = self.I,
+                    gamma = self.gamma
+                )
         elif self.inference_algo == "MMP":
 
             future_qs_seq = self.get_future_qs()
 
-            q_pi, G = control.update_posterior_policies_full(
+            q_pi, G = control.update_posterior_policies_full_factorized(
                 future_qs_seq,
                 self.A,
                 self.B,
                 self.C,
+                self.A_factor_list,
+                self.B_factor_list,
                 self.policies,
                 self.use_utility,
                 self.use_states_info_gain,
@@ -560,9 +677,10 @@ def infer_policies(self):
                 self.latest_belief,
                 self.pA,
                 self.pB,
-                F = self.F,
-                E = self.E,
-                gamma = self.gamma
+                F=self.F,
+                E=self.E,
+                I=self.I,
+                gamma=self.gamma
             )
 
         if hasattr(self, "q_pi_hist"):
@@ -644,6 +762,37 @@ def update_A(self, obs):
             Posterior Dirichlet parameters over observation model (same shape as ``A``), after having updated it with observations.
         """
 
+        qA = learning.update_obs_likelihood_dirichlet_factorized(
+            self.pA, 
+            self.A, 
+            obs, 
+            self.qs, 
+            self.A_factor_list,
+            self.lr_pA, 
+            self.modalities_to_learn
+        )
+
+        self.pA = qA # set new prior to posterior
+        self.A = utils.norm_dist_obj_arr(qA) # take expected value of posterior Dirichlet parameters to calculate posterior over A array
+
+        return qA
+
+    def _update_A_old(self, obs):
+        """
+        Update approximate posterior beliefs about Dirichlet parameters that parameterise the observation likelihood or ``A`` array.
+
+        Parameters
+        ----------
+        observation: ``list`` or ``tuple`` of ints
+            The observation input. Each entry ``observation[m]`` stores the index of the discrete
+            observation for modality ``m``.
+
+        Returns
+        -----------
+        qA: ``numpy.ndarray`` of dtype object
+            Posterior Dirichlet parameters over observation model (same shape as ``A``), after having updated it with observations.
+        """
+
         qA = learning.update_obs_likelihood_dirichlet(
             self.pA, 
             self.A, 
@@ -673,6 +822,37 @@ def update_B(self, qs_prev):
             Posterior Dirichlet parameters over transition model (same shape as ``B``), after having updated it with state beliefs and actions.
         """
 
+        qB = learning.update_state_likelihood_dirichlet_interactions(
+            self.pB,
+            self.B,
+            self.action,
+            self.qs,
+            qs_prev,
+            self.B_factor_list,
+            self.lr_pB,
+            self.factors_to_learn
+        )
+
+        self.pB = qB # set new prior to posterior
+        self.B = utils.norm_dist_obj_arr(qB)  # take expected value of posterior Dirichlet parameters to calculate posterior over B array
+
+        return qB
+    
+    def _update_B_old(self, qs_prev):
+        """
+        Update posterior beliefs about Dirichlet parameters that parameterise the transition likelihood 
+        
+        Parameters
+        -----------
+        qs_prev: 1D ``numpy.ndarray`` or ``numpy.ndarray`` of dtype object
+            Marginal posterior beliefs over hidden states at previous timepoint.
+    
+        Returns
+        -----------
+        qB: ``numpy.ndarray`` of dtype object
+            Posterior Dirichlet parameters over transition model (same shape as ``B``), after having updated it with state beliefs and actions.
+        """
+
         qB = learning.update_state_likelihood_dirichlet(
             self.pB,
             self.B,
@@ -744,7 +924,7 @@ def _get_default_params(self):
         method = self.inference_algo
         default_params = None
         if method == "VANILLA":
-            default_params = {"num_iter": 10, "dF": 1.0, "dF_tol": 0.001}
+            default_params = {"num_iter": 10, "dF": 1.0, "dF_tol": 0.001, "compute_vfe": True}
         elif method == "MMP":
             default_params = {"num_iter": 10, "grad_descent": True, "tau": 0.25}
         elif method == "VMP":
diff --git a/pymdp/algos/__init__.py b/pymdp/algos/__init__.py
index 09e9272f..bb08cc41 100644
--- a/pymdp/algos/__init__.py
+++ b/pymdp/algos/__init__.py
@@ -1,2 +1,2 @@
-from .fpi import run_vanilla_fpi
-from .mmp import run_mmp, _run_mmp_testing
+from .fpi import run_vanilla_fpi, run_vanilla_fpi_factorized
+from .mmp import run_mmp, run_mmp_factorized, _run_mmp_testing
diff --git a/pymdp/algos/fpi.py b/pymdp/algos/fpi.py
index 37532130..e007d9a9 100644
--- a/pymdp/algos/fpi.py
+++ b/pymdp/algos/fpi.py
@@ -3,11 +3,12 @@
 # pylint: disable=no-member
 
 import numpy as np
-from pymdp.maths import spm_dot, get_joint_likelihood, softmax, calc_free_energy, spm_log_single, spm_log_obj_array
-from pymdp.utils import to_obj_array, obj_array_uniform
+from pymdp.maths import spm_dot, dot_likelihood, get_joint_likelihood, softmax, calc_free_energy, spm_log_single, spm_log_obj_array
+from pymdp.utils import to_obj_array, obj_array, obj_array_uniform
 from itertools import chain
+from copy import deepcopy
 
-def run_vanilla_fpi(A, obs, num_obs, num_states, prior=None, num_iter=10, dF=1.0, dF_tol=0.001):
+def run_vanilla_fpi(A, obs, num_obs, num_states, prior=None, num_iter=10, dF=1.0, dF_tol=0.001, compute_vfe=True):
     """
     Update marginal posterior beliefs over hidden states using mean-field variational inference, via
     fixed point iteration. 
@@ -24,7 +25,7 @@ def run_vanilla_fpi(A, obs, num_obs, num_states, prior=None, num_iter=10, dF=1.0
     num_obs: list of ints
         List of dimensionalities of each observation modality
     num_states: list of ints
-        List of dimensionalities of each observation modality
+        List of dimensionalities of each hidden state factor
     prior: numpy ndarray of dtype object, default None
         Prior over hidden states. If absent, prior is set to be the log uniform distribution over hidden states (identical to the 
         initialisation of the posterior)
@@ -36,6 +37,9 @@ def run_vanilla_fpi(A, obs, num_obs, num_states, prior=None, num_iter=10, dF=1.0
         Threshold value of the time derivative of the variational free energy (dF/dt), to be checked at 
         each iteration. If dF <= dF_tol, the iterations are halted pre-emptively and the final 
         marginal posterior belief(s) is(are) returned
+    compute_vfe: bool, default True
+        Whether to compute the variational free energy at each iteration. If False, the function runs through 
+        all variational iterations.
   
     Returns
     ----------
@@ -63,9 +67,7 @@ def run_vanilla_fpi(A, obs, num_obs, num_states, prior=None, num_iter=10, dF=1.0
         Create a flat posterior (and prior if necessary)
     """
 
-    qs = np.empty(n_factors, dtype=object)
-    for factor in range(n_factors):
-        qs[factor] = np.ones(num_states[factor]) / num_states[factor]
+    qs = obj_array_uniform(num_states)
 
     """
     If prior is not provided, initialise prior to be identical to posterior 
@@ -82,7 +84,8 @@ def run_vanilla_fpi(A, obs, num_obs, num_states, prior=None, num_iter=10, dF=1.0
     =========== Step 3 ===========
         Initialize initial free energy
     """
-    prev_vfe = calc_free_energy(qs, prior, n_factors)
+    if compute_vfe:
+        prev_vfe = calc_free_energy(qs, prior, n_factors)
 
     """
     =========== Step 4 ===========
@@ -102,8 +105,14 @@ def run_vanilla_fpi(A, obs, num_obs, num_states, prior=None, num_iter=10, dF=1.0
         Run the FPI scheme
         """
 
+        # change stop condition for fixed point iterations based on whether we are computing the variational free energy or not
+        condition_check_both = lambda curr_iter, dF: curr_iter < num_iter and dF >= dF_tol
+        condition_check_just_numiter = lambda curr_iter, dF: curr_iter < num_iter
+        check_stop_condition = condition_check_both if compute_vfe else condition_check_just_numiter
+
         curr_iter = 0
-        while curr_iter < num_iter and dF >= dF_tol:
+
+        while check_stop_condition(curr_iter, dF):
             # Initialise variational free energy
             vfe = 0
 
@@ -121,6 +130,9 @@ def run_vanilla_fpi(A, obs, num_obs, num_states, prior=None, num_iter=10, dF=1.0
                 qL = np.einsum(LL_tensor, list(range(n_factors)), [factor])/qs_i
                 qs[factor] = softmax(qL + prior[factor])
 
+            # print(f'Posteriors at iteration {curr_iter}:\n')
+            # print(qs[0])
+            # print(qs[1])
             # List of orders in which marginal posteriors are sequentially multiplied into the joint likelihood:
             # First order loops over factors starting at index = 0, second order goes in reverse
             # factor_orders = [range(n_factors), range((n_factors - 1), -1, -1)]
@@ -132,17 +144,183 @@ def run_vanilla_fpi(A, obs, num_obs, num_states, prior=None, num_iter=10, dF=1.0
             #         qL = spm_dot(likelihood, qs, [factor])
             #         qs[factor] = softmax(qL + prior[factor])
 
-            # calculate new free energy
-            vfe = calc_free_energy(qs, prior, n_factors, likelihood)
+            if compute_vfe:
+                # calculate new free energy
+                vfe = calc_free_energy(qs, prior, n_factors, likelihood)
 
-            # stopping condition - time derivative of free energy
-            dF = np.abs(prev_vfe - vfe)
-            prev_vfe = vfe
+                # print(f'VFE at iteration {curr_iter}: {vfe}\n')
+                # stopping condition - time derivative of free energy
+                dF = np.abs(prev_vfe - vfe)
+                prev_vfe = vfe
 
             curr_iter += 1
 
         return qs
 
+def run_vanilla_fpi_factorized(A, obs, num_obs, num_states, mb_dict, prior=None, num_iter=10, dF=1.0, dF_tol=0.001, compute_vfe=True):
+    """
+    Update marginal posterior beliefs over hidden states using mean-field variational inference, via
+    fixed point iteration. 
+
+    Parameters
+    ----------
+    A: ``numpy.ndarray`` of dtype object
+        Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of
+        stores an ``np.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store 
+        the probability of observation level ``i`` given hidden state levels ``j, k, ...``
+    obs: numpy 1D array or numpy ndarray of dtype object
+        The observation (generated by the environment). If single modality, this should be a 1D ``np.ndarray``
+        (one-hot vector representation). If multi-modality, this should be ``np.ndarray`` of dtype object whose entries are 1D one-hot vectors.
+    num_obs: ``list`` of ints
+        List of dimensionalities of each observation modality
+    num_states: ``list`` of ints
+        List of dimensionalities of each hidden state factor
+    mb_dict: ``Dict``
+        Dictionary with two keys (``A_factor_list`` and ``A_modality_list``), that stores the factor indices that influence each modality (``A_factor_list``)
+        and the modality indices influenced by each factor (``A_modality_list``).
+    prior: numpy ndarray of dtype object, default None
+        Prior over hidden states. If absent, prior is set to be the log uniform distribution over hidden states (identical to the 
+        initialisation of the posterior)
+    num_iter: int, default 10
+        Number of variational fixed-point iterations to run until convergence.
+    dF: float, default 1.0
+        Initial free energy gradient (dF/dt) before updating in the course of gradient descent.
+    dF_tol: float, default 0.001
+        Threshold value of the time derivative of the variational free energy (dF/dt), to be checked at 
+        each iteration. If dF <= dF_tol, the iterations are halted pre-emptively and the final 
+        marginal posterior belief(s) is(are) returned
+    compute_vfe: bool, default True
+        Whether to compute the variational free energy at each iteration. If False, the function runs through 
+        all variational iterations.
+  
+    Returns
+    ----------
+    qs: numpy 1D array, numpy ndarray of dtype object, optional
+        Marginal posterior beliefs over hidden states at current timepoint
+    """
+
+    # get model dimensions
+    n_modalities = len(num_obs)
+    n_factors = len(num_states)
+
+    """
+    =========== Step 1 ===========
+        Generate modality-specific log-likelihood tensors (will be tensors of different-shapes,
+        where `likelihood[m].ndim` will be equal to  `len(mb_dict['A_factor_list'][m])`
+    """
+
+    likelihood = obj_array(n_modalities)
+    obs = to_obj_array(obs)
+    for (m, A_m) in enumerate(A):
+        likelihood[m] = dot_likelihood(A_m, obs[m])
+
+    log_likelihood = spm_log_obj_array(likelihood)
+
+    """
+    =========== Step 2 ===========
+        Create a flat posterior (and prior if necessary)
+    """
+
+    qs = obj_array_uniform(num_states)
+
+    """
+    If prior is not provided, initialise prior to be identical to posterior 
+    (namely, a flat categorical distribution). Take the logarithm of it (required for 
+    FPI algorithm below).
+    """
+    if prior is None:
+        prior = obj_array_uniform(num_states)
+        
+    prior = spm_log_obj_array(prior) # log the prior
+
+
+    """
+    =========== Step 3 ===========
+        Initialize initial free energy
+    """
+    prev_vfe = calc_free_energy(qs, prior, n_factors)
+
+    """
+    =========== Step 4 ===========
+        If we have a single factor, we can just add prior and likelihood because there is a unique FE minimum that can reached instantaneously,
+        otherwise we run fixed point iteration
+    """
+
+    if n_factors == 1:
+
+        joint_loglikelihood = np.zeros(tuple(num_states))
+        for m in range(n_modalities):
+            joint_loglikelihood += log_likelihood[m] # add up all the log-likelihoods, since we know they will all have the same dimension in the case of a single hidden state factor
+        qL = spm_dot(joint_loglikelihood, qs, [0])
+
+        qs = to_obj_array(softmax(qL + prior[0]))
+
+    else:
+        """
+        =========== Step 5 ===========
+        Run the factorized FPI scheme
+        """
+
+        A_factor_list, A_modality_list = mb_dict['A_factor_list'], mb_dict['A_modality_list']
+
+        if compute_vfe:
+            joint_loglikelihood = np.zeros(tuple(num_states))
+            for m in range(n_modalities):
+                reshape_dims = n_factors*[1]
+                for _f_id in A_factor_list[m]:
+                    reshape_dims[_f_id] = num_states[_f_id]
+
+                joint_loglikelihood += log_likelihood[m].reshape(reshape_dims) # add up all the log-likelihoods after reshaping them to the global common dimensions of all hidden state factors
+
+        curr_iter = 0
+
+        # change stop condition for fixed point iterations based on whether we are computing the variational free energy or not
+        condition_check_both = lambda curr_iter, dF: curr_iter < num_iter and dF >= dF_tol
+        condition_check_just_numiter = lambda curr_iter, dF: curr_iter < num_iter
+        check_stop_condition = condition_check_both if compute_vfe else condition_check_just_numiter
+
+        while check_stop_condition(curr_iter, dF):
+            
+            # vfe = 0 
+
+            qs_new = obj_array(n_factors)
+            for f in range(n_factors):
+            
+                '''
+                Sum the expected log likelihoods E_q(s_i/f)[ln P(o=obs[m]|s)] for independent modalities together,
+                since they may have differing dimension. This obtains a marginal log-likelihood for the current factor index `factor`,
+                which includes the evidence for that particular factor afforded by the different modalities. 
+                '''
+            
+                qL = np.zeros(num_states[f])
+
+                for ii, m in enumerate(A_modality_list[f]):
+                
+                    qL += spm_dot(log_likelihood[m], qs[A_factor_list[m]], [A_factor_list[m].index(f)])
+
+                qs_new[f] = softmax(qL + prior[f])
+
+                # vfe -= qL.sum() # accuracy part of vfe, sum of factor-level expected energies E_q(s_i/f)[ln P(o=obs|s)]
+            
+            qs = deepcopy(qs_new)
+            # print(f'Posteriors at iteration {curr_iter}:\n')
+            # print(qs[0])
+            # print(qs[1])
+            # calculate new free energy, leaving out the accuracy term
+            # vfe += calc_free_energy(qs, prior, n_factors)
+
+            if compute_vfe:
+                vfe = calc_free_energy(qs, prior, n_factors, likelihood=joint_loglikelihood)
+
+                # print(f'VFE at iteration {curr_iter}: {vfe}\n')
+                # stopping condition - time derivative of free energy
+                dF = np.abs(prev_vfe - vfe)
+                prev_vfe = vfe
+
+            curr_iter += 1
+            
+    return qs
+
 
 def _run_vanilla_fpi_faster(A, obs, n_observations, n_states, prior=None, num_iter=10, dF=1.0, dF_tol=0.001):
     """
diff --git a/pymdp/algos/mmp.py b/pymdp/algos/mmp.py
index e38b5b7f..019e81df 100644
--- a/pymdp/algos/mmp.py
+++ b/pymdp/algos/mmp.py
@@ -4,10 +4,9 @@
 import numpy as np
 
 from pymdp.utils import to_obj_array, get_model_dimensions, obj_array, obj_array_zeros, obj_array_uniform
-from pymdp.maths import spm_dot, spm_norm, softmax, calc_free_energy, spm_log_single
+from pymdp.maths import spm_dot, spm_norm, softmax, calc_free_energy, spm_log_single, factor_dot_flex
 import copy
 
-
 def run_mmp(
     lh_seq, B, policy, prev_actions=None, prior=None, num_iter=10, grad_descent=True, tau=0.25, last_timestep = False):
     """
@@ -90,6 +89,7 @@ def run_mmp(
                 # likelihood
                 if t < past_len:
                     lnA = spm_log_single(spm_dot(lh_seq[t], qs_seq[t], [f]))
+                    print(f'Enumerated version: lnA at time {t}: {lnA}')    
                 else:
                     lnA = np.zeros(num_states[f])
                 
@@ -113,7 +113,7 @@ def run_mmp(
                     lnqs = spm_log_single(sx)
                     coeff = 1 if (t >= future_cutoff) else 2
                     err = (coeff * lnA + lnB_past + lnB_future) - coeff * lnqs
-                    lnqs = lnqs + tau * (err - err.mean())
+                    lnqs = lnqs + tau * (err - err.mean()) # for numerical stability, before passing into the softmax
                     qs_seq[t][f] = softmax(lnqs)
                     if (t == 0) or (t == (infer_len-1)):
                         F += sx.dot(0.5*err)
@@ -131,6 +131,170 @@ def run_mmp(
 
     return qs_seq, F
 
+def run_mmp_factorized(
+    lh_seq, mb_dict, B, B_factor_list, policy, prev_actions=None, prior=None, num_iter=10, grad_descent=True, tau=0.25, last_timestep = False):
+    """
+    Marginal message passing scheme for updating marginal posterior beliefs about hidden states over time, 
+    conditioned on a particular policy.
+
+    Parameters
+    ----------
+    lh_seq: ``numpy.ndarray`` of dtype object
+        Log likelihoods of hidden states under a sequence of observations over time. This is assumed to already be log-transformed. Each ``lh_seq[t]`` contains
+        the log likelihood of hidden states for a particular observation at time ``t``
+    mb_dict: ``Dict``
+        Dictionary with two keys (``A_factor_list`` and ``A_modality_list``), that stores the factor indices that influence each modality (``A_factor_list``)
+        and the modality indices influenced by each factor (``A_modality_list``).
+    B: ``numpy.ndarray`` of dtype object
+        Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.
+        Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability
+        of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.
+    B_factor_list: ``list`` of ``list`` of ``int``
+        List of lists of hidden state factors each hidden state factor depends on. Each element ``B_factor_list[i]`` is a list of the factor indices that factor i's dynamics depend on.
+    policy: 2D ``numpy.ndarray``
+        Matrix of shape ``(policy_len, num_control_factors)`` that indicates the indices of each action (control state index) upon timestep ``t`` and control_factor ``f` in the element ``policy[t,f]`` for a given policy.
+    prev_actions: ``numpy.ndarray``, default None
+        If provided, should be a matrix of previous actions of shape ``(infer_len, num_control_factors)`` that indicates the indices of each action (control state index) taken in the past (up until the current timestep).
+    prior: ``numpy.ndarray`` of dtype object, default None
+        If provided, the prior beliefs about initial states (at t = 0, relative to ``infer_len``). If ``None``, this defaults
+        to a flat (uninformative) prior over hidden states.
+    numiter: int, default 10
+        Number of variational iterations.
+    grad_descent: Bool, default True
+        Flag for whether to use gradient descent (free energy gradient updates) instead of fixed point solution to the posterior beliefs
+    tau: float, default 0.25
+        Decay constant for use in ``grad_descent`` version. Tunes the size of the gradient descent updates to the posterior.
+    last_timestep: Bool, default False
+        Flag for whether we are at the last timestep of belief updating
+        
+    Returns
+    ---------
+    qs_seq: ``numpy.ndarray`` of dtype object
+        Posterior beliefs over hidden states under the policy. Nesting structure is timepoints, factors,
+        where e.g. ``qs_seq[t][f]`` stores the marginal belief about factor ``f`` at timepoint ``t`` under the policy in question.
+    F: float
+        Variational free energy of the policy.
+    """
+
+    # window
+    past_len = len(lh_seq)
+    future_len = policy.shape[0]
+
+    if last_timestep:
+        infer_len = past_len + future_len - 1
+    else:
+        infer_len = past_len + future_len
+    
+    future_cutoff = past_len + future_len - 2
+
+    # dimensions
+    _, num_states, _, num_factors = get_model_dimensions(A=None, B=B)
+
+    # beliefs
+    qs_seq = obj_array(infer_len)
+    for t in range(infer_len):
+        qs_seq[t] = obj_array_uniform(num_states)
+
+    # last message
+    qs_T = obj_array_zeros(num_states)
+
+    # prior
+    if prior is None:
+        prior = obj_array_uniform(num_states)
+
+    # transposed transition
+    trans_B = obj_array(num_factors)
+        
+    for f in range(num_factors):
+        trans_B[f] = spm_norm(np.swapaxes(B[f],0,1))
+
+    if prev_actions is not None:
+        policy = np.vstack((prev_actions, policy))
+
+    A_factor_list, A_modality_list = mb_dict['A_factor_list'], mb_dict['A_modality_list']
+
+    joint_lh_seq = obj_array(len(lh_seq))
+    num_modalities = len(A_factor_list)
+    for t in range(len(lh_seq)):
+        joint_loglikelihood = np.zeros(tuple(num_states))
+        for m in range(num_modalities):
+            reshape_dims = num_factors*[1]
+            for _f_id in A_factor_list[m]:
+                reshape_dims[_f_id] = num_states[_f_id]
+            joint_loglikelihood += lh_seq[t][m].reshape(reshape_dims) # add up all the log-likelihoods after reshaping them to the global common dimensions of all hidden state factors
+        joint_lh_seq[t] = joint_loglikelihood
+
+    # compute inverse B dependencies, which is a list that for each hidden state factor, lists the indices of the other hidden state factors that it 'drives' or is a parent of in the HMM graphical model
+    inv_B_deps = [[i for i, d in enumerate(B_factor_list) if f in d] for f in range(num_factors)]
+    for itr in range(num_iter):
+        F = 0.0 # reset variational free energy (accumulated over time and factors, but reset per iteration)
+        for t in range(infer_len):
+            for f in range(num_factors):
+                # likelihood
+                lnA = np.zeros(num_states[f])
+                if t < past_len:
+                    for m in A_modality_list[f]:
+                        lnA += spm_log_single(spm_dot(lh_seq[t][m], qs_seq[t][A_factor_list[m]], [A_factor_list[m].index(f)]))  
+                    print(f'Factorized version: lnA at time {t}: {lnA}')                
+                
+                # past message
+                if t == 0:
+                    lnB_past = spm_log_single(prior[f])
+                else:
+                    past_msg = spm_dot(B[f][...,int(policy[t - 1, f])], qs_seq[t-1][B_factor_list[f]])
+                    lnB_past = spm_log_single(past_msg)
+
+                # future message
+                if t >= future_cutoff:
+                    lnB_future = qs_T[f]
+                else:
+                    # list of future_msgs, one for each of the factors that factor f is driving
+
+                    B_marg_list = [] # list of the marginalized B matrices, that correspond to mapping between the factor of interest `f` and each of its children factors `i`
+                    for i in inv_B_deps[f]: #loop over all the hidden state factors that are driven by f
+                        b = B[i][...,int(policy[t,i])]
+                        keep_dims = (0,1+B_factor_list[i].index(f))
+                        dims = []
+                        idxs = []
+                        for j, d in enumerate(B_factor_list[i]): # loop over the list of factors that drive each child `i` of factor-of-interest `f` (i.e. the co-parents of `f`, with respect to child `i`)
+                            if f != d:
+                                dims.append((1 + j,))
+                                idxs.append(d)
+                        xs = [qs_seq[t+1][f_i] for f_i in idxs]
+                        B_marg_list.append( factor_dot_flex(b, xs, tuple(dims), keep_dims=keep_dims) ) # marginalize out all parents of `i` besides `f`
+
+                    lnB_future = np.zeros(num_states[f])
+                    for i, b in enumerate(B_marg_list):
+                        b_norm_T = spm_norm(b.T)
+                        lnB_future += spm_log_single(b_norm_T.dot(qs_seq[t + 1][inv_B_deps[f][i]]))
+                    
+                    
+                    lnB_future *= 0.5
+                
+                # inference
+                if grad_descent:
+                    sx = qs_seq[t][f] # save this as a separate variable so that it can be used in VFE computation
+                    lnqs = spm_log_single(sx)
+                    coeff = 1 if (t >= future_cutoff) else 2
+                    err = (coeff * lnA + lnB_past + lnB_future) - coeff * lnqs
+                    lnqs = lnqs + tau * (err - err.mean())
+                    qs_seq[t][f] = softmax(lnqs)
+                    if (t == 0) or (t == (infer_len-1)):
+                        F += sx.dot(0.5*err)
+                    else:
+                        F += sx.dot(0.5*(err - (num_factors - 1)*lnA/num_factors)) # @NOTE: not sure why Karl does this in SPM_MDP_VB_X, we should look into this
+                else:
+                    qs_seq[t][f] = softmax(lnA + lnB_past + lnB_future)
+            
+            if not grad_descent:
+
+                if t < past_len:
+                    F += calc_free_energy(qs_seq[t], prior, num_factors, likelihood = spm_log_single(joint_lh_seq[t]) )
+                else:
+                    F += calc_free_energy(qs_seq[t], prior, num_factors)
+
+    return qs_seq, F
+
 def _run_mmp_testing(
     lh_seq, B, policy, prev_actions=None, prior=None, num_iter=10, grad_descent=True, tau=0.25, last_timestep = False):
     """
diff --git a/pymdp/control.py b/pymdp/control.py
index 497dd30a..ba7a218f 100644
--- a/pymdp/control.py
+++ b/pymdp/control.py
@@ -5,7 +5,8 @@
 
 import itertools
 import numpy as np
-from pymdp.maths import softmax, softmax_obj_arr, spm_dot, spm_wnorm, spm_MDP_G, spm_log_single, spm_log_obj_array
+from pymdp.maths import softmax, softmax_obj_arr, spm_dot, spm_wnorm, spm_MDP_G, spm_log_single, kl_div, entropy
+from pymdp.inference import update_posterior_states_factorized, average_states_over_policies
 from pymdp import utils
 import copy
 
@@ -21,8 +22,9 @@ def update_posterior_policies_full(
     prior=None,
     pA=None,
     pB=None,
-    F = None,
-    E = None,
+    F=None,
+    E=None,
+    I=None,
     gamma=16.0
 ):  
     """
@@ -67,6 +69,9 @@ def update_posterior_policies_full(
         Vector of variational free energies for each policy
     E: 1D ``numpy.ndarray``, default ``None``
         Vector of prior probabilities of each policy (what's referred to in the active inference literature as "habits"). If ``None``, this defaults to a flat (uninformative) prior over policies.
+    I: ``numpy.ndarray`` of dtype object
+        For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability 
+        of reaching the goal state backwards from state j after i steps.
     gamma: ``float``, default 16.0
         Prior precision over policies, scales the contribution of the expected free energy to the posterior over policies
 
@@ -100,6 +105,9 @@ def update_posterior_policies_full(
     else:
         lnE = spm_log_single(E) 
 
+    if I is not None:
+        init_qs_all_pi = [qs_seq_pi[p][0] for p in range(num_policies)]
+        qs_bma = average_states_over_policies(init_qs_all_pi, softmax(E))
 
     for p_idx, policy in enumerate(policies):
 
@@ -116,11 +124,144 @@ def update_posterior_policies_full(
                 G[p_idx] += calc_pA_info_gain(pA, qo_seq_pi[p_idx], qs_seq_pi[p_idx])
             if pB is not None:
                 G[p_idx] += calc_pB_info_gain(pB, qs_seq_pi[p_idx], prior, policy)
+        
+        if I is not None:
+            G[p_idx] += calc_inductive_cost(qs_bma, qs_seq_pi[p_idx], I)
 
     q_pi = softmax(G * gamma - F + lnE)
     
     return q_pi, G
 
+def update_posterior_policies_full_factorized(
+    qs_seq_pi,
+    A,
+    B,
+    C,
+    A_factor_list,
+    B_factor_list,
+    policies,
+    use_utility=True,
+    use_states_info_gain=True,
+    use_param_info_gain=False,
+    prior=None,
+    pA=None,
+    pB=None,
+    F=None,
+    E=None,
+    I=None,
+    gamma=16.0
+):  
+    """
+    Update posterior beliefs about policies by computing expected free energy of each policy and integrating that
+    with the variational free energy of policies ``F`` and prior over policies ``E``. This is intended to be used in conjunction
+    with the ``update_posterior_states_full`` method of ``inference.py``, since the full posterior over future timesteps, under all policies, is
+    assumed to be provided in the input array ``qs_seq_pi``.
+
+    Parameters
+    ----------
+    qs_seq_pi: ``numpy.ndarray`` of dtype object
+        Posterior beliefs over hidden states for each policy. Nesting structure is policies, timepoints, factors,
+        where e.g. ``qs_seq_pi[p][t][f]`` stores the marginal belief about factor ``f`` at timepoint ``t`` under policy ``p``.
+    A: ``numpy.ndarray`` of dtype object
+        Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of
+        stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store 
+        the probability of observation level ``i`` given hidden state levels ``j, k, ...``
+    B: ``numpy.ndarray`` of dtype object
+        Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.
+        Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability
+        of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.
+    C: ``numpy.ndarray`` of dtype object
+       Prior over observations or 'prior preferences', storing the "value" of each outcome in terms of relative log probabilities. 
+       This is softmaxed to form a proper probability distribution before being used to compute the expected utility term of the expected free energy.
+    A_factor_list: ``list`` of ``list``s of ``int``
+        ``list`` that stores the indices of the hidden state factor indices that each observation modality depends on. For example, if ``A_factor_list[m] = [0, 1]``, then
+        observation modality ``m`` depends on hidden state factors 0 and 1.
+    B_factor_list: ``list`` of ``list``s of ``int``
+        ``list`` that stores the indices of the hidden state factor indices that each hidden state factor depends on. For example, if ``B_factor_list[f] = [0, 1]``, then
+        the transitions in hidden state factor ``f`` depend on hidden state factors 0 and 1.
+    policies: ``list`` of 2D ``numpy.ndarray``
+        ``list`` that stores each policy in ``policies[p_idx]``. Shape of ``policies[p_idx]`` is ``(num_timesteps, num_factors)`` where `num_timesteps` is the temporal
+        depth of the policy and ``num_factors`` is the number of control factors.
+    use_utility: ``Bool``, default ``True``
+        Boolean flag that determines whether expected utility should be incorporated into computation of EFE.
+    use_states_info_gain: ``Bool``, default ``True``
+        Boolean flag that determines whether state epistemic value (info gain about hidden states) should be incorporated into computation of EFE.
+    use_param_info_gain: ``Bool``, default ``False`` 
+        Boolean flag that determines whether parameter epistemic value (info gain about generative model parameters) should be incorporated into computation of EFE. 
+    prior: ``numpy.ndarray`` of dtype object, default ``None``
+        If provided, this is a ``numpy`` object array with one sub-array per hidden state factor, that stores the prior beliefs about initial states. 
+        If ``None``, this defaults to a flat (uninformative) prior over hidden states.
+    pA: ``numpy.ndarray`` of dtype object, default ``None``
+        Dirichlet parameters over observation model (same shape as ``A``)
+    pB: ``numpy.ndarray`` of dtype object, default ``None``
+        Dirichlet parameters over transition model (same shape as ``B``)
+    F: 1D ``numpy.ndarray``, default ``None``
+        Vector of variational free energies for each policy
+    E: 1D ``numpy.ndarray``, default ``None``
+        Vector of prior probabilities of each policy (what's referred to in the active inference literature as "habits"). If ``None``, this defaults to a flat (uninformative) prior over policies.
+    I: ``numpy.ndarray`` of dtype object
+        For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability 
+        of reaching the goal state backwards from state j after i steps.
+    gamma: ``float``, default 16.0
+        Prior precision over policies, scales the contribution of the expected free energy to the posterior over policies
+
+    Returns
+    ----------
+    q_pi: 1D ``numpy.ndarray``
+        Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.
+    G: 1D ``numpy.ndarray``
+        Negative expected free energies of each policy, i.e. a vector containing one negative expected free energy per policy.
+    """
+
+    num_obs, num_states, num_modalities, num_factors = utils.get_model_dimensions(A, B)
+    horizon = len(qs_seq_pi[0])
+    num_policies = len(qs_seq_pi)
+
+    qo_seq = utils.obj_array(horizon)
+    for t in range(horizon):
+        qo_seq[t] = utils.obj_array_zeros(num_obs)
+
+    # initialise expected observations
+    qo_seq_pi = utils.obj_array(num_policies)
+
+    # initialize (negative) expected free energies for all policies
+    G = np.zeros(num_policies)
+
+    if F is None:
+        F = spm_log_single(np.ones(num_policies) / num_policies)
+
+    if E is None:
+        lnE = spm_log_single(np.ones(num_policies) / num_policies)
+    else:
+        lnE = spm_log_single(E) 
+
+    if I is not None:
+        init_qs_all_pi = [qs_seq_pi[p][0] for p in range(num_policies)]
+        qs_bma = average_states_over_policies(init_qs_all_pi, softmax(E))
+
+    for p_idx, policy in enumerate(policies):
+
+        qo_seq_pi[p_idx] = get_expected_obs_factorized(qs_seq_pi[p_idx], A, A_factor_list)
+
+        if use_utility:
+            G[p_idx] += calc_expected_utility(qo_seq_pi[p_idx], C)
+        
+        if use_states_info_gain:
+            G[p_idx] += calc_states_info_gain_factorized(A, qs_seq_pi[p_idx], A_factor_list)
+        
+        if use_param_info_gain:
+            if pA is not None:
+                G[p_idx] += calc_pA_info_gain_factorized(pA, qo_seq_pi[p_idx], qs_seq_pi[p_idx], A_factor_list)
+            if pB is not None:
+                G[p_idx] += calc_pB_info_gain_interactions(pB, qs_seq_pi[p_idx], qs_seq_pi[p_idx], B_factor_list, policy)
+        
+        if I is not None:
+            G[p_idx] += calc_inductive_cost(qs_bma, qs_seq_pi[p_idx], I)
+            
+    q_pi = softmax(G * gamma - F + lnE)
+    
+    return q_pi, G
+
 
 def update_posterior_policies(
     qs,
@@ -133,7 +274,8 @@ def update_posterior_policies(
     use_param_info_gain=False,
     pA=None,
     pB=None,
-    E = None,
+    E=None,
+    I=None,
     gamma=16.0
 ):
     """
@@ -173,6 +315,9 @@ def update_posterior_policies(
         Dirichlet parameters over transition model (same shape as ``B``)
     E: 1D ``numpy.ndarray``, optional
         Vector of prior probabilities of each policy (what's referred to in the active inference literature as "habits")
+    I: ``numpy.ndarray`` of dtype object
+        For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability 
+        of reaching the goal state backwards from state j after i steps.
     gamma: float, default 16.0
         Prior precision over policies, scales the contribution of the expected free energy to the posterior over policies
 
@@ -205,9 +350,118 @@ def update_posterior_policies(
 
         if use_param_info_gain:
             if pA is not None:
-                G[idx] += calc_pA_info_gain(pA, qo_pi, qs_pi)
+                G[idx] += calc_pA_info_gain(pA, qo_pi, qs_pi).item()
             if pB is not None:
-                G[idx] += calc_pB_info_gain(pB, qs_pi, qs, policy)
+                G[idx] += calc_pB_info_gain(pB, qs_pi, qs, policy).item()
+        
+        if I is not None:
+            G[idx] += calc_inductive_cost(qs, qs_pi, I)
+
+    q_pi = softmax(G * gamma + lnE)    
+
+    return q_pi, G
+
+def update_posterior_policies_factorized(
+    qs,
+    A,
+    B,
+    C,
+    A_factor_list,
+    B_factor_list,
+    policies,
+    use_utility=True,
+    use_states_info_gain=True,
+    use_param_info_gain=False,
+    pA=None,
+    pB=None,
+    E=None,
+    I=None,
+    gamma=16.0
+):
+    """
+    Update posterior beliefs about policies by computing expected free energy of each policy and integrating that
+    with the prior over policies ``E``. This is intended to be used in conjunction
+    with the ``update_posterior_states`` method of the ``inference`` module, since only the posterior about the hidden states at the current timestep
+    ``qs`` is assumed to be provided, unconditional on policies. The predictive posterior over hidden states under all policies Q(s, pi) is computed 
+    using the starting posterior about states at the current timestep ``qs`` and the generative model (e.g. ``A``, ``B``, ``C``)
+
+    Parameters
+    ----------
+    qs: ``numpy.ndarray`` of dtype object
+        Marginal posterior beliefs over hidden states at current timepoint (unconditioned on policies)
+    A: ``numpy.ndarray`` of dtype object
+        Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of
+        stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store 
+        the probability of observation level ``i`` given hidden state levels ``j, k, ...``
+    B: ``numpy.ndarray`` of dtype object
+        Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.
+        Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability
+        of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.
+    C: ``numpy.ndarray`` of dtype object
+       Prior over observations or 'prior preferences', storing the "value" of each outcome in terms of relative log probabilities. 
+       This is softmaxed to form a proper probability distribution before being used to compute the expected utility term of the expected free energy.
+    A_factor_list: ``list`` of ``list``s of ``int``
+        ``list`` that stores the indices of the hidden state factor indices that each observation modality depends on. For example, if ``A_factor_list[m] = [0, 1]``, then
+        observation modality ``m`` depends on hidden state factors 0 and 1.
+    B_factor_list: ``list`` of ``list``s of ``int``
+        ``list`` that stores the indices of the hidden state factor indices that each hidden state factor depends on. For example, if ``B_factor_list[f] = [0, 1]``, then
+        the transitions in hidden state factor ``f`` depend on hidden state factors 0 and 1.
+    policies: ``list`` of 2D ``numpy.ndarray``
+        ``list`` that stores each policy in ``policies[p_idx]``. Shape of ``policies[p_idx]`` is ``(num_timesteps, num_factors)`` where `num_timesteps` is the temporal
+        depth of the policy and ``num_factors`` is the number of control factors.
+    use_utility: ``Bool``, default ``True``
+        Boolean flag that determines whether expected utility should be incorporated into computation of EFE.
+    use_states_info_gain: ``Bool``, default ``True``
+        Boolean flag that determines whether state epistemic value (info gain about hidden states) should be incorporated into computation of EFE.
+    use_param_info_gain: ``Bool``, default ``False`` 
+        Boolean flag that determines whether parameter epistemic value (info gain about generative model parameters) should be incorporated into computation of EFE.
+    pA: ``numpy.ndarray`` of dtype object, optional
+        Dirichlet parameters over observation model (same shape as ``A``)
+    pB: ``numpy.ndarray`` of dtype object, optional
+        Dirichlet parameters over transition model (same shape as ``B``)
+    E: 1D ``numpy.ndarray``, optional
+        Vector of prior probabilities of each policy (what's referred to in the active inference literature as "habits")
+    I: ``numpy.ndarray`` of dtype object
+        For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability 
+        of reaching the goal state backwards from state j after i steps.
+    gamma: float, default 16.0
+        Prior precision over policies, scales the contribution of the expected free energy to the posterior over policies
+
+    Returns
+    ----------
+    q_pi: 1D ``numpy.ndarray``
+        Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.
+    G: 1D ``numpy.ndarray``
+        Negative expected free energies of each policy, i.e. a vector containing one negative expected free energy per policy.
+    """
+
+    n_policies = len(policies)
+    G = np.zeros(n_policies)
+    q_pi = np.zeros((n_policies, 1))
+
+    if E is None:
+        lnE = spm_log_single(np.ones(n_policies) / n_policies)
+    else:
+        lnE = spm_log_single(E) 
+
+    for idx, policy in enumerate(policies):
+        qs_pi = get_expected_states_interactions(qs, B, B_factor_list, policy)
+        qo_pi = get_expected_obs_factorized(qs_pi, A, A_factor_list)
+
+        if use_utility:
+            G[idx] += calc_expected_utility(qo_pi, C)
+
+        if use_states_info_gain:
+            G[idx] += calc_states_info_gain_factorized(A, qs_pi, A_factor_list)
+
+        if use_param_info_gain:
+            if pA is not None:
+                G[idx] += calc_pA_info_gain_factorized(pA, qo_pi, qs_pi, A_factor_list).item()
+            if pB is not None:
+                G[idx] += calc_pB_info_gain_interactions(pB, qs_pi, qs, B_factor_list, policy).item()
+        
+        if I is not None:
+            G[idx] += calc_inductive_cost(qs, qs_pi, I)
 
     q_pi = softmax(G * gamma + lnE)    
 
@@ -247,8 +501,45 @@ def get_expected_states(qs, B, policy):
             qs_pi[t+1][control_factor] = B[control_factor][:,:,int(action)].dot(qs_pi[t][control_factor])
 
     return qs_pi[1:]
- 
+    
+def get_expected_states_interactions(qs, B, B_factor_list, policy):
+    """
+    Compute the expected states under a policy, also known as the posterior predictive density over states
 
+    Parameters
+    ----------
+    qs: ``numpy.ndarray`` of dtype object
+        Marginal posterior beliefs over hidden states at a given timepoint.
+    B: ``numpy.ndarray`` of dtype object
+        Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.
+        Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability
+        of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.
+    B_factor_list: ``list`` of ``list`` of ``int``
+        List of lists of hidden state factors each hidden state factor depends on. Each element ``B_factor_list[i]`` is a list of the factor indices that factor i's dynamics depend on.
+    policy: 2D ``numpy.ndarray``
+        Array that stores actions entailed by a policy over time. Shape is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal
+        depth of the policy and ``num_factors`` is the number of control factors.
+
+    Returns
+    -------
+    qs_pi: ``list`` of ``numpy.ndarray`` of dtype object
+        Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about
+        hidden states expected under the policy at time ``t``
+    """
+    n_steps = policy.shape[0]
+    n_factors = policy.shape[1]
+
+    # initialise posterior predictive density as a list of beliefs over time, including current posterior beliefs about hidden states as the first element
+    qs_pi = [qs] + [utils.obj_array(n_factors) for t in range(n_steps)]
+    
+    # get expected states over time
+    for t in range(n_steps):
+        for control_factor, action in enumerate(policy[t,:]):
+            factor_idx = B_factor_list[control_factor] # list of the hidden state factor indices that the dynamics of `qs[control_factor]` depend on
+            qs_pi[t+1][control_factor] = spm_dot(B[control_factor][...,int(action)], qs_pi[t][factor_idx])
+
+    return qs_pi[1:]
+ 
 def get_expected_obs(qs_pi, A):
     """
     Compute the expected observations under a policy, also known as the posterior predictive density over observations
@@ -286,6 +577,45 @@ def get_expected_obs(qs_pi, A):
 
     return qo_pi
 
+def get_expected_obs_factorized(qs_pi, A, A_factor_list):
+    """
+    Compute the expected observations under a policy, also known as the posterior predictive density over observations
+
+    Parameters
+    ----------
+    qs_pi: ``list`` of ``numpy.ndarray`` of dtype object
+        Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about
+        hidden states expected under the policy at time ``t``
+    A: ``numpy.ndarray`` of dtype object
+        Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of
+        stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store 
+        the probability of observation level ``i`` given hidden state levels ``j, k, ...``
+    A_factor_list: ``list`` of ``list`` of ``int``
+        List of lists of hidden state factor indices that each observation modality depends on. Each element ``A_factor_list[i]`` is a list of the factor indices that modality i's observation model depends on.
+    Returns
+    -------
+    qo_pi: ``list`` of ``numpy.ndarray`` of dtype object
+        Predictive posterior beliefs over observations expected under the policy, where ``qo_pi[t]`` stores the beliefs about
+        observations expected under the policy at time ``t``
+    """
+
+    n_steps = len(qs_pi) # each element of the list is the PPD at a different timestep
+
+    # initialise expected observations
+    qo_pi = []
+
+    for t in range(n_steps):
+        qo_pi_t = utils.obj_array(len(A))
+        qo_pi.append(qo_pi_t)
+
+    # compute expected observations over time
+    for t in range(n_steps):
+        for modality, A_m in enumerate(A):
+            factor_idx = A_factor_list[modality] # list of the hidden state factor indices that observation modality with the index `modality` depends on
+            qo_pi[t][modality] = spm_dot(A_m, qs_pi[t][factor_idx])
+
+    return qo_pi
+
 def calc_expected_utility(qo_pi, C):
     """
     Computes the expected utility of a policy, using the observation distribution expected under that policy and a prior preference vector.
@@ -360,6 +690,39 @@ def calc_states_info_gain(A, qs_pi):
 
     return states_surprise
 
+def calc_states_info_gain_factorized(A, qs_pi, A_factor_list):
+    """
+    Computes the Bayesian surprise or information gain about states of a policy, 
+    using the observation model and the hidden state distribution expected under that policy.
+
+    Parameters
+    ----------
+    A: ``numpy.ndarray`` of dtype object
+        Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of
+        stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store 
+        the probability of observation level ``i`` given hidden state levels ``j, k, ...``
+    qs_pi: ``list`` of ``numpy.ndarray`` of dtype object
+        Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about
+        hidden states expected under the policy at time ``t``
+    A_factor_list: ``list`` of ``list`` of ``int``
+        List of lists, where ``A_factor_list[m]`` is a list of the hidden state factor indices that observation modality with the index ``m`` depends on
+
+    Returns
+    -------
+    states_surprise: float
+        Bayesian surprise (about states) or salience expected under the policy in question
+    """
+
+    n_steps = len(qs_pi)
+
+    states_surprise = 0
+    for t in range(n_steps):
+        for m, A_m in enumerate(A):
+            factor_idx = A_factor_list[m] # list of the hidden state factor indices that observation modality with the index `m` depends on
+            states_surprise += spm_MDP_G(A_m, qs_pi[t][factor_idx])
+
+    return states_surprise
+
 
 def calc_pA_info_gain(pA, qo_pi, qs_pi):
     """
@@ -398,6 +761,46 @@ def calc_pA_info_gain(pA, qo_pi, qs_pi):
 
     return pA_infogain
 
+def calc_pA_info_gain_factorized(pA, qo_pi, qs_pi, A_factor_list):
+    """
+    Compute expected Dirichlet information gain about parameters ``pA`` under a policy.
+    In this version of the function, we assume that the observation model is factorized, i.e. that each observation modality depends on a subset of the hidden state factors.
+
+    Parameters
+    ----------
+    pA: ``numpy.ndarray`` of dtype object
+        Dirichlet parameters over observation model (same shape as ``A``)
+    qo_pi: ``list`` of ``numpy.ndarray`` of dtype object
+        Predictive posterior beliefs over observations expected under the policy, where ``qo_pi[t]`` stores the beliefs about
+        observations expected under the policy at time ``t``
+    qs_pi: ``list`` of ``numpy.ndarray`` of dtype object
+        Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about
+        hidden states expected under the policy at time ``t``
+    A_factor_list: ``list`` of ``list`` of ``int``
+        List of lists, where ``A_factor_list[m]`` is a list of the hidden state factor indices that observation modality with the index ``m`` depends on
+
+    Returns
+    -------
+    infogain_pA: float
+        Surprise (about Dirichlet parameters) expected under the policy in question
+    """
+
+    n_steps = len(qo_pi)
+    
+    num_modalities = len(pA)
+    wA = utils.obj_array(num_modalities)
+    for modality, pA_m in enumerate(pA):
+        wA[modality] = spm_wnorm(pA[modality])
+
+    pA_infogain = 0
+    
+    for modality in range(num_modalities):
+        wA_modality = wA[modality] * (pA[modality] > 0).astype("float")
+        factor_idx = A_factor_list[modality]
+        for t in range(n_steps):
+            pA_infogain -= qo_pi[t][modality].dot(spm_dot(wA_modality, qs_pi[t][factor_idx])[:, np.newaxis])
+
+    return pA_infogain
 
 def calc_pB_info_gain(pB, qs_pi, qs_prev, policy):
     """
@@ -450,6 +853,103 @@ def calc_pB_info_gain(pB, qs_pi, qs_prev, policy):
 
     return pB_infogain
 
+def calc_pB_info_gain_interactions(pB, qs_pi, qs_prev, B_factor_list, policy):
+    """
+    Compute expected Dirichlet information gain about parameters ``pB`` under a given policy
+
+    Parameters
+    ----------
+    pB: ``numpy.ndarray`` of dtype object
+        Dirichlet parameters over transition model (same shape as ``B``)
+    qs_pi: ``list`` of ``numpy.ndarray`` of dtype object
+        Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about
+        hidden states expected under the policy at time ``t``
+    qs_prev: ``numpy.ndarray`` of dtype object
+        Posterior over hidden states at beginning of trajectory (before receiving observations)
+    B_factor_list: ``list`` of ``list`` of ``int``
+        List of lists, where ``B_factor_list[f]`` is a list of the hidden state factor indices that hidden state factor with the index ``f`` depends on
+    policy: 2D ``numpy.ndarray``
+        Array that stores actions entailed by a policy over time. Shape is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal
+        depth of the policy and ``num_factors`` is the number of control factors.
+    
+    Returns
+    -------
+    infogain_pB: float
+        Surprise (about dirichlet parameters) expected under the policy in question
+    """
+
+    n_steps = len(qs_pi)
+
+    num_factors = len(pB)
+    wB = utils.obj_array(num_factors)
+    for factor, pB_f in enumerate(pB):
+        wB[factor] = spm_wnorm(pB_f)
+
+    pB_infogain = 0
+
+    for t in range(n_steps):
+        # the 'past posterior' used for the information gain about pB here is the posterior
+        # over expected states at the timestep previous to the one under consideration
+        # if we're on the first timestep, we just use the latest posterior in the
+        # entire action-perception cycle as the previous posterior
+        if t == 0:
+            previous_qs = qs_prev
+        # otherwise, we use the expected states for the timestep previous to the timestep under consideration
+        else:
+            previous_qs = qs_pi[t - 1]
+
+        # get the list of action-indices for the current timestep
+        policy_t = policy[t, :]
+        for factor, a_i in enumerate(policy_t):
+            wB_factor_t = wB[factor][...,int(a_i)] * (pB[factor][...,int(a_i)] > 0).astype("float")
+            f_idx = B_factor_list[factor]
+            pB_infogain -= qs_pi[t][factor].dot(spm_dot(wB_factor_t, previous_qs[f_idx]))
+
+    return pB_infogain
+
+def calc_inductive_cost(qs, qs_pi, I, epsilon=1e-3):
+    """
+    Computes the inductive cost of a state.
+
+    Parameters
+    ----------
+    qs: ``numpy.ndarray`` of dtype object
+        Marginal posterior beliefs over hidden states at a given timepoint.
+    qs_pi: ``list`` of ``numpy.ndarray`` of dtype object
+        Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about
+        states expected under the policy at time ``t``
+    I: ``numpy.ndarray`` of dtype object
+        For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability 
+        of reaching the goal state backwards from state j after i steps.
+
+    Returns
+    -------
+    inductive_cost: float
+        Cost of visited this state using backwards induction under the policy in question
+    """
+    n_steps = len(qs_pi)
+    
+    # initialise inductive cost
+    inductive_cost = 0
+
+    # loop over time points and modalities
+    num_factors = len(I)
+
+    for t in range(n_steps):
+        for factor in range(num_factors):
+            # we also assume precise beliefs here?!
+            idx = np.argmax(qs[factor])
+            # m = arg max_n p_n < sup p
+            # i.e. find first I idx equals 1 and m is the index before
+            m = np.where(I[factor][:, idx] == 1)[0]
+            # we might find no path to goal (i.e. when no goal specified)
+            if len(m) > 0:
+                m = max(m[0]-1, 0)
+                I_m = (1-I[factor][m, :]) * np.log(epsilon)
+                inductive_cost += I_m.dot(qs_pi[t][factor])
+                
+    return inductive_cost
+
 def construct_policies(num_states, num_controls = None, policy_len=1, control_fac_idx=None):
     """
     Generate a ``list`` of policies. The returned array ``policies`` is a ``list`` that stores one policy per entry.
@@ -754,3 +1254,213 @@ def _select_highest_test(options_array, seed=None):
         return int(same_prob[rng.choice(len(same_prob))])
 
     return int(same_prob[0])
+
+
+def backwards_induction(H, B, B_factor_list, threshold, depth):
+    """
+    Runs backwards induction of reaching a goal state H given a transition model B.
+    
+    Parameters
+    ----------    
+    H: ``numpy.ndarray`` of dtype object
+       Prior over states
+    B: ``numpy.ndarray`` of dtype object
+        Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.
+        Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability
+        of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.
+    B_factor_list: ``list`` of ``list`` of ``int``
+        List of lists of hidden state factors each hidden state factor depends on. Each element ``B_factor_list[i]`` is a list of the factor indices that factor i's dynamics depend on.
+    threshold: ``float``
+        The threshold for pruning transitions that are below a certain probability
+    depth: ``int``
+        The temporal depth of the backward induction
+
+    Returns
+    ----------
+    I: ``numpy.ndarray`` of dtype object
+        For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability 
+        of reaching the goal state backwards from state j after i steps.
+    """
+    # TODO can this be done with arbitrary B_factor_list?
+    
+    num_factors = len(H)
+    I = utils.obj_array(num_factors)
+    for factor in range(num_factors):
+        I[factor] = np.zeros((depth, H[factor].shape[0]))
+        I[factor][0, :] = H[factor]
+
+        bf = factor
+        if B_factor_list is not None:
+            if len(B_factor_list[factor]) > 1:
+                raise ValueError("Backwards induction with factorized transition model not yet implemented")
+            bf = B_factor_list[factor][0]
+
+        num_states, _, _ = B[bf].shape
+        b = np.zeros((num_states, num_states))
+        
+        for state in range(num_states):
+            for next_state in range(num_states):
+                # If there exists an action that allows transitioning 
+                # from state to next_state, with probability larger than threshold
+                # set b[state, next_state] to 1
+                if np.any(B[bf][next_state, state, :] > threshold):
+                    b[next_state, state] = 1
+
+        for i in range(1, depth):
+            I[factor][i, :] = np.dot(b, I[factor][i-1, :])
+            I[factor][i, :] = np.where(I[factor][i, :] > 0.1, 1.0, 0.0)
+            # TODO stop when all 1s?
+
+    return I
+
+def calc_ambiguity_factorized(qs_pi, A, A_factor_list):
+    """
+    Computes the Ambiguity term.
+
+    Parameters
+    ----------
+    qs_pi: ``list`` of ``numpy.ndarray`` of dtype object
+        Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about
+        hidden states expected under the policy at time ``t``
+    A: ``numpy.ndarray`` of dtype object
+        Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of
+        stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store 
+        the probability of observation level ``i`` given hidden state levels ``j, k, ...``
+    A_factor_list: ``list`` of ``list`` of ``int``
+        List of lists, where ``A_factor_list[m]`` is a list of the hidden state factor indices that observation modality with the index ``m`` depends on
+
+    Returns
+    -------
+    ambiguity: float
+    """
+
+    n_steps = len(qs_pi)
+
+    ambiguity = 0
+    # TODO check if we do this correctly!
+    H = entropy(A)
+    for t in range(n_steps):
+        for m, H_m in enumerate(H):
+            factor_idx = A_factor_list[m]
+            # TODO why does spm_dot return an array here?
+            # joint_x = maths.spm_cross(qs_pi[t][factor_idx])
+            # ambiguity += (H_m * joint_x).sum()
+            ambiguity += np.sum(spm_dot(H_m, qs_pi[t][factor_idx]))
+
+    return ambiguity
+
+
+def sophisticated_inference_search(qs, policies, A, B, C, A_factor_list, B_factor_list, I=None, horizon=1,
+                                   policy_prune_threshold=1/16, state_prune_threshold=1/16, prune_penalty=512, gamma=16,
+                                   inference_params = {"num_iter": 10, "dF": 1.0, "dF_tol": 0.001, "compute_vfe": False}, n=0):
+    """
+    Performs sophisticated inference to find the optimal policy for a given generative model and prior preferences.
+
+    Parameters
+    ----------
+    qs: ``numpy.ndarray`` of dtype object
+        Marginal posterior beliefs over hidden states at a given timepoint.
+    policies: ``list`` of 1D ``numpy.ndarray``                    inference_params = {"num_iter": 10, "dF": 1.0, "dF_tol": 0.001, "compute_vfe": False}
+
+        ``list`` that stores each policy as a 1D array in ``policies[p_idx]``. Shape of ``policies[p_idx]`` 
+        is ``(num_factors)`` where ``num_factors`` is the number of control factors.        
+    A: ``numpy.ndarray`` of dtype object
+        Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of
+        stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store 
+        the probability of observation level ``i`` given hidden state levels ``j, k, ...``
+    B: ``numpy.ndarray`` of dtype object
+        Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.
+        Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability
+        of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.
+    C: ``numpy.ndarray`` of dtype object
+       Prior over observations or 'prior preferences', storing the "value" of each outcome in terms of relative log probabilities. 
+       This is softmaxed to form a proper probability distribution before being used to compute the expected utility term of the expected free energy.
+    A_factor_list: ``list`` of ``list`` of ``int``
+        List of lists, where ``A_factor_list[m]`` is a list of the hidden state factor indices that observation modality with the index ``m`` depends on
+    B_factor_list: ``list`` of ``list`` of ``int``
+        List of lists of hidden state factors each hidden state factor depends on. Each element ``B_factor_list[i]`` is a list of the factor indices that factor i's dynamics depend on.
+    I: ``numpy.ndarray`` of dtype object
+        For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability 
+        of reaching the goal state backwards from state j after i steps.
+    horizon: ``int``
+        The temporal depth of the policy
+    policy_prune_threshold: ``float``
+        The threshold for pruning policies that are below a certain probability
+    state_prune_threshold: ``float``
+        The threshold for pruning states in the expectation that are below a certain probability
+    prune_penalty: ``float``
+        Penalty to add to the EFE when a policy is pruned
+    gamma: ``float``, default 16.0
+        Prior precision over policies, scales the contribution of the expected free energy to the posterior over policies
+    n: ``int``
+        timestep in the future we are calculating
+        
+    Returns
+    ----------
+    q_pi: 1D ``numpy.ndarray``
+        Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.
+     
+    G: 1D ``numpy.ndarray``
+        Negative expected free energies of each policy, i.e. a vector containing one negative expected free energy per policy.
+    """
+
+    n_policies = len(policies)
+    G = np.zeros(n_policies)
+    q_pi = np.zeros((n_policies, 1))
+    qs_pi = utils.obj_array(n_policies)
+    qo_pi = utils.obj_array(n_policies)
+
+    for idx, policy in enumerate(policies):
+        qs_pi[idx] = get_expected_states_interactions(qs, B, B_factor_list, policy)
+        qo_pi[idx] = get_expected_obs_factorized(qs_pi[idx], A, A_factor_list)
+
+        G[idx] += calc_expected_utility(qo_pi[idx], C)
+        G[idx] += calc_states_info_gain_factorized(A, qs_pi[idx], A_factor_list)
+
+        if I is not None:
+            G[idx] += calc_inductive_cost(qs, qs_pi[idx], I)
+
+    q_pi = softmax(G * gamma)
+
+    if n < horizon - 1:
+        # ignore low probability actions in the search tree
+        # TODO shouldnt we have to add extra penalty for branches no longer considered?
+        # or assume these are already low EFE (high NEFE) anyway?
+        policies_to_consider = list(np.where(q_pi >= policy_prune_threshold)[0])
+        for idx in range(n_policies):
+            if idx not in policies_to_consider:
+                G[idx] -= prune_penalty
+            else :
+                # average over outcomes
+                qo_next = qo_pi[idx][0]
+                for k in itertools.product(*[range(s.shape[0]) for s in qo_next]):
+                    prob = 1.0
+                    for i in range(len(k)):
+                        prob *= qo_pi[idx][0][i][k[i]]
+                    
+                    # ignore low probability states in the search tree
+                    if prob < state_prune_threshold:
+                        continue
+
+                    qo_one_hot = utils.obj_array(len(qo_next))
+                    for i in range(len(qo_one_hot)):
+                        qo_one_hot[i] = utils.onehot(k[i], qo_next[i].shape[0])
+                    
+                    num_obs = [A[m].shape[0] for m in range(len(A))]
+                    num_states = [B[f].shape[0] for f in range(len(B))]
+                    A_modality_list = []
+                    for f in range(len(B)):
+                        A_modality_list.append( [m for m in range(len(A)) if f in A_factor_list[m]] )
+                    mb_dict = {
+                        'A_factor_list': A_factor_list,
+                        'A_modality_list': A_modality_list
+                        }
+                    qs_next = update_posterior_states_factorized(A, qo_one_hot, num_obs, num_states, mb_dict, qs_pi[idx][0], **inference_params)
+                    q_pi_next, G_next = sophisticated_inference_search(qs_next, policies, A, B, C, A_factor_list, B_factor_list, I,
+                                                                       horizon, policy_prune_threshold, state_prune_threshold,
+                                                                       prune_penalty, gamma, inference_params, n+1)
+                    G_weighted = np.dot(q_pi_next, G_next) * prob
+                    G[idx] += G_weighted
+
+    q_pi = softmax(G * gamma)
+    return q_pi, G 
\ No newline at end of file
diff --git a/pymdp/inference.py b/pymdp/inference.py
index 8a77e74c..1b5296b5 100644
--- a/pymdp/inference.py
+++ b/pymdp/inference.py
@@ -5,8 +5,8 @@
 import numpy as np
 
 from pymdp import utils
-from pymdp.maths import get_joint_likelihood_seq
-from pymdp.algos import run_vanilla_fpi, run_mmp, _run_mmp_testing
+from pymdp.maths import get_joint_likelihood_seq, get_joint_likelihood_seq_by_modality
+from pymdp.algos import run_vanilla_fpi, run_vanilla_fpi_factorized, run_mmp, run_mmp_factorized, _run_mmp_testing
 
 VANILLA = "VANILLA"
 VMP = "VMP"
@@ -86,6 +86,86 @@ def update_posterior_states_full(
 
     return qs_seq_pi, F
 
+def update_posterior_states_full_factorized(
+    A,
+    mb_dict,
+    B,
+    B_factor_list,
+    prev_obs,
+    policies,
+    prev_actions=None,
+    prior=None,
+    policy_sep_prior = True,
+    **kwargs,
+):
+    """
+    Update posterior over hidden states using marginal message passing
+
+    Parameters
+    ----------
+    A: ``numpy.ndarray`` of dtype object
+        Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of
+        stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store 
+        the probability of observation level ``i`` given hidden state levels ``j, k, ...``
+    mb_dict: ``Dict``
+        Dictionary with two keys (``A_factor_list`` and ``A_modality_list``), that stores the factor indices that influence each modality (``A_factor_list``)
+        and the modality indices influenced by each factor (``A_modality_list``).
+    B: ``numpy.ndarray`` of dtype object
+        Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.
+        Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability
+        of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.
+    B_factor_list: ``list`` of ``list`` of ``int``
+        List of lists of hidden state factors each hidden state factor depends on. Each element ``B_factor_list[i]`` is a list of the factor indices that factor i's dynamics depend on.
+    prev_obs: ``list``
+        List of observations over time. Each observation in the list can be an ``int``, a ``list`` of ints, a ``tuple`` of ints, a one-hot vector or an object array of one-hot vectors.
+    policies: ``list`` of 2D ``numpy.ndarray``
+        List that stores each policy in ``policies[p_idx]``. Shape of ``policies[p_idx]`` is ``(num_timesteps, num_factors)`` where `num_timesteps` is the temporal
+        depth of the policy and ``num_factors`` is the number of control factors.
+    prior: ``numpy.ndarray`` of dtype object, default ``None``
+        If provided, this a ``numpy.ndarray`` of dtype object, with one sub-array per hidden state factor, that stores the prior beliefs about initial states. 
+        If ``None``, this defaults to a flat (uninformative) prior over hidden states.
+    policy_sep_prior: ``Bool``, default ``True``
+        Flag determining whether the prior beliefs from the past are unconditioned on policy, or separated by /conditioned on the policy variable.
+    **kwargs: keyword arguments
+        Optional keyword arguments for the function ``algos.mmp.run_mmp``
+
+    Returns
+    ---------
+    qs_seq_pi: ``numpy.ndarray`` of dtype object
+        Posterior beliefs over hidden states for each policy. Nesting structure is policies, timepoints, factors,
+        where e.g. ``qs_seq_pi[p][t][f]`` stores the marginal belief about factor ``f`` at timepoint ``t`` under policy ``p``.
+    F: 1D ``numpy.ndarray``
+        Vector of variational free energies for each policy
+    """
+
+    num_obs, num_states, num_modalities, num_factors = utils.get_model_dimensions(A, B)
+    
+    prev_obs = utils.process_observation_seq(prev_obs, num_modalities, num_obs)
+   
+    lh_seq = get_joint_likelihood_seq_by_modality(A, prev_obs, num_states)
+
+    if prev_actions is not None:
+        prev_actions = np.stack(prev_actions,0)
+
+    qs_seq_pi = utils.obj_array(len(policies))
+    F = np.zeros(len(policies)) # variational free energy of policies
+
+    for p_idx, policy in enumerate(policies):
+
+            # get sequence and the free energy for policy
+            qs_seq_pi[p_idx], F[p_idx] = run_mmp_factorized(
+                lh_seq,
+                mb_dict,
+                B,
+                B_factor_list,
+                policy,
+                prev_actions=prev_actions,
+                prior= prior[p_idx] if policy_sep_prior else prior, 
+                **kwargs
+            )
+
+    return qs_seq_pi, F
+
 def _update_posterior_states_full_test(
     A,
     B,
@@ -232,7 +312,7 @@ def update_posterior_states(A, obs, prior=None, **kwargs):
         Marginal posterior beliefs over hidden states at current timepoint
     """
 
-    num_obs, num_states, num_modalities, num_factors = utils.get_model_dimensions(A = A)
+    num_obs, num_states, num_modalities, _ = utils.get_model_dimensions(A = A)
     
     obs = utils.process_observation(obs, num_modalities, num_obs)
 
@@ -240,4 +320,52 @@ def update_posterior_states(A, obs, prior=None, **kwargs):
         prior = utils.to_obj_array(prior)
 
     return run_vanilla_fpi(A, obs, num_obs, num_states, prior, **kwargs)
-   
+
+def update_posterior_states_factorized(A, obs, num_obs, num_states, mb_dict, prior=None, **kwargs):
+    """
+    Update marginal posterior over hidden states using mean-field fixed point iteration 
+    FPI or Fixed point iteration. This version identifies the Markov blanket of each factor using `A_factor_list`
+
+    See the following links for details:
+    http://www.cs.cmu.edu/~guestrin/Class/10708/recitations/r9/VI-view.pdf, slides 13- 18, and http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.137.221&rep=rep1&type=pdf, slides 24 - 38.
+    
+    Parameters
+    ----------
+    A: ``numpy.ndarray`` of dtype object
+        Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of
+        stores an ``np.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store 
+        the probability of observation level ``i`` given hidden state levels ``j, k, ...``
+    obs: 1D ``numpy.ndarray``, ``numpy.ndarray`` of dtype object, int or tuple
+        The observation (generated by the environment). If single modality, this can be a 1D ``np.ndarray``
+        (one-hot vector representation) or an ``int`` (observation index)
+        If multi-modality, this can be ``np.ndarray`` of dtype object whose entries are 1D one-hot vectors,
+        or a tuple (of ``int``)
+    num_obs: ``list`` of ``int``
+        List of dimensionalities of each observation modality
+    num_states: ``list`` of ``int``
+        List of dimensionalities of each hidden state factor
+    mb_dict: ``Dict``
+        Dictionary with two keys (``A_factor_list`` and ``A_modality_list``), that stores the factor indices that influence each modality (``A_factor_list``)
+        and the modality indices influenced by each factor (``A_modality_list``).
+    prior: 1D ``numpy.ndarray`` or ``numpy.ndarray`` of dtype object, default None
+        Prior beliefs about hidden states, to be integrated with the marginal likelihood to obtain
+        a posterior distribution. If not provided, prior is set to be equal to a flat categorical distribution (at the level of
+        the individual inference functions).
+    **kwargs: keyword arguments 
+        List of keyword/parameter arguments corresponding to parameter values for the fixed-point iteration
+        algorithm ``algos.fpi.run_vanilla_fpi.py``
+
+    Returns
+    ----------
+    qs: 1D ``numpy.ndarray`` or ``numpy.ndarray`` of dtype object
+        Marginal posterior beliefs over hidden states at current timepoint
+    """
+    
+    num_modalities = len(num_obs)
+    
+    obs = utils.process_observation(obs, num_modalities, num_obs)
+
+    if prior is not None:
+        prior = utils.to_obj_array(prior)
+
+    return run_vanilla_fpi_factorized(A, obs, num_obs, num_states, mb_dict, prior, **kwargs)
diff --git a/pymdp/jax/__init__.py b/pymdp/jax/__init__.py
new file mode 100644
index 00000000..e69de29b
diff --git a/pymdp/jax/agent.py b/pymdp/jax/agent.py
new file mode 100644
index 00000000..776a65dd
--- /dev/null
+++ b/pymdp/jax/agent.py
@@ -0,0 +1,469 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+""" Agent Class implementation in Jax
+
+__author__: Conor Heins, Dimitrije Markovic, Alexander Tschantz, Daphne Demekas, Brennan Klein
+
+"""
+
+import math as pymath
+import jax.numpy as jnp
+import jax.tree_util as jtu
+from jax import nn, vmap, random
+from . import inference, control, learning, utils, maths
+from equinox import Module, field, tree_at
+
+from typing import List, Optional
+from jaxtyping import Array
+from functools import partial
+
+class Agent(Module):
+    """ 
+    The Agent class, the highest-level API that wraps together processes for action, perception, and learning under active inference.
+
+    The basic usage is as follows:
+
+    >>> my_agent = Agent(A = A, B = C, <more_params>)
+    >>> observation = env.step(initial_action)
+    >>> qs = my_agent.infer_states(observation)
+    >>> q_pi, G = my_agent.infer_policies()
+    >>> next_action = my_agent.sample_action()
+    >>> next_observation = env.step(next_action)
+
+    This represents one timestep of an active inference process. Wrapping this step in a loop with an ``Env()`` class that returns
+    observations and takes actions as inputs, would entail a dynamic agent-environment interaction.
+    """
+
+    A: List[Array]
+    B: List[Array]
+    C: List[Array] 
+    D: List[Array]
+    E: Array
+    # empirical_prior: List
+    gamma: Array
+    alpha: Array
+    qs: Optional[List[Array]]
+    q_pi: Optional[List[Array]]
+
+    # parameters used for inductive inference
+    inductive_threshold: Array # threshold for inductive inference (the threshold for pruning transitions that are below a certain probability)
+    inductive_epsilon: Array # epsilon for inductive inference (trade-off/weight for how much inductive value contributes to EFE of policies)
+
+    H: List[Array] # H vectors (one per hidden state factor) used for inductive inference -- these encode goal states or constraints
+    I: List[Array] # I matrices (one per hidden state factor) used for inductive inference -- these encode the 'reachability' matrices of goal states encoded in `self.H`
+
+    pA: List[Array]
+    pB: List[Array]
+    
+    # static parameters not leaves of the PyTree
+    A_dependencies: Optional[List] = field(static=True)
+    B_dependencies: Optional[List] = field(static=True)
+    batch_size: int = field(static=True)
+    num_iter: int = field(static=True)
+    num_obs: List[int] = field(static=True)
+    num_modalities: int = field(static=True)
+    num_states: List[int] = field(static=True)
+    num_factors: int = field(static=True)
+    num_controls: List[int] = field(static=True)
+    control_fac_idx: Optional[List[int]] = field(static=True)
+    policy_len: int = field(static=True) # depth of planning during roll-outs (i.e. number of timesteps to look ahead when computing expected free energy of policies)
+    inductive_depth: int = field(static=True) # depth of inductive inference (i.e. number of future timesteps to use when computing inductive `I` matrix)
+    policies: Array = field(static=True)  # matrix of all possible policies (each row is a policy of shape (num_controls[0], num_controls[1], ..., num_controls[num_control_factors-1])
+    use_utility: bool = field(static=True) # flag for whether to use expected utility ("reward" or "preference satisfaction") when computing expected free energy
+    use_states_info_gain: bool = field(static=True) # flag for whether to use state information gain ("salience") when computing expected free energy
+    use_param_info_gain: bool = field(static=True)  # flag for whether to use parameter information gain ("novelty") when computing expected free energy
+    use_inductive: bool = field(static=True)   # flag for whether to use inductive inference ("intentional inference") when computing expected free energy
+    onehot_obs: bool = field(static=True)
+    action_selection: str = field(static=True) # determinstic or stochastic action selection 
+    sampling_mode : str = field(static=True) # whether to sample from full posterior over policies ("full") or from marginal posterior over actions ("marginal")
+    inference_algo: str = field(static=True) # fpi, vmp, mmp, ovf
+
+    learn_A: bool = field(static=True)
+    learn_B: bool = field(static=True)
+    learn_C: bool = field(static=True)
+    learn_D: bool = field(static=True)
+    learn_E: bool = field(static=True)
+
+    def __init__(
+        self,
+        A,
+        B,
+        C,
+        D,
+        E,
+        pA,
+        pB,
+        A_dependencies=None,
+        B_dependencies=None,
+        qs=None,
+        q_pi=None,
+        H=None,
+        I=None,
+        policy_len=1,
+        control_fac_idx=None,
+        policies=None,
+        gamma=16.0,
+        alpha=16.0,
+        inductive_depth=1,
+        inductive_threshold=0.1,
+        inductive_epsilon=1e-3,
+        use_utility=True,
+        use_states_info_gain=True,
+        use_param_info_gain=False,
+        use_inductive=False,
+        onehot_obs=False,
+        action_selection="deterministic",
+        sampling_mode="marginal",
+        inference_algo="fpi",
+        num_iter=16,
+        learn_A=True,
+        learn_B=True,
+        learn_C=False,
+        learn_D=True,
+        learn_E=False
+    ):
+        ### PyTree leaves
+        self.A = A
+        self.B = B
+        self.C = C
+        self.D = D
+        # self.empirical_prior = D
+        self.H = H
+        self.pA = pA
+        self.pB = pB
+        self.qs = qs
+        self.q_pi = q_pi
+
+        self.onehot_obs = onehot_obs
+
+        element_size = lambda x: x.shape[1]
+        self.num_factors = len(self.B)
+        self.num_states = jtu.tree_map(element_size, self.B) 
+
+        self.num_modalities = len(self.A)
+        self.num_obs = jtu.tree_map(element_size, self.A)
+
+        # Ensure consistency of A_dependencies with num_states and num_factors
+        if A_dependencies is not None:
+            self.A_dependencies = A_dependencies
+        else:
+            # assume full dependence of A matrices and state factors
+            self.A_dependencies = [list(range(self.num_factors)) for _ in range(self.num_modalities)]
+        
+        for m in range(self.num_modalities):
+            factor_dims = tuple([self.num_states[f] for f in self.A_dependencies[m]])
+            assert self.A[m].shape[2:] == factor_dims, f"Please input an `A_dependencies` whose {m}-th indices correspond to the hidden state factors that line up with lagging dimensions of A[{m}]..." 
+            if self.pA != None:
+                assert self.pA[m].shape[2:] == factor_dims, f"Please input an `A_dependencies` whose {m}-th indices correspond to the hidden state factors that line up with lagging dimensions of pA[{m}]..." 
+            assert max(self.A_dependencies[m]) <= (self.num_factors - 1), f"Check modality {m} of `A_dependencies` - must be consistent with `num_states` and `num_factors`..."
+           
+        # Ensure consistency of B_dependencies with num_states and num_factors
+        if B_dependencies is not None:
+            self.B_dependencies = B_dependencies
+        else:
+            self.B_dependencies = [[f] for f in range(self.num_factors)] # defaults to having all factors depend only on themselves
+
+        for f in range(self.num_factors):
+            factor_dims = tuple([self.num_states[f] for f in self.B_dependencies[f]])
+            assert self.B[f].shape[2:-1] == factor_dims, f"Please input a `B_dependencies` whose {f}-th indices pick out the hidden state factors that line up with the all-but-final lagging dimensions of B[{f}]..." 
+            if self.pB != None:
+                assert self.pB[f].shape[2:-1] == factor_dims, f"Please input a `B_dependencies` whose {f}-th indices pick out the hidden state factors that line up with the all-but-final lagging dimensions of pB[{f}]..." 
+            assert max(self.B_dependencies[f]) <= (self.num_factors - 1), f"Check factor {f} of `B_dependencies` - must be consistent with `num_states` and `num_factors`..."
+
+        self.batch_size = self.A[0].shape[0]
+
+        self.gamma = jnp.broadcast_to(gamma, (self.batch_size,))
+        self.alpha = jnp.broadcast_to(alpha, (self.batch_size,))
+        self.inductive_threshold = jnp.broadcast_to(inductive_threshold, (self.batch_size,))
+        self.inductive_epsilon = jnp.broadcast_to(inductive_epsilon, (self.batch_size,))
+
+        ### Static parameters ###
+        self.num_iter = num_iter
+        self.inference_algo = inference_algo
+        self.inductive_depth = inductive_depth
+
+        # policy parameters
+        self.policy_len = policy_len
+        self.action_selection = action_selection
+        self.sampling_mode = sampling_mode
+        self.use_utility = use_utility
+        self.use_states_info_gain = use_states_info_gain
+        self.use_param_info_gain = use_param_info_gain
+        self.use_inductive = use_inductive
+
+        if self.use_inductive and self.H is not None:
+            # print("Using inductive inference...")
+            self.I = self._construct_I()
+        elif self.use_inductive and I is not None:
+            self.I = I
+        else:
+            self.I = jtu.tree_map(lambda x: jnp.expand_dims(jnp.zeros_like(x), 1), self.D)
+
+        # learning parameters
+        self.learn_A = learn_A
+        self.learn_B = learn_B
+        self.learn_C = learn_C
+        self.learn_D = learn_D
+        self.learn_E = learn_E
+
+        """ Determine number of observation modalities and their respective dimensions """
+        self.num_obs = [self.A[m].shape[1] for m in range(len(self.A))]
+        self.num_modalities = len(self.num_obs)
+
+        # If no `num_controls` are given, then this is inferred from the shapes of the input B matrices
+        self.num_controls = [self.B[f].shape[-1] for f in range(self.num_factors)]
+
+        # Users have the option to make only certain factors controllable.
+        # default behaviour is to make all hidden state factors controllable
+        # (i.e. self.num_states == self.num_controls)
+        # Users have the option to make only certain factors controllable.
+        # default behaviour is to make all hidden state factors controllable, i.e. `self.num_factors == len(self.num_controls)`
+        if control_fac_idx == None:
+            self.control_fac_idx = [f for f in range(self.num_factors) if self.num_controls[f] > 1]
+        else:
+            assert max(control_fac_idx) <= (self.num_factors - 1), "Check control_fac_idx - must be consistent with `num_states` and `num_factors`..."
+            self.control_fac_idx = control_fac_idx
+
+            for factor_idx in self.control_fac_idx:
+                assert self.num_controls[factor_idx] > 1, "Control factor (and B matrix) dimensions are not consistent with user-given control_fac_idx"
+
+        if policies is not None:
+            self.policies = policies
+        else:
+            self._construct_policies()
+        
+        # set E to uniform/uninformative prior over policies if not given
+        if E is None:
+            self.E = jnp.ones((self.batch_size, len(self.policies)))/ len(self.policies)
+        else:
+            self.E = E
+
+    def _construct_policies(self):
+        
+        self.policies =  control.construct_policies(
+            self.num_states, self.num_controls, self.policy_len, self.control_fac_idx
+        )
+
+    @vmap
+    def _construct_I(self):
+        return control.generate_I_matrix(self.H, self.B, self.inductive_threshold, self.inductive_depth)
+
+    @property
+    def unique_multiactions(self):
+        size = pymath.prod(self.num_controls)
+        return jnp.unique(self.policies[:, 0], axis=0, size=size, fill_value=-1)
+
+    @vmap
+    def learning(self, beliefs_A, outcomes, actions, beliefs_B=None, lr_pA=1., lr_pB=1., **kwargs):
+        agent = self
+        if self.learn_A:
+            o_vec_seq = jtu.tree_map(lambda o, dim: nn.one_hot(o, dim), outcomes, self.num_obs)
+            qA = learning.update_obs_likelihood_dirichlet(self.pA, o_vec_seq, beliefs_A, self.A_dependencies, lr=lr_pA)
+            E_qA = jtu.tree_map(lambda x: maths.dirichlet_expected_value(x), qA)
+            agent = tree_at(lambda x: (x.A, x.pA), agent, (E_qA, qA))
+            
+        if self.learn_B:
+            beliefs_B = beliefs_A if beliefs_B is None else beliefs_B
+            actions_seq = [actions[..., i] for i in range(actions.shape[-1])] # as many elements as there are control factors, where each element is a jnp.ndarray of shape (n_timesteps, )
+            assert beliefs_B[0].shape[0] == actions_seq[0].shape[0] + 1
+            actions_onehot = jtu.tree_map(lambda a, dim: nn.one_hot(a, dim, axis=-1), actions_seq, self.num_controls)
+            qB = learning.update_state_likelihood_dirichlet(self.pB, beliefs_B, actions_onehot, self.B_dependencies, lr=lr_pB)
+            E_qB = jtu.tree_map(lambda x: maths.dirichlet_expected_value(x), qB)
+
+            # if you have updated your beliefs about transitions, you need to re-compute the I matrix used for inductive inferenece
+            if self.use_inductive and self.H is not None:
+                I_updated = control.generate_I_matrix(self.H, E_qB, self.inductive_threshold, self.inductive_depth)
+            else:
+                I_updated = self.I
+
+            agent = tree_at(lambda x: (x.B, x.pB, x.I), agent, (E_qB, qB, I_updated))
+ 
+        # if self.learn_C:
+        #     self.qC = learning.update_C(self.C, *args, **kwargs)
+        #     self.C = jtu.tree_map(lambda x: maths.dirichlet_expected_value(x), self.qC)
+        # if self.learn_D:
+        #     self.qD = learning.update_D(self.D, *args, **kwargs)
+        #     self.D = jtu.tree_map(lambda x: maths.dirichlet_expected_value(x), self.qD)
+        # if self.learn_E:
+        #     self.qE = learning.update_E(self.E, *args, **kwargs)
+        #     self.E = maths.dirichlet_expected_value(self.qE)
+
+        # do stuff
+        # variables = ...
+        # parameters = ...
+        # varibles = {'A': jnp.ones(5)}
+
+        # agent = tree_at(lambda x: (x.A, x.pA, x.B, x.pB, x.I), self, (E_qA, qA, E_qB, qB, I_updated))
+
+        return agent
+    
+    @vmap
+    def infer_states(self, observations, past_actions, empirical_prior, qs_hist, mask=None):
+        """
+        Update approximate posterior over hidden states by solving variational inference problem, given an observation.
+
+        Parameters
+        ----------
+        observations: ``list`` or ``tuple`` of ints
+            The observation input. Each entry ``observation[m]`` stores one-hot vectors representing the observations for modality ``m``.
+        past_actions: ``list`` or ``tuple`` of ints
+            The action input. Each entry ``past_actions[f]`` stores indices (or one-hots?) representing the actions for control factor ``f``.
+        empirical_prior: ``list`` or ``tuple`` of ``jax.numpy.ndarray`` of dtype object
+            Empirical prior beliefs over hidden states. Depending on the inference algorithm chosen, the resulting ``empirical_prior`` variable may be a matrix (or list of matrices) 
+            of additional dimensions to encode extra conditioning variables like timepoint and policy.
+        Returns
+        ---------
+        qs: ``numpy.ndarray`` of dtype object
+            Posterior beliefs over hidden states. Depending on the inference algorithm chosen, the resulting ``qs`` variable will have additional sub-structure to reflect whether
+            beliefs are additionally conditioned on timepoint and policy.
+            For example, in case the ``self.inference_algo == 'MMP' `` indexing structure is policy->timepoint-->factor, so that 
+            ``qs[p_idx][t_idx][f_idx]`` refers to beliefs about marginal factor ``f_idx`` expected under policy ``p_idx`` 
+            at timepoint ``t_idx``.
+        """
+        if not self.onehot_obs:
+            o_vec = [nn.one_hot(o, self.num_obs[m]) for m, o in enumerate(observations)]
+        else:
+            o_vec = observations
+        
+        A = self.A
+        if mask is not None:
+            for i, m in enumerate(mask):
+                o_vec[i] = m * o_vec[i] + (1 - m) * jnp.ones_like(o_vec[i]) / self.num_obs[i]
+                A[i] = m * A[i] + (1 - m) * jnp.ones_like(A[i]) / self.num_obs[i]
+        
+        output = inference.update_posterior_states(
+            A,
+            self.B,
+            o_vec,
+            past_actions,
+            prior=empirical_prior,
+            qs_hist=qs_hist,
+            A_dependencies=self.A_dependencies,
+            B_dependencies=self.B_dependencies,
+            num_iter=self.num_iter,
+            method=self.inference_algo
+        )
+
+        return output
+
+    @partial(vmap, in_axes=(0, 0, 0))
+    def update_empirical_prior(self, action, qs):
+        # return empirical_prior, and the history of posterior beliefs (filtering distributions) held about hidden states at times 1, 2 ... t
+
+        qs_last = jtu.tree_map( lambda x: x[-1], qs)
+        # this computation of the predictive prior is correct only for fully factorised Bs.
+        pred = control.compute_expected_state(qs_last, self.B, action, B_dependencies=self.B_dependencies)
+        
+        return (pred, qs)
+
+    @vmap
+    def infer_policies(self, qs: List):
+        """
+        Perform policy inference by optimizing a posterior (categorical) distribution over policies.
+        This distribution is computed as the softmax of ``G * gamma + lnE`` where ``G`` is the negative expected
+        free energy of policies, ``gamma`` is a policy precision and ``lnE`` is the (log) prior probability of policies.
+        This function returns the posterior over policies as well as the negative expected free energy of each policy.
+
+        Returns
+        ----------
+        q_pi: 1D ``numpy.ndarray``
+            Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.
+        G: 1D ``numpy.ndarray``
+            Negative expected free energies of each policy, i.e. a vector containing one negative expected free energy per policy.
+        """
+
+        latest_belief = jtu.tree_map(lambda x: x[-1], qs) # only get the posterior belief held at the current timepoint
+        q_pi, G = control.update_posterior_policies_inductive(
+            self.policies,
+            latest_belief, 
+            self.A,
+            self.B,
+            self.C,
+            self.E,
+            self.pA,
+            self.pB,
+            A_dependencies=self.A_dependencies,
+            B_dependencies=self.B_dependencies,
+            I = self.I,
+            gamma=self.gamma,
+            inductive_epsilon=self.inductive_epsilon,
+            use_utility=self.use_utility,
+            use_states_info_gain=self.use_states_info_gain,
+            use_param_info_gain=self.use_param_info_gain,
+            use_inductive=self.use_inductive
+        )
+
+        return q_pi, G
+    
+    @vmap
+    def multiaction_probabilities(self, q_pi: Array):
+        """
+        Compute probabilities of unique multi-actions from the posterior over policies.
+
+        Parameters
+        ----------
+        q_pi: 1D ``numpy.ndarray``
+        Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.
+        
+        Returns
+        ----------
+        multi-action: 1D ``jax.numpy.ndarray``
+            Vector containing probabilities of possible multi-actions for different factors
+        """
+
+        if self.sampling_mode == "marginal":
+            marginals = control.get_marginals(q_pi, self.policies, self.num_controls)
+            outer = lambda a, b: jnp.outer(a, b).reshape(-1)
+            marginals = jtu.tree_reduce(outer, marginals)
+
+        elif self.sampling_mode == "full":
+            locs = jnp.all(
+                self.policies[:, 0] == jnp.expand_dims(self.unique_multiactions, -2),
+                  -1
+            )
+            marginals = jnp.where(locs, q_pi, 0.).sum(-1)
+
+        # assert jnp.isclose(jnp.sum(marginals), 1.)  # this fails inside scan           
+        return marginals
+
+    @vmap
+    def sample_action(self, q_pi: Array, rng_key=None):
+        """
+        Sample or select a discrete action from the posterior over control states.
+        
+        Returns
+        ----------
+        action: 1D ``jax.numpy.ndarray``
+            Vector containing the indices of the actions for each control factor
+        action_probs: 2D ``jax.numpy.ndarray``
+            Array of action probabilities
+        """
+
+        if (rng_key is None) and (self.action_selection == "stochastic"):
+            raise ValueError("Please provide a random number generator key to sample actions stochastically")
+
+        if self.sampling_mode == "marginal":
+            action = control.sample_action(q_pi, self.policies, self.num_controls, self.action_selection, self.alpha, rng_key=rng_key)
+        elif self.sampling_mode == "full":
+            action = control.sample_policy(q_pi, self.policies, self.num_controls, self.action_selection, self.alpha, rng_key=rng_key)
+
+        return action
+    
+    def _get_default_params(self):
+        method = self.inference_algo
+        default_params = None
+        if method == "VANILLA":
+            default_params = {"num_iter": 8, "dF": 1.0, "dF_tol": 0.001}
+        elif method == "MMP":
+            raise NotImplementedError("MMP is not implemented")
+        elif method == "VMP":
+            raise NotImplementedError("VMP is not implemented")
+        elif method == "BP":
+            raise NotImplementedError("BP is not implemented")
+        elif method == "EP":
+            raise NotImplementedError("EP is not implemented")
+        elif method == "CV":
+            raise NotImplementedError("CV is not implemented")
+
+        return default_params
\ No newline at end of file
diff --git a/pymdp/jax/algos.py b/pymdp/jax/algos.py
new file mode 100644
index 00000000..754d10ce
--- /dev/null
+++ b/pymdp/jax/algos.py
@@ -0,0 +1,377 @@
+import jax.numpy as jnp
+import jax.tree_util as jtu
+
+from jax import jit, vmap, grad, lax, nn
+# from jax.config import config
+# config.update("jax_enable_x64", True)
+
+from .maths import compute_log_likelihood, compute_log_likelihood_per_modality, log_stable, MINVAL, factor_dot, factor_dot_flex
+from typing import Any, List
+
+def add(x, y):
+    return x + y
+
+def marginal_log_likelihood(qs, log_likelihood, i):
+    xs = [q for j, q in enumerate(qs) if j != i]
+    return factor_dot(log_likelihood, xs, keep_dims=(i,))
+
+def all_marginal_log_likelihood(qs, log_likelihoods, all_factor_lists):
+    qL_marginals = jtu.tree_map(lambda ll_m, factor_list_m: mll_factors(qs, ll_m, factor_list_m), log_likelihoods, all_factor_lists)
+    
+    num_factors = len(qs)
+
+    # insted of a double loop we could have a list defining m to f mapping
+    # which could be resolved with a single tree_map cast
+    qL_all = [jnp.zeros(1)] * num_factors
+    for m, factor_list_m in enumerate(all_factor_lists):
+        for l, f in enumerate(factor_list_m):
+            qL_all[f] += qL_marginals[m][l]
+
+    return qL_all
+
+def mll_factors(qs, ll_m, factor_list_m) -> List:
+    relevant_factors = [qs[f] for f in factor_list_m]
+    marginal_ll_f = jtu.Partial(marginal_log_likelihood, relevant_factors, ll_m)
+    loc_nf = len(factor_list_m)
+    loc_factors = list(range(loc_nf))
+    return jtu.tree_map(marginal_ll_f, loc_factors)
+
+def run_vanilla_fpi(A, obs, prior, num_iter=1, distr_obs=True):
+    """ Vanilla fixed point iteration (jaxified) """
+
+    nf = len(prior)
+    factors = list(range(nf))
+    # Step 1: Compute log likelihoods for each factor
+    ll = compute_log_likelihood(obs, A, distr_obs=distr_obs)
+    # log_likelihoods = [ll] * nf
+
+    # Step 2: Map prior to log space and create initial log-posterior
+    log_prior = jtu.tree_map(log_stable, prior)
+    log_q = jtu.tree_map(jnp.zeros_like, prior)
+
+    # Step 3: Iterate until convergence
+    def scan_fn(carry, t):
+        log_q = carry
+        q = jtu.tree_map(nn.softmax, log_q)
+        mll = jtu.Partial(marginal_log_likelihood, q, ll)
+        marginal_ll = jtu.tree_map(mll, factors)
+        log_q = jtu.tree_map(add, marginal_ll, log_prior)
+
+        return log_q, None
+
+    res, _ = lax.scan(scan_fn, log_q, jnp.arange(num_iter))
+
+    # Step 4: Map result to factorised posterior
+    qs = jtu.tree_map(nn.softmax, res)
+    return qs
+
+def run_factorized_fpi(A, obs, prior, A_dependencies, num_iter=1):
+    """
+    Run the fixed point iteration algorithm with sparse dependencies between factors and outcomes (stored in `A_dependencies`)
+    """
+
+    # Step 1: Compute log likelihoods for each factor
+    log_likelihoods = compute_log_likelihood_per_modality(obs, A)
+
+    # Step 2: Map prior to log space and create initial log-posterior
+    log_prior = jtu.tree_map(log_stable, prior)
+    log_q = jtu.tree_map(jnp.zeros_like, prior)
+
+    # Step 3: Iterate until convergence
+    def scan_fn(carry, t):
+        log_q = carry
+        q = jtu.tree_map(nn.softmax, log_q)
+        marginal_ll = all_marginal_log_likelihood(q, log_likelihoods, A_dependencies)
+        log_q = jtu.tree_map(add, marginal_ll, log_prior)
+
+        return log_q, None
+
+    res, _ = lax.scan(scan_fn, log_q, jnp.arange(num_iter))
+
+    # Step 4: Map result to factorised posterior
+    qs = jtu.tree_map(nn.softmax, res)
+    return qs
+
+def mirror_gradient_descent_step(tau, ln_A, lnB_past, lnB_future, ln_qs):
+    """
+    u_{k+1} = u_{k} - \nabla_p F_k
+    p_k = softmax(u_k)
+    """
+    err = ln_A - ln_qs + lnB_past + lnB_future
+    ln_qs = ln_qs + tau * err
+    qs = nn.softmax(ln_qs - ln_qs.mean(axis=-1, keepdims=True))
+
+    return qs
+
+def update_marginals(get_messages, obs, A, B, prior, A_dependencies, B_dependencies, num_iter=1, tau=1.,):
+    """" Version of marginal update that uses a sparse dependency matrix for A """
+
+    T = obs[0].shape[0]
+    ln_B = jtu.tree_map(log_stable, B)
+    # log likelihoods -> $\ln(A)$ for all time steps
+    # for $k > t$ we have $\ln(A) = 0$
+
+    def get_log_likelihood(obs_t, A):
+       # # mapping over batch dimension
+       # return vmap(compute_log_likelihood_per_modality)(obs_t, A)
+       return compute_log_likelihood_per_modality(obs_t, A)
+
+    # mapping over time dimension of obs array
+    log_likelihoods = vmap(get_log_likelihood, (0, None))(obs, A) # this gives a sequence of log-likelihoods (one for each `t`)
+
+    # log marginals -> $\ln(q(s_t))$ for all time steps and factors
+    ln_qs = jtu.tree_map( lambda p: jnp.broadcast_to(jnp.zeros_like(p), (T,) + p.shape), prior)
+
+    # log prior -> $\ln(p(s_t))$ for all factors
+    ln_prior = jtu.tree_map(log_stable, prior)
+
+    qs = jtu.tree_map(nn.softmax, ln_qs)
+
+    def scan_fn(carry, iter):
+        qs = carry
+
+        ln_qs = jtu.tree_map(log_stable, qs)
+        # messages from future $m_+(s_t)$ and past $m_-(s_t)$ for all time steps and factors. For t = T we have that $m_+(s_T) = 0$
+        
+        lnB_past, lnB_future = get_messages(ln_B, B, qs, ln_prior, B_dependencies)
+
+        mgds = jtu.Partial(mirror_gradient_descent_step, tau)
+
+        ln_As = vmap(all_marginal_log_likelihood, in_axes=(0, 0, None))(qs, log_likelihoods, A_dependencies)
+
+        qs = jtu.tree_map(mgds, ln_As, lnB_past, lnB_future, ln_qs)
+
+        return qs, None
+
+    qs, _ = lax.scan(scan_fn, qs, jnp.arange(num_iter))
+
+    return qs
+
+def variational_filtering_step(prior, Bs, ln_As, A_dependencies):
+
+    ln_prior = jtu.tree_map(log_stable, prior)
+    
+    #TODO: put this inside scan
+    ####
+    marg_ln_As = all_marginal_log_likelihood(prior, ln_As, A_dependencies)
+
+    # compute posterior q(z_t) -> n x 1 x d
+    post = jtu.tree_map( 
+            lambda x, y: nn.softmax(x + y, -1), marg_ln_As, ln_prior 
+        )
+    ####
+
+    # compute prediction p(z_{t+1}) = \int p(z_{t+1}|z_t) q(z_t) -> n x d x 1
+    pred = jtu.tree_map(
+            lambda x, y: jnp.sum(x * jnp.expand_dims(y, -2), -1), Bs, post
+        )
+    
+    # compute reverse conditional distribution q(z_t|z_{t+1})
+    cond = jtu.tree_map(
+        lambda x, y, z: x * jnp.expand_dims(y, -2) / jnp.expand_dims(z, -1),
+        Bs,
+        post, 
+        pred
+    )
+
+    return post, pred, cond
+
+def update_variational_filtering(obs, A, B, prior, A_dependencies, **kwargs):
+    """Online variational filtering belief update that uses a sparse dependency matrix for A"""
+
+    T = obs[0].shape[0]
+    def pad(x):
+        npad = [(0, 0)] * jnp.ndim(x)
+        npad[0] = (0, 1)
+        return jnp.pad(x, npad, constant_values=1.)
+    
+    B = jtu.tree_map(pad, B)
+ 
+    def get_log_likelihood(obs_t, A):
+        # mapping over batch dimension
+        return vmap(compute_log_likelihood_per_modality)(obs_t, A)
+
+    # mapping over time dimension of obs array
+    log_likelihoods = vmap(get_log_likelihood, (0, None))(obs, A) # this gives a sequence of log-likelihoods (one for each `t`)
+    
+    def scan_fn(carry, iter):
+        _, prior = carry
+        Bs, ln_As = iter
+
+        post, pred, cond = variational_filtering_step(prior, Bs, ln_As, A_dependencies)
+        
+        return (post, pred), cond
+
+    init = (prior, prior)
+    iterator = (B, log_likelihoods)
+    # get q_T(s_t), p_T(s_{t+1}) and the history q_{T}(s_{t}|s_{t+1})q_{T-1}(s_{t-1}|s_{t}) ...
+    (qs, ps), qss = lax.scan(scan_fn, init, iterator)
+
+    return qs, ps, qss
+
+def get_vmp_messages(ln_B, B, qs, ln_prior, B_dependencies):
+    
+    num_factors = len(qs)
+    factors = list(range(num_factors))
+    get_deps = lambda x, f_idx: [x[f] for f in f_idx] # function that effectively "slices" a list with a set of indices `f_idx`
+
+    # make a list of lists, where each list contains all dependencies of a factor except itself
+    all_deps_except_f = jtu.tree_map( 
+        lambda f: [d for d in B_dependencies[f] if d != f], 
+        factors
+    )
+
+    # make list of integers, where each integer is the position of the self-factor in its dependencies list
+    position = jtu.tree_map(
+        lambda f: B_dependencies[f].index(f),
+        factors
+    )
+
+    if ln_B is not None:
+        ln_B_marg = jtu.tree_map( # this is a list of matrices, where each matrix is the marginal transition tensor for factor f
+            lambda b, f: factor_dot(b, get_deps(qs, all_deps_except_f[f]), keep_dims=(0, 1, 2 + position[f])), 
+            ln_B, 
+            factors
+        )  # shape = (T, states_f_{t+1}, states_f_{t})
+    else:
+        ln_B_marg = None
+
+    def forward(ln_b, q, ln_prior):
+        msg = vmap(lambda x, y: y @ x)(q[:-1], ln_b) # ln_b has shape (num_states, num_states) qs[:-1] has shape (T-1, num_states)
+        return jnp.concatenate([jnp.expand_dims(ln_prior, 0), msg], axis=0)
+    
+    def backward(ln_b, q):
+        # q_i B_ij
+        msg = vmap(lambda x, y: x @ y)(q[1:], ln_b)
+        return jnp.pad(msg, ((0, 1), (0, 0)))
+
+    if ln_B_marg is not None:
+        lnB_future = jtu.tree_map(forward, ln_B_marg, qs, ln_prior)
+        lnB_past = jtu.tree_map(backward, ln_B_marg, qs)
+    else:
+        lnB_future = jtu.tree_map(lambda x: 0., qs)
+        lnB_past = jtu.tree_map(lambda x: 0., qs)
+    
+    return lnB_future, lnB_past 
+
+def run_vmp(A, B, obs, prior, A_dependencies, B_dependencies, num_iter=1, tau=1.):
+    '''
+    Run variational message passing (VMP) on a sequence of observations
+    '''
+
+    qs = update_marginals(
+        get_vmp_messages, 
+        obs, 
+        A, 
+        B, 
+        prior, 
+        A_dependencies, 
+        B_dependencies, 
+        num_iter=num_iter, 
+        tau=tau
+    )
+    return qs
+
+def get_mmp_messages(ln_B, B, qs, ln_prior, B_deps):
+    
+    num_factors = len(qs)
+    factors = list(range(num_factors))
+
+    get_deps_forw = lambda x, f_idx: [x[f][:-1] for f in f_idx]
+    get_deps_back = lambda x, f_idx: [x[f][1:] for f in f_idx]
+
+    def forward(b, ln_prior, f):
+        xs = get_deps_forw(qs, B_deps[f])
+        dims = tuple((0, 2 + i) for i in range(len(B_deps[f])))
+        msg = log_stable(factor_dot_flex(b, xs, dims, keep_dims=(0, 1) ))
+        # append log_prior as a first message 
+        msg = jnp.concatenate([jnp.expand_dims(ln_prior, 0), msg], axis=0)
+        # mutliply with 1/2 all but the last msg
+        T = len(msg)
+        if T > 1:
+            msg = msg * jnp.pad( 0.5 * jnp.ones(T - 1), (0, 1), constant_values=1.)[:, None]
+
+        return msg
+    
+    def backward(Bs, xs):
+        msg = 0.
+        for i, b in enumerate(Bs):
+            b_norm = b / (b.sum(-1, keepdims=True) + 1e-16)
+            msg += log_stable(vmap(lambda x, y: y @ x)(b_norm, xs[i])) * .5
+        
+        return jnp.pad(msg, ((0, 1), (0, 0)))
+
+    def marg(inv_deps, f):
+        B_marg = []
+        for i in inv_deps:
+            b = B[i]
+            keep_dims = (0, 1, 2 + B_deps[i].index(f))
+            dims = []
+            idxs = []
+            for j, d in enumerate(B_deps[i]):
+                if f != d:
+                    dims.append((0, 2 + j))
+                    idxs.append(d)
+            xs = get_deps_forw(qs, idxs)
+            B_marg.append( factor_dot_flex(b, xs, tuple(dims), keep_dims=keep_dims) )
+        
+        return B_marg
+
+    if B is not None:
+        inv_B_deps = [[i for i, d in enumerate(B_deps) if f in d] for f in factors]
+        B_marg = jtu.tree_map(lambda f: marg(inv_B_deps[f], f), factors)
+        lnB_future = jtu.tree_map(forward, B, ln_prior, factors) 
+        lnB_past = jtu.tree_map(lambda f: backward(B_marg[f], get_deps_back(qs, inv_B_deps[f])), factors)
+    else: 
+        lnB_future = jtu.tree_map(lambda x: jnp.expand_dims(x, 0), ln_prior)
+        lnB_past = jtu.tree_map(lambda x: 0., qs)
+
+    return lnB_future, lnB_past
+
+def run_mmp(A, B, obs, prior, A_dependencies, B_dependencies, num_iter=1, tau=1.):
+    qs = update_marginals(
+        get_mmp_messages, 
+        obs, 
+        A, 
+        B, 
+        prior, 
+        A_dependencies, 
+        B_dependencies, 
+        num_iter=num_iter, 
+        tau=tau
+    )
+    return qs
+
+def run_online_filtering(A, B, obs, prior, A_dependencies, num_iter=1, tau=1.):
+    """Runs online filtering (HAVE TO REPLACE WITH OVF CODE)"""
+    qs = update_marginals(get_mmp_messages, obs, A, B, prior, A_dependencies, num_iter=num_iter, tau=tau)
+    return qs 
+
+if __name__ == "__main__":
+    prior = [jnp.ones(2)/2, jnp.ones(2)/2, nn.softmax(jnp.array([0, -80., -80., -80, -80.]))]
+    obs = [nn.one_hot(0, 5), nn.one_hot(5, 10)]
+    A = [jnp.ones((5, 2, 2, 5))/5, jnp.ones((10, 2, 2, 5))/10]
+    
+    qs = jit(run_vanilla_fpi)(A, obs, prior)
+
+    # test if differentiable
+    from functools import partial
+
+    def sum_prod(prior):
+        qs = jnp.concatenate(run_vanilla_fpi(A, obs, prior))
+        return (qs * log_stable(qs)).sum()
+
+    print(jit(grad(sum_prod))(prior))
+
+    # def sum_prod(precision):
+    #     # prior = [jnp.ones(2)/2, jnp.ones(2)/2, nn.softmax(log_prior)]
+    #     prior = [jnp.ones(2)/2, jnp.ones(2)/2, nn.softmax(precision*nn.one_hot(0, 5))]
+    #     qs = jnp.concatenate(run_vanilla_fpi(A, obs, prior))
+    #     return (qs * log_stable(qs)).sum()
+
+    # precis_to_test = 1.
+    # print(jit(grad(sum_prod))(precis_to_test))
+
+    # log_prior = jnp.array([0, -80., -80., -80, -80.])
+    # print(jit(grad(sum_prod))(log_prior))
+
diff --git a/pymdp/jax/control.py b/pymdp/jax/control.py
new file mode 100644
index 00000000..b02cafe0
--- /dev/null
+++ b/pymdp/jax/control.py
@@ -0,0 +1,480 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+# pylint: disable=no-member
+# pylint: disable=not-an-iterable
+
+import itertools
+import jax.numpy as jnp
+import jax.tree_util as jtu
+from typing import List, Tuple, Optional
+from functools import partial
+from jax.scipy.special import xlogy
+from jax import lax, jit, vmap, nn
+from jax import random as jr
+from itertools import chain
+from jaxtyping import Array
+
+from pymdp.jax.maths import *
+# import pymdp.jax.utils as utils
+
+def get_marginals(q_pi, policies, num_controls):
+    """
+    Computes the marginal posterior(s) over actions by integrating their posterior probability under the policies that they appear within.
+
+    Parameters
+    ----------
+    q_pi: 1D ``numpy.ndarray``
+        Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.
+    policies: ``list`` of 2D ``numpy.ndarray``
+        ``list`` that stores each policy as a 2D array in ``policies[p_idx]``. Shape of ``policies[p_idx]`` 
+        is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal
+        depth of the policy and ``num_factors`` is the number of control factors.
+    num_controls: ``list`` of ``int``
+        ``list`` of the dimensionalities of each control state factor.
+    
+    Returns
+    ----------
+    action_marginals: ``list`` of ``jax.numpy.ndarrays``
+       List of arrays corresponding to marginal probability of each action possible action
+    """
+    num_factors = len(num_controls)    
+
+    action_marginals = []
+    for factor_i in range(num_factors):
+        actions = jnp.arange(num_controls[factor_i])[:, None]
+        action_marginals.append(jnp.where(actions==policies[:, 0, factor_i], q_pi, 0).sum(-1))
+    
+    return action_marginals
+
+def sample_action(q_pi, policies, num_controls, action_selection="deterministic", alpha=16.0, rng_key=None):
+    """
+    Samples an action from posterior marginals, one action per control factor.
+
+    Parameters
+    ----------
+    q_pi: 1D ``numpy.ndarray``
+        Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.
+    policies: ``list`` of 2D ``numpy.ndarray``
+        ``list`` that stores each policy as a 2D array in ``policies[p_idx]``. Shape of ``policies[p_idx]`` 
+        is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal
+        depth of the policy and ``num_factors`` is the number of control factors.
+    num_controls: ``list`` of ``int``
+        ``list`` of the dimensionalities of each control state factor.
+    action_selection: string, default "deterministic"
+        String indicating whether whether the selected action is chosen as the maximum of the posterior over actions,
+        or whether it's sampled from the posterior marginal over actions
+    alpha: float, default 16.0
+        Action selection precision -- the inverse temperature of the softmax that is used to scale the 
+        action marginals before sampling. This is only used if ``action_selection`` argument is "stochastic"
+
+    Returns
+    ----------
+    selected_policy: 1D ``numpy.ndarray``
+        Vector containing the indices of the actions for each control factor
+    """
+
+    marginal = get_marginals(q_pi, policies, num_controls)
+    
+    if action_selection == 'deterministic':
+        selected_policy = jtu.tree_map(lambda x: jnp.argmax(x, -1), marginal)
+    elif action_selection == 'stochastic':
+        logits = lambda x: alpha * log_stable(x)
+        selected_policy = jtu.tree_map(lambda x: jr.categorical(rng_key, logits(x)), marginal)
+    else:
+        raise NotImplementedError
+
+    return jnp.array(selected_policy)
+
+def sample_policy(q_pi, policies, num_controls, action_selection="deterministic", alpha = 16.0, rng_key=None):
+
+    if action_selection == "deterministic":
+        policy_idx = jnp.argmax(q_pi)
+    elif action_selection == "stochastic":
+        log_p_policies = log_stable(q_pi) * alpha
+        policy_idx = jr.categorical(rng_key, log_p_policies)
+
+    selected_multiaction = policies[policy_idx, 0]
+    return selected_multiaction
+
+def construct_policies(num_states, num_controls = None, policy_len=1, control_fac_idx=None):
+    """
+    Generate a ``list`` of policies. The returned array ``policies`` is a ``list`` that stores one policy per entry.
+    A particular policy (``policies[i]``) has shape ``(num_timesteps, num_factors)`` 
+    where ``num_timesteps`` is the temporal depth of the policy and ``num_factors`` is the number of control factors.
+
+    Parameters
+    ----------
+    num_states: ``list`` of ``int``
+        ``list`` of the dimensionalities of each hidden state factor
+    num_controls: ``list`` of ``int``, default ``None``
+        ``list`` of the dimensionalities of each control state factor. If ``None``, then is automatically computed as the dimensionality of each hidden state factor that is controllable
+    policy_len: ``int``, default 1
+        temporal depth ("planning horizon") of policies
+    control_fac_idx: ``list`` of ``int``
+        ``list`` of indices of the hidden state factors that are controllable (i.e. those state factors ``i`` where ``num_controls[i] > 1``)
+
+    Returns
+    ----------
+    policies: ``list`` of 2D ``numpy.ndarray``
+        ``list`` that stores each policy as a 2D array in ``policies[p_idx]``. Shape of ``policies[p_idx]`` 
+        is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal
+        depth of the policy and ``num_factors`` is the number of control factors.
+    """
+
+    num_factors = len(num_states)
+    if control_fac_idx is None:
+        if num_controls is not None:
+            control_fac_idx = [f for f, n_c in enumerate(num_controls) if n_c > 1]
+        else:
+            control_fac_idx = list(range(num_factors))
+
+    if num_controls is None:
+        num_controls = [num_states[c_idx] if c_idx in control_fac_idx else 1 for c_idx in range(num_factors)]
+        
+    x = num_controls * policy_len
+    policies = list(itertools.product(*[list(range(i)) for i in x]))
+    
+    for pol_i in range(len(policies)):
+        policies[pol_i] = jnp.array(policies[pol_i]).reshape(policy_len, num_factors)
+
+    return jnp.stack(policies)
+
+
+def update_posterior_policies(policy_matrix, qs_init, A, B, C, E, pA, pB, A_dependencies, B_dependencies, gamma=16.0, use_utility=True, use_states_info_gain=True, use_param_info_gain=False):
+    # policy --> n_levels_factor_f x 1
+    # factor --> n_levels_factor_f x n_policies
+    ## vmap across policies
+    compute_G_fixed_states = partial(compute_G_policy, qs_init, A, B, C, pA, pB, A_dependencies, B_dependencies,
+                                     use_utility=use_utility, use_states_info_gain=use_states_info_gain, use_param_info_gain=use_param_info_gain)
+
+    # only in the case of policy-dependent qs_inits
+    # in_axes_list = (1,) * n_factors
+    # all_efe_of_policies = vmap(compute_G_policy, in_axes=(in_axes_list, 0))(qs_init_pi, policy_matrix)
+
+    # policies needs to be an NDarray of shape (n_policies, n_timepoints, n_control_factors)
+    neg_efe_all_policies = vmap(compute_G_fixed_states)(policy_matrix)
+
+    return nn.softmax(gamma * neg_efe_all_policies + log_stable(E)), neg_efe_all_policies
+
+def compute_expected_state(qs_prior, B, u_t, B_dependencies=None): 
+    """
+    Compute posterior over next state, given belief about previous state, transition model and action...
+    """
+    #Note: this algorithm is only correct if each factor depends only on itself. For any interactions, 
+    # we will have empirical priors with codependent factors. 
+    assert len(u_t) == len(B)  
+    qs_next = []
+    for B_f, u_f, deps in zip(B, u_t, B_dependencies):
+        relevant_factors = [qs_prior[idx] for idx in deps]
+        qs_next_f = factor_dot(B_f[...,u_f], relevant_factors, keep_dims=(0,))
+        qs_next.append(qs_next_f)
+        
+    # P(s'|s, u) = \sum_{s, u} P(s'|s) P(s|u) P(u|pi)P(pi) because u </-> pi
+    return qs_next
+
+def compute_expected_state_and_Bs(qs_prior, B, u_t): 
+    """
+    Compute posterior over next state, given belief about previous state, transition model and action...
+    """
+    assert len(u_t) == len(B)  
+    qs_next = []
+    Bs = []
+    for qs_f, B_f, u_f in zip(qs_prior, B, u_t):
+        qs_next.append( B_f[..., u_f].dot(qs_f) )
+        Bs.append(B_f[..., u_f])
+    
+    return qs_next, Bs
+
+def compute_expected_obs(qs, A, A_dependencies):
+    """
+    New version of expected observation (computation of Q(o|pi)) that takes into account sparse dependencies between observation
+    modalities and hidden state factors
+    """
+        
+    def compute_expected_obs_modality(A_m, m):
+        deps = A_dependencies[m]
+        relevant_factors = [qs[idx] for idx in deps]
+        return factor_dot(A_m, relevant_factors, keep_dims=(0,))
+
+    return jtu.tree_map(compute_expected_obs_modality, A, list(range(len(A))))
+
+def compute_info_gain(qs, qo, A, A_dependencies):
+    """
+    New version of expected information gain that takes into account sparse dependencies between observation modalities and hidden state factors.
+    """
+
+    def compute_info_gain_for_modality(qo_m, A_m, m):
+        H_qo = - xlogy(qo_m, qo_m).sum()
+        # H_qo = - (qo_m * log_stable(qo_m)).sum()
+        H_A_m = - xlogy(A_m, A_m).sum(0)
+        # H_A_m = - (A_m * log_stable(A_m)).sum(0)
+        deps = A_dependencies[m]
+        relevant_factors = [qs[idx] for idx in deps]
+        qs_H_A_m = factor_dot(H_A_m, relevant_factors)
+        return H_qo - qs_H_A_m
+    
+    info_gains_per_modality = jtu.tree_map(compute_info_gain_for_modality, qo, A, list(range(len(A))))
+        
+    return jtu.tree_reduce(lambda x,y: x+y, info_gains_per_modality)
+
+# qs_H_A = 0 # expected entropy of the likelihood, under Q(s)
+# H_qo = 0 # marginal entropy of Q(o)
+# for a, o, deps in zip(A, qo, A_dependencies):
+#     relevant_factors = jtu.tree_map(lambda idx: qs[idx], deps)
+#     qs_joint_relevant = relevant_factors[0]
+#     for q in relevant_factors[1:]:
+#         qs_joint_relevant = jnp.expand_dims(qs_joint_relevant, -1) * q
+#     H_A_m = -(a * log_stable(a)).sum(0)
+#     qs_H_A += (H_A_m * qs_joint_relevant).sum()
+
+#     H_qo -= (o * log_stable(o)).sum()
+
+def compute_expected_utility(qo, C):
+    
+    util = 0.
+    for o_m, C_m in zip(qo, C):
+        util += (o_m * C_m).sum()
+    
+    return util
+
+def calc_pA_info_gain(pA, qo, qs, A_dependencies):
+    """
+    Compute expected Dirichlet information gain about parameters ``pA`` for a given posterior predictive distribution over observations ``qo`` and states ``qs``.
+
+    Parameters
+    ----------
+    pA: ``numpy.ndarray`` of dtype object
+        Dirichlet parameters over observation model (same shape as ``A``)
+    qo: ``list`` of ``numpy.ndarray`` of dtype object
+        Predictive posterior beliefs over observations; stores the beliefs about
+        observations expected under the policy at some arbitrary time ``t``
+    qs: ``list`` of ``numpy.ndarray`` of dtype object
+        Predictive posterior beliefs over hidden states, stores the beliefs about
+        hidden states expected under the policy at some arbitrary time ``t``
+
+    Returns
+    -------
+    infogain_pA: float
+        Surprise (about Dirichlet parameters) expected for the pair of posterior predictive distributions ``qo`` and ``qs``
+    """
+
+    wA = lambda pa: spm_wnorm(pa) * (pa > 0.)
+    fd = lambda x, i: factor_dot(x, [s for f, s in enumerate(qs) if f in A_dependencies[i]], keep_dims=(0,))[..., None]
+    pA_infogain_per_modality = jtu.tree_map(
+        lambda pa, qo, m: qo.dot(fd( wA(pa), m)), pA, qo, list(range(len(qo)))
+    )
+    infogain_pA = jtu.tree_reduce(lambda x, y: x + y, pA_infogain_per_modality)[0]
+    return infogain_pA
+
+def calc_pB_info_gain(pB, qs_t, qs_t_minus_1, B_dependencies, u_t_minus_1):
+    """
+    Compute expected Dirichlet information gain about parameters ``pB`` under a given policy
+
+    Parameters
+    ----------
+    pB: ``Array`` of dtype object
+        Dirichlet parameters over transition model (same shape as ``B``)
+    qs_t: ``list`` of ``Array`` of dtype object
+        Predictive posterior beliefs over hidden states expected under the policy at time ``t``
+    qs_t_minus_1: ``list`` of ``Array`` of dtype object
+        Posterior over hidden states at time ``t-1`` (before receiving observations)
+    u_t_minus_1: "Array"
+        Actions in time step t-1 for each factor
+
+    Returns
+    -------
+    infogain_pB: float
+        Surprise (about Dirichlet parameters) expected under the policy in question
+    """
+    
+    wB = lambda pb:  spm_wnorm(pb) * (pb > 0.)
+    fd = lambda x, i: factor_dot(x, [s for f, s in enumerate(qs_t_minus_1) if f in B_dependencies[i]], keep_dims=(0,))[..., None]
+    
+    pB_infogain_per_factor = jtu.tree_map(lambda pb, qs, f: qs.dot(fd(wB(pb[..., u_t_minus_1[f]]), f)), pB, qs_t, list(range(len(qs_t))))
+    infogain_pB = jtu.tree_reduce(lambda x, y: x + y, pB_infogain_per_factor)[0]
+    return infogain_pB
+
+def compute_G_policy(qs_init, A, B, C, pA, pB, A_dependencies, B_dependencies, policy_i, use_utility=True, use_states_info_gain=True, use_param_info_gain=False):
+    """ Write a version of compute_G_policy that does the same computations as `compute_G_policy` but using `lax.scan` instead of a for loop. """
+
+    def scan_body(carry, t):
+
+        qs, neg_G = carry
+
+        qs_next = compute_expected_state(qs, B, policy_i[t], B_dependencies)
+
+        qo = compute_expected_obs(qs_next, A, A_dependencies)
+
+        info_gain = compute_info_gain(qs_next, qo, A, A_dependencies) if use_states_info_gain else 0.
+
+        utility = compute_expected_utility(qo, C) if use_utility else 0.
+
+        param_info_gain = calc_pA_info_gain(pA, qo, qs_next) if use_param_info_gain else 0.
+        param_info_gain += calc_pB_info_gain(pB, qs_next, qs, policy_i[t]) if use_param_info_gain else 0.
+
+        neg_G += info_gain + utility + param_info_gain
+
+        return (qs_next, neg_G), None
+
+    qs = qs_init
+    neg_G = 0.
+    final_state, _ = lax.scan(scan_body, (qs, neg_G), jnp.arange(policy_i.shape[0]))
+    qs_final, neg_G = final_state
+    return neg_G
+
+def compute_G_policy_inductive(qs_init, A, B, C, pA, pB, A_dependencies, B_dependencies, I, policy_i, inductive_epsilon=1e-3, use_utility=True, use_states_info_gain=True, use_param_info_gain=False, use_inductive=False):
+    """ 
+    Write a version of compute_G_policy that does the same computations as `compute_G_policy` but using `lax.scan` instead of a for loop.
+    This one further adds computations used for inductive planning.
+    """
+
+    def scan_body(carry, t):
+
+        qs, neg_G = carry
+
+        qs_next = compute_expected_state(qs, B, policy_i[t], B_dependencies)
+
+        qo = compute_expected_obs(qs_next, A, A_dependencies)
+
+        info_gain = compute_info_gain(qs_next, qo, A, A_dependencies) if use_states_info_gain else 0.
+
+        utility = compute_expected_utility(qo, C) if use_utility else 0.
+
+        inductive_value = calc_inductive_value_t(qs_init, qs_next, I, epsilon=inductive_epsilon) if use_inductive else 0.
+
+        param_info_gain = calc_pA_info_gain(pA, qo, qs_next, A_dependencies) if use_param_info_gain else 0.
+        param_info_gain += calc_pB_info_gain(pB, qs_next, qs, B_dependencies, policy_i[t]) if use_param_info_gain else 0.
+
+        neg_G += info_gain + utility - param_info_gain + inductive_value
+
+        return (qs_next, neg_G), None
+
+    qs = qs_init
+    neg_G = 0.
+    final_state, _ = lax.scan(scan_body, (qs, neg_G), jnp.arange(policy_i.shape[0]))
+    _, neg_G = final_state
+    return neg_G
+
+def update_posterior_policies_inductive(policy_matrix, qs_init, A, B, C, E, pA, pB, A_dependencies, B_dependencies, I, gamma=16.0, inductive_epsilon=1e-3, use_utility=True, use_states_info_gain=True, use_param_info_gain=False, use_inductive=True):
+    # policy --> n_levels_factor_f x 1
+    # factor --> n_levels_factor_f x n_policies
+    ## vmap across policies
+    compute_G_fixed_states = partial(compute_G_policy_inductive, qs_init, A, B, C, pA, pB, A_dependencies, B_dependencies, I, inductive_epsilon=inductive_epsilon,
+                                     use_utility=use_utility,  use_states_info_gain=use_states_info_gain, use_param_info_gain=use_param_info_gain, use_inductive=use_inductive)
+
+    # only in the case of policy-dependent qs_inits
+    # in_axes_list = (1,) * n_factors
+    # all_efe_of_policies = vmap(compute_G_policy, in_axes=(in_axes_list, 0))(qs_init_pi, policy_matrix)
+
+    # policies needs to be an NDarray of shape (n_policies, n_timepoints, n_control_factors)
+    neg_efe_all_policies = vmap(compute_G_fixed_states)(policy_matrix)
+
+    return nn.softmax(gamma * neg_efe_all_policies + log_stable(E)), neg_efe_all_policies
+
+def generate_I_matrix(H: List[Array], B: List[Array], threshold: float, depth: int):
+    """ 
+    Generates the `I` matrices used in inductive planning. These matrices stores the probability of reaching the goal state backwards from state j (columns) after i (rows) steps.
+    Parameters
+    ----------    
+    H: ``list`` of ``jax.numpy.ndarray``
+        Constraints over desired states (1 if you want to reach that state, 0 otherwise)
+    B: ``list`` of ``jax.numpy.ndarray``
+        Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.
+        Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability
+        of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.
+    threshold: ``float``
+        The threshold for pruning transitions that are below a certain probability
+    depth: ``int``
+        The temporal depth of the backward induction
+
+    Returns
+    ----------
+    I: ``numpy.ndarray`` of dtype object
+        For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability 
+        of reaching the goal state backwards from state j after i steps.
+    """
+    
+    num_factors = len(H)
+    I = []
+    for f in range(num_factors):
+        """
+        For each factor, we need to compute the probability of reaching the goal state
+        """
+
+        # If there exists an action that allows transitioning 
+        # from state to next_state, with probability larger than threshold
+        # set b_reachable[current_state, previous_state] to 1
+        b_reachable = jnp.where(B[f] > threshold, 1.0, 0.0).sum(axis=-1)
+        b_reachable = jnp.where(b_reachable > 0., 1.0, 0.0)
+
+        def step_fn(carry, i):
+            I_prev = carry
+            I_next = jnp.dot(b_reachable, I_prev)
+            I_next = jnp.where(I_next > 0.1, 1.0, 0.0) # clamp I_next to 1.0 if it's above 0.1, 0 otherwise
+            return I_next, I_next
+    
+        _, I_f = lax.scan(step_fn, H[f], jnp.arange(depth-1))
+        I_f = jnp.concatenate([H[f][None,...], I_f], axis=0)
+
+        I.append(I_f)
+    
+    return I
+
+def calc_inductive_value_t(qs, qs_next, I, epsilon=1e-3):
+    """
+    Computes the inductive value of a state at a particular time (translation of @tverbele's `numpy` implementation of inductive planning, formerly
+    called `calc_inductive_cost`).
+
+    Parameters
+    ----------
+    qs: ``list`` of ``jax.numpy.ndarray`` 
+        Marginal posterior beliefs over hidden states at a given timepoint.
+    qs_next: ```list`` of ``jax.numpy.ndarray`` 
+        Predictive posterior beliefs over hidden states expected under the policy.
+    I: ``numpy.ndarray`` of dtype object
+        For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability 
+        of reaching the goal state backwards from state j after i steps.
+    epsilon: ``float``
+        Value that tunes the strength of the inductive value (how much it contributes to the expected free energy of policies)
+
+    Returns
+    -------
+    inductive_val: float
+        Value (negative inductive cost) of visiting this state using backwards induction under the policy in question
+    """
+    
+    # initialise inductive value
+    inductive_val = 0.
+
+    log_eps = log_stable(epsilon)
+    for f in range(len(qs)):
+        # we also assume precise beliefs here?!
+        idx = jnp.argmax(qs[f])
+        # m = arg max_n p_n < sup p
+
+        # i.e. find first entry at which I_idx equals 1, and then m is the index before that
+        m = jnp.maximum(jnp.argmax(I[f][:, idx])-1, 0)
+        I_m = (1. - I[f][m, :]) * log_eps
+        path_available = jnp.clip(I[f][:, idx].sum(0), min=0, max=1) # if there are any 1's at all in that column of I, then this == 1, otherwise 0
+        inductive_val += path_available * I_m.dot(qs_next[f]) # scaling by path_available will nullify the addition of inductive value in the case we find no path to goal (i.e. when no goal specified)
+
+    return inductive_val
+
+# if __name__ == '__main__':
+
+#     from jax import random as jr
+#     key = jr.PRNGKey(1)
+#     num_obs = [3, 4]
+
+#     A = [jr.uniform(key, shape = (no, 2, 2)) for no in num_obs]
+#     B = [jr.uniform(key, shape = (2, 2, 2)), jr.uniform(key, shape = (2, 2, 2))]
+#     C = [log_stable(jnp.array([0.8, 0.1, 0.1])), log_stable(jnp.ones(4)/4)]
+#     policy_1 = jnp.array([[0, 1],
+#                          [1, 1]])
+#     policy_2 = jnp.array([[1, 0],
+#                          [0, 0]])
+#     policy_matrix = jnp.stack([policy_1, policy_2]) # 2 x 2 x 2 tensor
+    
+#     qs_init = [jnp.ones(2)/2, jnp.ones(2)/2]
+#     neg_G_all_policies = jit(update_posterior_policies)(policy_matrix, qs_init, A, B, C)
+#     print(neg_G_all_policies)
diff --git a/pymdp/jax/inference.py b/pymdp/jax/inference.py
new file mode 100644
index 00000000..790ae354
--- /dev/null
+++ b/pymdp/jax/inference.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+# pylint: disable=no-member
+
+import jax.numpy as jnp
+from .algos import run_factorized_fpi, run_mmp, run_vmp
+from jax import tree_util as jtu
+
+def update_posterior_states(
+        A, 
+        B, 
+        obs, 
+        past_actions, 
+        prior=None, 
+        qs_hist=None, 
+        A_dependencies=None, 
+        B_dependencies=None, 
+        num_iter=16, 
+        method='fpi'
+    ):
+
+    if method == 'fpi' or method == "ovf":
+        # format obs to select only last observation
+        curr_obs = jtu.tree_map(lambda x: x[-1], obs)
+        qs = run_factorized_fpi(A, curr_obs, prior, A_dependencies, num_iter=num_iter)
+    else:
+        # format B matrices using action sequences here
+        # TODO: past_actions can be None
+        if past_actions is not None:
+            nf = len(B)
+            actions_tree = [past_actions[:, i] for i in range(nf)]
+            
+            # move time steps to the leading axis (leftmost)
+            # this assumes that a policy is always specified as the rightmost axis of Bs
+            B = jtu.tree_map(lambda b, a_idx: jnp.moveaxis(b[..., a_idx], -1, 0), B, actions_tree)
+        else:
+            B = None
+
+        # outputs of both VMP and MMP should be a list of hidden state factors, where each qs[f].shape = (T, batch_dim, num_states_f)
+        if method == 'vmp':
+            qs = run_vmp(A, B, obs, prior, A_dependencies, B_dependencies, num_iter=num_iter) 
+        if method == 'mmp':
+            qs = run_mmp(A, B, obs, prior, A_dependencies, B_dependencies, num_iter=num_iter)
+    
+    if qs_hist is not None:
+        if method == 'fpi' or method == "ovf":
+            qs_hist = jtu.tree_map(lambda x, y: jnp.concatenate([x, jnp.expand_dims(y, 0)], 0), qs_hist, qs)
+        else:
+            #TODO: return entire history of beliefs
+            qs_hist = qs
+    else:
+        if method == 'fpi' or method == "ovf":
+            qs_hist = jtu.tree_map(lambda x: jnp.expand_dims(x, 0), qs)
+        else:
+            qs_hist = qs
+    
+    return qs_hist
+    
diff --git a/pymdp/jax/learning.py b/pymdp/jax/learning.py
new file mode 100644
index 00000000..c075aab6
--- /dev/null
+++ b/pymdp/jax/learning.py
@@ -0,0 +1,314 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+# pylint: disable=no-member
+
+import numpy as np
+from .maths import multidimensional_outer
+from jax.tree_util import tree_map
+from jax import vmap
+import jax.numpy as jnp
+
+def update_obs_likelihood_dirichlet_m(pA_m, obs_m, qs, dependencies_m, lr=1.0):
+    """ JAX version of ``pymdp.learning.update_obs_likelihood_dirichlet_m`` """
+    # pA_m - parameters of the dirichlet from the prior
+    # pA_m.shape = (no_m x num_states[k] x num_states[j] x ... x num_states[n]) where (k, j, n) are indices of the hidden state factors that are parents of modality m
+
+    # \alpha^{*} = \alpha_{0} + \kappa * \sum_{t=t_begin}^{t=T} o_{m,t} \otimes \mathbf{s}_{f \in parents(m), t}
+
+    # \alpha^{*} is the VFE-minimizing solution for the parameters of q(A)
+    # \alpha_{0} are the Dirichlet parameters of p(A)
+    # o_{m,t} = observation (one-hot vector) of modality m at time t
+    # \mathbf{s}_{f \in parents(m), t} = categorical parameters of marginal posteriors over hidden state factors that are parents of modality m, at time t
+    # \otimes is a multidimensional outer product, not just a outer product of two vectors
+    # \kappa is an optional learning rate
+
+    relevant_factors = tree_map(lambda f_idx: qs[f_idx], dependencies_m)
+
+    dfda = vmap(multidimensional_outer)([obs_m] + relevant_factors).sum(axis=0)
+
+    return pA_m + lr * dfda
+    
+def update_obs_likelihood_dirichlet(pA, obs, qs, A_dependencies, lr=1.0):
+    """ JAX version of ``pymdp.learning.update_obs_likelihood_dirichlet`` """
+
+    update_A_fn = lambda pA_m, obs_m, dependencies_m: update_obs_likelihood_dirichlet_m(pA_m, obs_m, qs, dependencies_m, lr=lr)
+    qA = tree_map(update_A_fn, pA, obs, A_dependencies)
+
+    return qA
+
+def update_state_likelihood_dirichlet_f(pB_f, actions_f, current_qs, qs_seq, dependencies_f, lr=1.0):
+    """ JAX version of ``pymdp.learning.update_state_likelihood_dirichlet_f`` """
+    # pB_f - parameters of the dirichlet from the prior
+    # pB_f.shape = (num_states[f] x num_states[f] x num_actions[f]) where f is the index of the hidden state factor
+
+    # \alpha^{*} = \alpha_{0} + \kappa * \sum_{t=t_begin}^{t=T} \mathbf{s}_{f, t} \otimes \mathbf{s}_{f, t-1} \otimes \mathbf{a}_{f, t-1}
+
+    # \alpha^{*} is the VFE-minimizing solution for the parameters of q(B)
+    # \alpha_{0} are the Dirichlet parameters of p(B)
+    # \mathbf{s}_{f, t} = categorical parameters of marginal posteriors over hidden state factor f, at time t
+    # \mathbf{a}_{f, t-1} = categorical parameters of marginal posteriors over control factor f, at time t-1
+    # \otimes is a multidimensional outer product, not just a outer product of two vectors
+    # \kappa is an optional learning rate
+
+    past_qs = tree_map(lambda f_idx: qs_seq[f_idx][:-1], dependencies_f)
+    dfdb = vmap(multidimensional_outer)([current_qs[1:]] + past_qs + [actions_f]).sum(axis=0)
+    qB_f = pB_f + lr * dfdb
+
+    return qB_f
+
+def update_state_likelihood_dirichlet(pB, beliefs, actions_onehot, B_dependencies, lr=1.0):
+
+    update_B_f_fn = lambda pB_f, action_f, qs_f, dependencies_f: update_state_likelihood_dirichlet_f(pB_f, action_f, qs_f, beliefs, dependencies_f, lr=lr)    
+    qB = tree_map(update_B_f_fn, pB, actions_onehot, beliefs, B_dependencies)
+
+    return qB
+    
+
+def update_state_prior_dirichlet(
+    pD, qs, lr=1.0, factors="all"
+):
+    """
+    Update Dirichlet parameters of the initial hidden state distribution 
+    (prior beliefs about hidden states at the beginning of the inference window).
+
+    Parameters
+    -----------
+    pD: ``numpy.ndarray`` of dtype object
+        Prior Dirichlet parameters over initial hidden state prior (same shape as ``qs``)
+    qs: 1D ``numpy.ndarray`` or ``numpy.ndarray`` of dtype object
+        Marginal posterior beliefs over hidden states at current timepoint
+    lr: float, default ``1.0``
+        Learning rate, scale of the Dirichlet pseudo-count update.
+    factors: ``list``, default "all"
+        Indices (ranging from 0 to ``n_factors - 1``) of the hidden state factors to include 
+        in learning. Defaults to "all", meaning that factor-specific sub-vectors of ``pD``
+        are all updated using the corresponding hidden state distributions.
+    
+    Returns
+    -----------
+    qD: ``numpy.ndarray`` of dtype object
+        Posterior Dirichlet parameters over initial hidden state prior (same shape as ``qs``), after having updated it with state beliefs.
+    """
+
+    num_factors = len(pD)
+
+    qD = copy.deepcopy(pD)
+   
+    if factors == "all":
+        factors = list(range(num_factors))
+
+    for factor in factors:
+        idx = pD[factor] > 0 # only update those state level indices that have some prior probability
+        qD[factor][idx] += (lr * qs[factor][idx])
+       
+    return qD
+
+def _prune_prior(prior, levels_to_remove, dirichlet = False):
+    """
+    Function for pruning a prior Categorical distribution (e.g. C, D)
+
+    Parameters
+    -----------
+    prior: 1D ``numpy.ndarray`` or ``numpy.ndarray`` of dtype object
+        The vector(s) containing the priors over hidden states of a generative model, e.g. the prior over hidden states (``D`` vector). 
+    levels_to_remove: ``list`` of ``int``, ``list`` of ``list``
+        A ``list`` of the levels (indices of the support) to remove. If the prior in question has multiple hidden state factors / multiple observation modalities, 
+        then this will be a ``list`` of ``list``, where each sub-list within ``levels_to_remove`` will contain the levels to prune for a particular hidden state factor or modality 
+    dirichlet: ``Bool``, default ``False``
+        A Boolean flag indicating whether the input vector(s) is/are a Dirichlet distribution, and therefore should not be normalized at the end. 
+        @TODO: Instead, the dirichlet parameters from the pruned levels should somehow be re-distributed among the remaining levels
+
+    Returns
+    -----------
+    reduced_prior: 1D ``numpy.ndarray`` or ``numpy.ndarray`` of dtype object
+        The prior vector(s), after pruning, that lacks the hidden state or modality levels indexed by ``levels_to_remove``
+    """
+
+    if utils.is_obj_array(prior): # in case of multiple hidden state factors
+
+        assert all([type(levels) == list for levels in levels_to_remove])
+
+        num_factors = len(prior)
+
+        reduced_prior = utils.obj_array(num_factors)
+
+        factors_to_remove = []
+        for f, s_i in enumerate(prior): # loop over factors (or modalities)
+            
+            ns = len(s_i)
+            levels_to_keep = list(set(range(ns)) - set(levels_to_remove[f]))
+            if len(levels_to_keep) == 0:
+                print(f'Warning... removing ALL levels of factor {f} - i.e. the whole hidden state factor is being removed\n')
+                factors_to_remove.append(f)
+            else:
+                if not dirichlet:
+                    reduced_prior[f] = utils.norm_dist(s_i[levels_to_keep])
+                else:
+                    raise(NotImplementedError("Need to figure out how to re-distribute concentration parameters from pruned levels, across remaining levels"))
+
+
+        if len(factors_to_remove) > 0:
+            factors_to_keep = list(set(range(num_factors)) - set(factors_to_remove))
+            reduced_prior = reduced_prior[factors_to_keep]
+
+    else: # in case of one hidden state factor
+
+        assert all([type(level_i) == int for level_i in levels_to_remove])
+
+        ns = len(prior)
+        levels_to_keep = list(set(range(ns)) - set(levels_to_remove))
+
+        if not dirichlet:
+            reduced_prior = utils.norm_dist(prior[levels_to_keep])
+        else:
+            raise(NotImplementedError("Need to figure out how to re-distribute concentration parameters from pruned levels, across remaining levels"))
+
+    return reduced_prior
+
+def _prune_A(A, obs_levels_to_prune, state_levels_to_prune, dirichlet = False):
+    """
+    Function for pruning a observation likelihood model (with potentially multiple hidden state factors)
+    :meta private:
+    Parameters
+    -----------
+    A: ``numpy.ndarray`` with ``ndim >= 2``, or ``numpy.ndarray`` of dtype object
+        Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of
+        stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store 
+        the probability of observation level ``i`` given hidden state levels ``j, k, ...``
+    obs_levels_to_prune: ``list`` of int or ``list`` of ``list``: 
+        A ``list`` of the observation levels to remove. If the likelihood in question has multiple observation modalities, 
+        then this will be a ``list`` of ``list``, where each sub-list within ``obs_levels_to_prune`` will contain the observation levels 
+        to remove for a particular observation modality 
+    state_levels_to_prune: ``list`` of ``int``
+        A ``list`` of the hidden state levels to remove (this will be the same across modalities)
+    dirichlet: ``Bool``, default ``False``
+        A Boolean flag indicating whether the input array(s) is/are a Dirichlet distribution, and therefore should not be normalized at the end. 
+        @TODO: Instead, the dirichlet parameters from the pruned columns should somehow be re-distributed among the remaining columns
+
+    Returns
+    -----------
+    reduced_A: ``numpy.ndarray`` with ndim >= 2, or ``numpy.ndarray ``of dtype object
+        The observation model, after pruning, which lacks the observation or hidden state levels given by the arguments ``obs_levels_to_prune`` and ``state_levels_to_prune``
+    """
+
+    columns_to_keep_list = []
+    if utils.is_obj_array(A):
+        num_states = A[0].shape[1:]
+        for f, ns in enumerate(num_states):
+            indices_f = np.array( list(set(range(ns)) - set(state_levels_to_prune[f])), dtype = np.intp)
+            columns_to_keep_list.append(indices_f)
+    else:
+        num_states = A.shape[1]
+        indices = np.array( list(set(range(num_states)) - set(state_levels_to_prune)), dtype = np.intp )
+        columns_to_keep_list.append(indices)
+
+    if utils.is_obj_array(A): # in case of multiple observation modality
+
+        assert all([type(o_m_levels) == list for o_m_levels in obs_levels_to_prune])
+
+        num_modalities = len(A)
+
+        reduced_A = utils.obj_array(num_modalities)
+        
+        for m, A_i in enumerate(A): # loop over modalities
+            
+            no = A_i.shape[0]
+            rows_to_keep = np.array(list(set(range(no)) - set(obs_levels_to_prune[m])), dtype = np.intp)
+            
+            reduced_A[m] = A_i[np.ix_(rows_to_keep, *columns_to_keep_list)]
+        if not dirichlet:    
+            reduced_A = utils.norm_dist_obj_arr(reduced_A)
+        else:
+            raise(NotImplementedError("Need to figure out how to re-distribute concentration parameters from pruned rows/columns, across remaining rows/columns"))
+    else: # in case of one observation modality
+
+        assert all([type(o_levels_i) == int for o_levels_i in obs_levels_to_prune])
+
+        no = A.shape[0]
+        rows_to_keep = np.array(list(set(range(no)) - set(obs_levels_to_prune)), dtype = np.intp)
+            
+        reduced_A = A[np.ix_(rows_to_keep, *columns_to_keep_list)]
+
+        if not dirichlet:
+            reduced_A = utils.norm_dist(reduced_A)
+        else:
+            raise(NotImplementedError("Need to figure out how to re-distribute concentration parameters from pruned rows/columns, across remaining rows/columns"))
+
+    return reduced_A
+
+def _prune_B(B, state_levels_to_prune, action_levels_to_prune, dirichlet = False):
+    """
+    Function for pruning a transition likelihood model (with potentially multiple hidden state factors)
+
+    Parameters
+    -----------
+    B: ``numpy.ndarray`` of ``ndim == 3`` or ``numpy.ndarray`` of dtype object
+        Dynamics likelihood mapping or 'transition model', mapping from hidden states at `t` to hidden states at `t+1`, given some control state `u`.
+        Each element B[f] of this object array stores a 3-D tensor for hidden state factor `f`, whose entries `B[f][s, v, u] store the probability
+        of hidden state level `s` at the current time, given hidden state level `v` and action `u` at the previous time.
+    state_levels_to_prune: ``list`` of ``int`` or ``list`` of ``list`` 
+        A ``list`` of the state levels to remove. If the likelihood in question has multiple hidden state factors, 
+        then this will be a ``list`` of ``list``, where each sub-list within ``state_levels_to_prune`` will contain the state levels 
+        to remove for a particular hidden state factor 
+    action_levels_to_prune: ``list`` of ``int`` or ``list`` of ``list`` 
+        A ``list`` of the control state or action levels to remove. If the likelihood in question has multiple control state factors, 
+        then this will be a ``list`` of ``list``, where each sub-list within ``action_levels_to_prune`` will contain the control state levels 
+        to remove for a particular control state factor 
+    dirichlet: ``Bool``, default ``False``
+        A Boolean flag indicating whether the input array(s) is/are a Dirichlet distribution, and therefore should not be normalized at the end. 
+        @TODO: Instead, the dirichlet parameters from the pruned rows/columns should somehow be re-distributed among the remaining rows/columns
+
+    Returns
+    -----------
+    reduced_B: ``numpy.ndarray`` of `ndim == 3` or ``numpy.ndarray`` of dtype object
+        The transition model, after pruning, which lacks the hidden state levels/action levels given by the arguments ``state_levels_to_prune`` and ``action_levels_to_prune``
+    """
+
+    slices_to_keep_list = []
+
+    if utils.is_obj_array(B):
+
+        num_controls = [B_arr.shape[2] for _, B_arr in enumerate(B)]
+
+        for c, nc in enumerate(num_controls):
+            indices_c = np.array( list(set(range(nc)) - set(action_levels_to_prune[c])), dtype = np.intp)
+            slices_to_keep_list.append(indices_c)
+    else:
+        num_controls = B.shape[2]
+        slices_to_keep = np.array( list(set(range(num_controls)) - set(action_levels_to_prune)), dtype = np.intp )
+
+    if utils.is_obj_array(B): # in case of multiple hidden state factors
+
+        assert all([type(ns_f_levels) == list for ns_f_levels in state_levels_to_prune])
+
+        num_factors = len(B)
+
+        reduced_B = utils.obj_array(num_factors)
+        
+        for f, B_f in enumerate(B): # loop over modalities
+            
+            ns = B_f.shape[0]
+            states_to_keep = np.array(list(set(range(ns)) - set(state_levels_to_prune[f])), dtype = np.intp)
+            
+            reduced_B[f] = B_f[np.ix_(states_to_keep, states_to_keep, slices_to_keep_list[f])]
+
+        if not dirichlet:    
+            reduced_B = utils.norm_dist_obj_arr(reduced_B)
+        else:
+            raise(NotImplementedError("Need to figure out how to re-distribute concentration parameters from pruned rows/columns, across remaining rows/columns"))
+
+    else: # in case of one hidden state factor
+
+        assert all([type(state_level_i) == int for state_level_i in state_levels_to_prune])
+
+        ns = B.shape[0]
+        states_to_keep = np.array(list(set(range(ns)) - set(state_levels_to_prune)), dtype = np.intp)
+            
+        reduced_B = B[np.ix_(states_to_keep, states_to_keep, slices_to_keep)]
+
+        if not dirichlet:
+            reduced_B = utils.norm_dist(reduced_B)
+        else:
+            raise(NotImplementedError("Need to figure out how to re-distribute concentration parameters from pruned rows/columns, across remaining rows/columns"))
+
+    return reduced_B
diff --git a/pymdp/jax/likelihoods.py b/pymdp/jax/likelihoods.py
new file mode 100644
index 00000000..3f44a152
--- /dev/null
+++ b/pymdp/jax/likelihoods.py
@@ -0,0 +1,45 @@
+import jax.numpy as jnp
+import numpyro.distributions as dist
+from jax import lax
+from numpyro import plate, sample, deterministic
+from numpyro.contrib.control_flow import scan
+
+def evolve_trials(agent, data):
+
+    def step_fn(carry, xs):
+        empirical_prior = carry
+        outcomes = xs['outcomes']
+        qs = agent.infer_states(outcomes, empirical_prior)
+        q_pi, _ = agent.infer_policies(qs)
+
+        probs = agent.action_probabilities(q_pi)
+
+        actions = xs['actions']
+        empirical_prior = agent.update_empirical_prior(actions, qs)
+        #TODO: if outcomes and actions are None, generate samples
+        return empirical_prior, (probs, outcomes, actions)
+
+    prior = agent.D
+    _, res = lax.scan(step_fn, prior, data)
+
+    return res
+
+def aif_likelihood(Nb, Nt, Na, data, agent):
+    # Na -> batch dimension - number of different subjects/agents
+    # Nb -> number of experimental blocks
+    # Nt -> number of trials within each block
+
+    def step_fn(carry, xs):
+        probs, outcomes, actions = evolve_trials(agent, xs)
+
+        deterministic('outcomes', outcomes)
+
+        with plate('num_agents', Na):
+            with plate('num_trials', Nt):
+                sample('actions', dist.Categorical(logits=probs).to_event(1), obs=actions)
+        
+        return None, None
+    
+    # TODO: See if some information has to be passed from one block to the next and change init and carry accordingly
+    init = None
+    scan(step_fn, init, data, length=Nb)
\ No newline at end of file
diff --git a/pymdp/jax/maths.py b/pymdp/jax/maths.py
new file mode 100644
index 00000000..58b34aff
--- /dev/null
+++ b/pymdp/jax/maths.py
@@ -0,0 +1,144 @@
+import jax.numpy as jnp
+
+from functools import partial
+from typing import Optional, Tuple, List
+from jax import tree_util, nn, jit
+from opt_einsum import contract
+
+MINVAL = jnp.finfo(float).eps
+
+def log_stable(x):
+    return jnp.log(jnp.clip(x, min=MINVAL))
+
+@partial(jit, static_argnames=['keep_dims'])
+def factor_dot(M, xs, keep_dims: Optional[Tuple[int]] = None):
+    """ Dot product of a multidimensional array with `x`.
+    
+    Parameters
+    ----------
+    - `qs` [list of 1D numpy.ndarray] - list of jnp.ndarrays
+    
+    Returns 
+    -------
+    - `Y` [1D numpy.ndarray] - the result of the dot product
+    """
+    d = len(keep_dims) if keep_dims is not None else 0
+    assert M.ndim == len(xs) + d
+    keep_dims = () if keep_dims is None else keep_dims
+    dims = tuple((i,) for i in range(M.ndim) if i not in keep_dims)
+    return factor_dot_flex(M, xs, dims, keep_dims=keep_dims)
+
+@partial(jit, static_argnames=['dims', 'keep_dims'])
+def factor_dot_flex(M, xs, dims: List[Tuple[int]], keep_dims: Optional[Tuple[int]] = None):
+    """ Dot product of a multidimensional array with `x`.
+    
+    Parameters
+    ----------
+    - `M` [numpy.ndarray] - tensor
+    - 'xs' [list of numpyr.ndarray] - list of tensors
+    - 'dims' [list of tuples] - list of dimensions of xs tensors in tensor M
+    - 'keep_dims' [tuple] - tuple of integers denoting dimesions to keep
+    Returns 
+    -------
+    - `Y` [1D numpy.ndarray] - the result of the dot product
+    """
+    all_dims = tuple(range(M.ndim))
+    matrix = [[xs[f], dims[f]] for f in range(len(xs))]
+    args = [M, all_dims]
+    for row in matrix:
+        args.extend(row)
+
+    args += [keep_dims]
+    return contract(*args, backend='jax')
+
+def compute_log_likelihood_single_modality(o_m, A_m, distr_obs=True):
+    """ Compute observation likelihood for a single modality (observation and likelihood)"""
+    if distr_obs:
+        expanded_obs = jnp.expand_dims(o_m, tuple(range(1, A_m.ndim)))
+        likelihood = (expanded_obs * A_m).sum(axis=0)
+    else:
+        likelihood = A_m[o_m]
+    
+    return log_stable(likelihood)
+
+def compute_log_likelihood(obs, A, distr_obs=True):
+    """ Compute likelihood over hidden states across observations from different modalities """
+    result = tree_util.tree_map(lambda o, a: compute_log_likelihood_single_modality(o, a, distr_obs=distr_obs), obs, A)
+    ll = jnp.sum(jnp.stack(result), 0)
+
+    return ll
+
+def compute_log_likelihood_per_modality(obs, A, distr_obs=True):
+    """ Compute likelihood over hidden states across observations from different modalities, and return them per modality """
+    ll_all = tree_util.tree_map(lambda o, a: compute_log_likelihood_single_modality(o, a, distr_obs=distr_obs), obs, A)
+
+    return ll_all
+
+def compute_accuracy(qs, obs, A):
+    """ Compute the accuracy portion of the variational free energy (expected log likelihood under the variational posterior) """
+
+    ll = compute_log_likelihood(obs, A)
+
+    x = qs[0]
+    for q in qs[1:]:
+        x = jnp.expand_dims(x, -1) * q
+
+    joint = log_likelihood * x
+    return joint.sum()
+
+def compute_free_energy(qs, prior, obs, A):
+    """ 
+    Calculate variational free energy by breaking its computation down into three steps:
+    1. computation of the negative entropy of the posterior -H[Q(s)]
+    2. computation of the cross entropy of the posterior with the prior H_{Q(s)}[P(s)]
+    3. computation of the accuracy E_{Q(s)}[lnP(o|s)] 
+    
+    Then add them all together -- except subtract the accuracy
+    """
+
+    vfe = 0.0 # initialize variational free energy
+    for q, p in zip(qs, prior):
+        negH_qs = q.dot(log_stable(q))
+        xH_qp = -q.dot(log_stable(p))
+        vfe += (negH_qs + xH_qp)
+    
+    vfe -= compute_accuracy(qs, obs, A)
+
+    return vfe
+
+def multidimensional_outer(arrs):
+    """ Compute the outer product of a list of arrays by iteratively expanding the first array and multiplying it with the next array """
+
+    x = arrs[0]
+    for q in arrs[1:]:
+        x = jnp.expand_dims(x, -1) * q
+
+    return x
+
+def spm_wnorm(A):
+    """ 
+    Returns Expectation of logarithm of Dirichlet parameters over a set of 
+    Categorical distributions, stored in the columns of A.
+    """
+    A = jnp.clip(A, a_min=MINVAL)
+    norm = 1. / A.sum(axis=0)
+    avg = 1. / A
+    wA = norm - avg
+    return wA
+
+def dirichlet_expected_value(dir_arr):
+    """ 
+    Returns Expectation of Dirichlet parameters over a set of 
+    Categorical distributions, stored in the columns of A.
+    """
+    dir_arr = jnp.clip(dir_arr, a_min=MINVAL)
+    expected_val = jnp.divide(dir_arr, dir_arr.sum(axis=0, keepdims=True))
+    return expected_val
+
+if __name__ == '__main__':
+    obs = [0, 1, 2]
+    obs_vec = [ nn.one_hot(o, 3) for o in obs]
+    A = [jnp.ones((3, 2)) / 3] * 3
+    res = jit(compute_log_likelihood)(obs_vec, A)
+    
+    print(res)
\ No newline at end of file
diff --git a/pymdp/jax/task.py b/pymdp/jax/task.py
new file mode 100644
index 00000000..5de0315e
--- /dev/null
+++ b/pymdp/jax/task.py
@@ -0,0 +1,79 @@
+# Task environmnet
+from typing import Optional, List, Dict
+from jaxtyping import Array, PRNGKeyArray
+from functools import partial
+
+from equinox import Module, field, tree_at
+from jax import vmap, random as jr, tree_util as jtu
+import jax.numpy as jnp
+
+def select_probs(positions, matrix, dependency_list, actions=None):
+    args = tuple(p for i, p in enumerate(positions) if i in dependency_list)
+    args += () if actions is None else (actions,)
+
+    return matrix[..., *args]
+
+def cat_sample(key, p):
+    a = jnp.arange(p.shape[-1])
+    if p.ndim > 1:
+        choice = lambda key, p: jr.choice(key, a, p=p)
+        keys = jr.split(key, len(p))
+        return vmap(choice)(keys, p)
+
+    return jr.choice(key, a, p=p)
+
+class PyMDPEnv(Module):
+    params: Dict
+    states: List[List[Array]]
+    dependencies: Dict = field(static=True)
+
+    def __init__(
+        self, params: Dict, dependencies: Dict, init_state: List[Array] = None
+    ):
+        self.params = params
+        self.dependencies = dependencies
+
+        if init_state is None:
+            init_state = jtu.tree_map(lambda x: jnp.argmax(x, -1), self.params["D"])
+
+        self.states = [init_state]
+
+    def reset(self, key: Optional[PRNGKeyArray] = None):
+        if key is None:
+            states = [self.states[0]]
+        else:
+            probs = self.params["D"]
+            keys = list(jr.split(key, len(probs)))
+            states = [jtu.tree_map(cat_sample, keys, probs)]
+
+        return tree_at(lambda x: x.states, self, states)
+
+    @vmap
+    def step(self, key: PRNGKeyArray, actions: Optional[Array] = None):
+        # return a list of random observations and states
+        key_state, key_obs = jr.split(key)
+        states = self.states
+        if actions is not None:
+            actions = list(actions)
+            _select_probs = partial(select_probs, states[-1])
+            state_probs = jtu.tree_map(
+                _select_probs, self.params["B"], self.dependencies["B"], actions
+            )
+
+            keys = list(jr.split(key_state, len(state_probs)))
+            new_states = jtu.tree_map(cat_sample, keys, state_probs)
+
+            states.append(new_states)
+
+        else:
+            new_states = states[-1]
+
+        _select_probs = partial(select_probs, new_states)
+        obs_probs = jtu.tree_map(
+            _select_probs, self.params["A"], self.dependencies["A"]
+        )
+
+        keys = list(jr.split(key_obs, len(obs_probs)))
+        new_obs = jtu.tree_map(cat_sample, keys, obs_probs)
+
+        return new_obs, tree_at(lambda x: (x.states), self, states)
\ No newline at end of file
diff --git a/pymdp/jax/utils.py b/pymdp/jax/utils.py
new file mode 100644
index 00000000..12bbc461
--- /dev/null
+++ b/pymdp/jax/utils.py
@@ -0,0 +1,596 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+""" Utility functions
+
+__author__: Conor Heins, Alexander Tschantz, Brennan Klein
+"""
+
+import jax.numpy as jnp
+
+from typing import (Any, Callable, List, NamedTuple, Optional, Sequence, Union, Tuple)
+
+Tensor = Any # maybe jnp.ndarray, but typing seems not to be well defined for jax
+Vector = List[Tensor]
+Shape = Sequence[int]
+ShapeList = list[Shape]
+
+def norm_dist(dist: Tensor) -> Tensor:
+    """ Normalizes a Categorical probability distribution"""
+    return dist/dist.sum(0)
+
+def list_array_uniform(shape_list: ShapeList) -> Vector:
+    """ 
+    Creates a list of jax arrays representing uniform Categorical
+    distributions with shapes given by shape_list[i]. The shapes (elements of shape_list)
+    can either be tuples or lists.
+    """
+    arr = []
+    for shape in shape_list:
+        arr.append( norm_dist(jnp.ones(shape)) )
+    return arr
+
+def list_array_zeros(shape_list: ShapeList) -> Vector:
+    """ 
+    Creates a list of 1-D jax arrays filled with zeros, with shapes given by shape_list[i]
+    """
+    arr = []
+    for shape in shape_list:
+        arr.append( jnp.zeros(shape) )
+    return arr
+
+def list_array_scaled(shape_list: ShapeList, scale: float=1.0) -> Vector:
+    """ 
+    Creates a list of 1-D jax arrays filled with scale, with shapes given by shape_list[i]
+    """
+    arr = []
+    for shape in shape_list:
+        arr.append( scale * jnp.ones(shape) )
+    
+    return arr
+
+# def onehot(value, num_values):
+#     arr = np.zeros(num_values)
+#     arr[value] = 1.0
+#     return arr
+
+# def random_A_matrix(num_obs, num_states):
+#     if type(num_obs) is int:
+#         num_obs = [num_obs]
+#     if type(num_states) is int:
+#         num_states = [num_states]
+#     num_modalities = len(num_obs)
+
+#     A = obj_array(num_modalities)
+#     for modality, modality_obs in enumerate(num_obs):
+#         modality_shape = [modality_obs] + num_states
+#         modality_dist = np.random.rand(*modality_shape)
+#         A[modality] = norm_dist(modality_dist)
+#     return A
+
+# def random_B_matrix(num_states, num_controls):
+#     if type(num_states) is int:
+#         num_states = [num_states]
+#     if type(num_controls) is int:
+#         num_controls = [num_controls]
+#     num_factors = len(num_states)
+#     assert len(num_controls) == len(num_states)
+
+#     B = obj_array(num_factors)
+#     for factor in range(num_factors):
+#         factor_shape = (num_states[factor], num_states[factor], num_controls[factor])
+#         factor_dist = np.random.rand(*factor_shape)
+#         B[factor] = norm_dist(factor_dist)
+#     return B
+
+# def random_single_categorical(shape_list):
+#     """
+#     Creates a random 1-D categorical distribution (or set of 1-D categoricals, e.g. multiple marginals of different factors) and returns them in an object array 
+#     """
+    
+#     num_sub_arrays = len(shape_list)
+
+#     out = obj_array(num_sub_arrays)
+
+#     for arr_idx, shape_i  in enumerate(shape_list):
+#         out[arr_idx] = norm_dist(np.random.rand(shape_i))
+    
+#     return out
+
+# def construct_controllable_B(num_states, num_controls):
+#     """
+#     Generates a fully controllable transition likelihood array, where each 
+#     action (control state) corresponds to a move to the n-th state from any 
+#     other state, for each control factor
+#     """
+
+#     num_factors = len(num_states)
+
+#     B = obj_array(num_factors)
+#     for factor, c_dim in enumerate(num_controls):
+#         tmp = np.eye(c_dim)[:, :, np.newaxis]
+#         tmp = np.tile(tmp, (1, 1, c_dim))
+#         B[factor] = tmp.transpose(1, 2, 0)
+
+#     return B
+
+# def dirichlet_like(template_categorical, scale = 1.0):
+#     """
+#     Helper function to construct a Dirichlet distribution based on an existing Categorical distribution
+#     """ 
+
+#     if not is_obj_array(template_categorical):
+#         warnings.warn(
+#                     "Input array is not an object array...\
+#                     Casting the input to an object array"
+#                 )
+#         template_categorical = to_obj_array(template_categorical)
+
+#     n_sub_arrays = len(template_categorical)
+
+#     dirichlet_out = obj_array(n_sub_arrays)
+    
+#     for i, arr in enumerate(template_categorical):
+#         dirichlet_out[i] = scale * arr
+
+#     return dirichlet_out
+
+# def get_model_dimensions(A=None, B=None):
+
+#     if A is None and B is None:
+#         raise ValueError(
+#                     "Must provide either `A` or `B`"
+#                 )
+
+#     if A is not None:
+#         num_obs = [a.shape[0] for a in A] if is_obj_array(A) else [A.shape[0]]
+#         num_modalities = len(num_obs)
+#     else:
+#         num_obs, num_modalities = None, None
+    
+#     if B is not None:
+#         num_states = [b.shape[0] for b in B] if is_obj_array(B) else [B.shape[0]]
+#         num_factors = len(num_states)
+#     else:
+#         if A is not None:
+#             num_states = list(A[0].shape[1:]) if is_obj_array(A) else list(A.shape[1:])
+#             num_factors = len(num_states)
+#         else:
+#             num_states, num_factors = None, None
+    
+#     return num_obs, num_states, num_modalities, num_factors
+
+# def get_model_dimensions_from_labels(model_labels):
+
+#     modalities = model_labels['observations']
+#     num_modalities = len(modalities.keys())
+#     num_obs = [len(modalities[modality]) for modality in modalities.keys()]
+
+#     factors = model_labels['states']
+#     num_factors = len(factors.keys())
+#     num_states = [len(factors[factor]) for factor in factors.keys()]
+
+#     if 'actions' in model_labels.keys():
+
+#         controls = model_labels['actions']
+#         num_control_fac = len(controls.keys())
+#         num_controls = [len(controls[cfac]) for cfac in controls.keys()]
+
+#         return num_obs, num_modalities, num_states, num_factors, num_controls, num_control_fac
+#     else:
+#         return num_obs, num_modalities, num_states, num_factors
+
+
+
+
+# def norm_dist_obj_arr(obj_arr):
+
+#     normed_obj_array = obj_array(len(obj_arr))
+#     for i, arr in enumerate(obj_arr):
+#         normed_obj_array[i] = norm_dist(arr)
+    
+#     return normed_obj_array
+
+# def is_normalized(dist):
+#     """
+#     Utility function for checking whether a single distribution or set of conditional categorical distributions is normalized.
+#     Returns True if all distributions integrate to 1.0
+#     """
+
+#     if is_obj_array(dist):
+#         normed_arrays = []
+#         for i, arr in enumerate(dist):
+#             column_sums = arr.sum(axis=0)
+#             normed_arrays.append(np.allclose(column_sums, np.ones_like(column_sums)))
+#         out = all(normed_arrays)
+#     else:
+#         column_sums = dist.sum(axis=0)
+#         out = np.allclose(column_sums, np.ones_like(column_sums))
+    
+#     return out
+
+# def is_obj_array(arr):
+#     return arr.dtype == "object"
+
+# def to_obj_array(arr):
+#     if is_obj_array(arr):
+#         return arr
+#     obj_array_out = obj_array(1)
+#     obj_array_out[0] = arr.squeeze()
+#     return obj_array_out
+
+# def obj_array_from_list(list_input):
+#     """
+#     Takes a list of `numpy.ndarray` and converts them to a `numpy.ndarray` of `dtype = object`
+#     """
+#     return np.array(list_input, dtype = object)
+
+# def process_observation_seq(obs_seq, n_modalities, n_observations):
+#     """
+#     Helper function for formatting observations    
+
+#         Observations can either be `int` (converted to one-hot)
+#         or `tuple` (obs for each modality), or `list` (obs for each modality)
+#         If list, the entries could be object arrays of one-hots, in which
+#         case this function returns `obs_seq` as is.
+#     """
+#     proc_obs_seq = obj_array(len(obs_seq))
+#     for t, obs_t in enumerate(obs_seq):
+#         proc_obs_seq[t] = process_observation(obs_t, n_modalities, n_observations)
+#     return proc_obs_seq
+
+# def process_observation(obs, num_modalities, num_observations):
+#     """
+#     Helper function for formatting observations    
+#     USAGE NOTES:
+#     - If `obs` is a 1D numpy array, it must be a one-hot vector, where one entry (the entry of the observation) is 1.0 
+#     and all other entries are 0. This therefore assumes it's a single modality observation. If these conditions are met, then
+#     this function will return `obs` unchanged. Otherwise, it'll throw an error.
+#     - If `obs` is an int, it assumes this is a single modality observation, whose observation index is given by the value of `obs`. This function will convert
+#     it to be a one hot vector.
+#     - If `obs` is a list, it assumes this is a multiple modality observation, whose len is equal to the number of observation modalities,
+#     and where each entry `obs[m]` is the index of the observation, for that modality. This function will convert it into an object array
+#     of one-hot vectors.
+#     - If `obs` is a tuple, same logic as applies for list (see above).
+#     - if `obs` is a numpy object array (array of arrays), this function will return `obs` unchanged.
+#     """
+
+#     if isinstance(obs, np.ndarray) and not is_obj_array(obs):
+#         assert num_modalities == 1, "If `obs` is a 1D numpy array, `num_modalities` must be equal to 1"
+#         assert len(np.where(obs)[0]) == 1, "If `obs` is a 1D numpy array, it must be a one hot vector (e.g. np.array([0.0, 1.0, 0.0, ....]))"
+
+#     if isinstance(obs, (int, np.integer)):
+#         obs = onehot(obs, num_observations[0])
+
+#     if isinstance(obs, tuple) or isinstance(obs,list):
+#         obs_arr_arr = obj_array(num_modalities)
+#         for m in range(num_modalities):
+#             obs_arr_arr[m] = onehot(obs[m], num_observations[m])
+#         obs = obs_arr_arr
+
+#     return obs
+
+# def convert_observation_array(obs, num_obs):
+#     """
+#     Converts from SPM-style observation array to infer-actively one-hot object arrays.
+    
+#     Parameters
+#     ----------
+#     - 'obs' [numpy 2-D nd.array]:
+#         SPM-style observation arrays are of shape (num_modalities, T), where each row 
+#         contains observation indices for a different modality, and columns indicate 
+#         different timepoints. Entries store the indices of the discrete observations 
+#         within each modality. 
+
+#     - 'num_obs' [list]:
+#         List of the dimensionalities of the observation modalities. `num_modalities` 
+#         is calculated as `len(num_obs)` in the function to determine whether we're 
+#         dealing with a single- or multi-modality 
+#         case.
+
+#     Returns
+#     ----------
+#     - `obs_t`[list]: 
+#         A list with length equal to T, where each entry of the list is either a) an object 
+#         array (in the case of multiple modalities) where each sub-array is a one-hot vector 
+#         with the observation for the correspond modality, or b) a 1D numpy array (in the case
+#         of one modality) that is a single one-hot vector encoding the observation for the 
+#         single modality.
+#     """
+
+#     T = obs.shape[1]
+#     num_modalities = len(num_obs)
+
+#     # Initialise the output
+#     obs_t = []
+#     # Case of one modality
+#     if num_modalities == 1:
+#         for t in range(T):
+#             obs_t.append(onehot(obs[0, t] - 1, num_obs[0]))
+#     else:
+#         for t in range(T):
+#             obs_AoA = obj_array(num_modalities)
+#             for g in range(num_modalities):
+#                 # Subtract obs[g,t] by 1 to account for MATLAB vs. Python indexing
+#                 # (MATLAB is 1-indexed)
+#                 obs_AoA[g] = onehot(obs[g, t] - 1, num_obs[g])
+#             obs_t.append(obs_AoA)
+
+#     return obs_t
+
+# def insert_multiple(s, indices, items):
+#     for idx in range(len(items)):
+#         s.insert(indices[idx], items[idx])
+#     return s
+
+# def reduce_a_matrix(A):
+#     """
+#     Utility function for throwing away dimensions (lagging dimensions, hidden state factors)
+#     of a particular A matrix that are independent of the observation. 
+#     Parameters:
+#     ==========
+#     - `A` [np.ndarray]:
+#         The A matrix or likelihood array that encodes probabilistic relationship
+#         of the generative model between hidden state factors (lagging dimensions, columns, slices, etc...)
+#         and observations (leading dimension, rows). 
+#     Returns:
+#     =========
+#     - `A_reduced` [np.ndarray]:
+#         The reduced A matrix, missing the lagging dimensions that correspond to hidden state factors
+#         that are statistically independent of observations
+#     - `original_factor_idx` [list]:
+#         List of the indices (in terms of the original dimensionality) of the hidden state factors
+#         that are maintained in the A matrix (and thus have an informative / non-degenerate relationship to observations
+#     """
+
+#     o_dim, num_states = A.shape[0], A.shape[1:]
+#     idx_vec_s = [slice(0, o_dim)]  + [slice(ns) for _, ns in enumerate(num_states)]
+
+#     original_factor_idx = []
+#     excluded_factor_idx = [] # the indices of the hidden state factors that are independent of the observation and thus marginalized away
+#     for factor_i, ns in enumerate(num_states):
+
+#         level_counter = 0
+#         break_flag = False
+#         while level_counter < ns and break_flag is False:
+#             idx_vec_i = idx_vec_s.copy()
+#             idx_vec_i[factor_i+1] = slice(level_counter,level_counter+1,None)
+#             if not np.isclose(A.mean(axis=factor_i+1), A[tuple(idx_vec_i)].squeeze()).all():
+#                 break_flag = True # this means they're not independent
+#                 original_factor_idx.append(factor_i)
+#             else:
+#                 level_counter += 1
+        
+#         if break_flag is False:
+#             excluded_factor_idx.append(factor_i+1)
+    
+#     A_reduced = A.mean(axis=tuple(excluded_factor_idx)).squeeze()
+
+#     return A_reduced, original_factor_idx
+
+# def construct_full_a(A_reduced, original_factor_idx, num_states):
+#     """
+#     Utility function for reconstruction a full A matrix from a reduced A matrix, using known factor indices
+#     to tile out the reduced A matrix along the 'non-informative' dimensions
+#     Parameters:
+#     ==========
+#     - `A_reduced` [np.ndarray]:
+#         The reduced A matrix or likelihood array that encodes probabilistic relationship
+#         of the generative model between hidden state factors (lagging dimensions, columns, slices, etc...)
+#         and observations (leading dimension, rows). 
+#     - `original_factor_idx` [list]:
+#         List of hidden state indices in terms of the full hidden state factor list, that comprise
+#         the lagging dimensions of `A_reduced`
+#     - `num_states` [list]:
+#         The list of all the dimensionalities of hidden state factors in the full generative model.
+#         `A_reduced.shape[1:]` should be equal to `num_states[original_factor_idx]`
+#     Returns:
+#     =========
+#     - `A` [np.ndarray]:
+#         The full A matrix, containing all the lagging dimensions that correspond to hidden state factors, including
+#         those that are statistically independent of observations
+    
+#     @ NOTE: This is the "inverse" of the reduce_a_matrix function, 
+#     i.e. `reduce_a_matrix(construct_full_a(A_reduced, original_factor_idx, num_states)) == A_reduced, original_factor_idx`
+#     """
+
+#     o_dim = A_reduced.shape[0] # dimensionality of the support of the likelihood distribution (i.e. the number of observation levels)
+#     full_dimensionality = [o_dim] + num_states # full dimensionality of the output (`A`)
+#     fill_indices = [0] +  [f+1 for f in original_factor_idx] # these are the indices of the dimensions we need to fill for this modality
+#     fill_dimensions = np.delete(full_dimensionality, fill_indices) 
+
+#     original_factor_dims = [num_states[f] for f in original_factor_idx] # dimensionalities of the relevant factors
+#     prefilled_slices = [slice(0, o_dim)] + [slice(0, ns) for ns in original_factor_dims] # these are the slices that are filled out by the provided `A_reduced`
+
+#     A = np.zeros(full_dimensionality)
+
+#     for item in itertools.product(*[list(range(d)) for d in fill_dimensions]):
+#         slice_ = list(item)
+#         A_indices = insert_multiple(slice_, fill_indices, prefilled_slices) #here we insert the correct values for the fill indices for this slice                    
+#         A[tuple(A_indices)] = A_reduced
+    
+#     return A
+
+# def create_A_matrix_stub(model_labels):
+
+#     num_obs, _, num_states, _= get_model_dimensions_from_labels(model_labels)
+
+#     obs_labels, state_labels = model_labels['observations'], model_labels['states']
+
+#     state_combinations = pd.MultiIndex.from_product(list(state_labels.values()), names=list(state_labels.keys()))
+#     num_state_combos = np.prod(num_states)
+#     # num_rows = (np.array(num_obs) * num_state_combos).sum()
+#     num_rows = sum(num_obs)
+
+#     cell_values = np.zeros((num_rows, len(state_combinations)))
+
+#     obs_combinations = []
+#     for modality in obs_labels.keys():
+#         levels_to_combine = [[modality]] + [obs_labels[modality]]
+#         # obs_combinations += num_state_combos * list(itertools.product(*levels_to_combine))
+#         obs_combinations += list(itertools.product(*levels_to_combine))
+
+
+#     obs_combinations = pd.MultiIndex.from_tuples(obs_combinations, names = ["Modality", "Level"])
+
+#     A_matrix = pd.DataFrame(cell_values, index = obs_combinations, columns=state_combinations)
+
+#     return A_matrix
+
+# def create_B_matrix_stubs(model_labels):
+
+#     _, _, num_states, _, num_controls, _ = get_model_dimensions_from_labels(model_labels)
+
+#     state_labels = model_labels['states']
+#     action_labels = model_labels['actions']
+
+#     B_matrices = {}
+
+#     for f_idx, factor in enumerate(state_labels.keys()):
+
+#         control_fac_name = list(action_labels)[f_idx]
+#         factor_list = [state_labels[factor]] + [action_labels[control_fac_name]]
+
+#         prev_state_action_combos = pd.MultiIndex.from_product(factor_list, names=[factor, list(action_labels.keys())[f_idx]])
+
+#         num_state_action_combos = num_states[f_idx] * num_controls[f_idx]
+
+#         num_rows = num_states[f_idx]
+
+#         cell_values = np.zeros((num_rows, num_state_action_combos))
+
+#         next_state_list = state_labels[factor]
+        
+#         B_matrix_f = pd.DataFrame(cell_values, index = next_state_list, columns=prev_state_action_combos)
+
+#         B_matrices[factor] = B_matrix_f
+
+#     return B_matrices
+
+# def read_A_matrix(path, num_hidden_state_factors):
+#     raw_table = pd.read_excel(path, header=None)
+#     level_counts = {
+#         "index": raw_table.iloc[0, :].dropna().index[0] + 1,
+#         "header": raw_table.iloc[0, :].dropna().index[0] + num_hidden_state_factors - 1,
+#     }
+#     return pd.read_excel(
+#         path,
+#         index_col=list(range(level_counts["index"])),
+#         header=list(range(level_counts["header"]))
+#         ).astype(np.float64)
+
+# def read_B_matrices(path):
+
+#     all_sheets = pd.read_excel(path, sheet_name = None, header=None)
+
+#     level_counts = {}
+#     for sheet_name, raw_table in all_sheets.items():
+    
+#         level_counts[sheet_name] = {
+#             "index": raw_table.iloc[0, :].dropna().index[0]+1,
+#             "header": raw_table.iloc[0, :].dropna().index[0]+2,
+#         }
+
+#     stub_dict = {}
+#     for sheet_name, level_counts_sheet in level_counts.items():
+#         sheet_f = pd.read_excel(
+#             path,
+#             sheet_name = sheet_name,
+#             index_col=list(range(level_counts_sheet["index"])),
+#             header=list(range(level_counts_sheet["header"]))
+#             ).astype(np.float64)
+#         stub_dict[sheet_name] = sheet_f
+        
+#     return stub_dict
+
+# def convert_A_stub_to_ndarray(A_stub, model_labels):
+#     """
+#     This function converts a multi-index pandas dataframe `A_stub` into an object array of different
+#     A matrices, one per observation modality. 
+#     """
+
+#     num_obs, num_modalities, num_states, num_factors = get_model_dimensions_from_labels(model_labels)
+
+#     A = obj_array(num_modalities)
+
+#     for g, modality_name in enumerate(model_labels['observations'].keys()):
+#         A[g] = A_stub.loc[modality_name].to_numpy().reshape(num_obs[g], *num_states)
+#         assert (A[g].sum(axis=0) == 1.0).all(), 'A matrix not normalized! Check your initialization....\n'
+
+#     return A
+
+# def convert_B_stubs_to_ndarray(B_stubs, model_labels):
+#     """
+#     This function converts a list of multi-index pandas dataframes `B_stubs` into an object array
+#     of different B matrices, one per hidden state factor
+#     """
+
+#     _, _, num_states, num_factors, num_controls, num_control_fac  = get_model_dimensions_from_labels(model_labels)
+
+#     B = obj_array(num_factors)
+
+#     for f, factor_name in enumerate(B_stubs.keys()):
+        
+#         B[f] = B_stubs[factor_name].to_numpy().reshape(num_states[f], num_states[f], num_controls[f])
+#         assert (B[f].sum(axis=0) == 1.0).all(), 'B matrix not normalized! Check your initialization....\n'
+
+#     return B
+
+# def build_belief_array(qx):
+
+#     """
+#     This function constructs array-ified (not nested) versions
+#     of the posterior belief arrays, that are separated 
+#     by policy, timepoint, and hidden state factor
+#     """
+
+#     num_policies = len(qx)
+#     num_timesteps = len(qx[0])
+#     num_factors = len(qx[0][0])
+
+#     if num_factors > 1:
+#         belief_array = utils.obj_array(num_factors)
+#         for factor in range(num_factors):
+#             belief_array[factor] = np.zeros( (num_policies, qx[0][0][factor].shape[0], num_timesteps) )
+#         for policy_i in range(num_policies):
+#             for timestep in range(num_timesteps):
+#                 for factor in range(num_factors):
+#                     belief_array[factor][policy_i, :, timestep] = qx[policy_i][timestep][factor]
+#     else:
+#         num_states = qx[0][0][0].shape[0]
+#         belief_array = np.zeros( (num_policies, num_states, num_timesteps) )
+#         for policy_i in range(num_policies):
+#             for timestep in range(num_timesteps):
+#                 belief_array[policy_i, :, timestep] = qx[policy_i][timestep][0]
+    
+#     return belief_array
+
+# def build_xn_vn_array(xn):
+
+#     """
+#     This function constructs array-ified (not nested) versions
+#     of the posterior xn (beliefs) or vn (prediction error) arrays, that are separated 
+#     by iteration, hidden state factor, timepoint, and policy
+#     """
+
+#     num_policies = len(xn)
+#     num_itr = len(xn[0])
+#     num_factors = len(xn[0][0])
+
+#     if num_factors > 1:
+#         xn_array = utils.obj_array(num_factors)
+#         for factor in range(num_factors):
+#             num_states, infer_len = xn[0][0][f].shape
+#             xn_array[factor] = np.zeros( (num_itr, num_states, infer_len, num_policies) )
+#         for policy_i in range(num_policies):
+#             for itr in range(num_itr):
+#                 for factor in range(num_factors):
+#                     xn_array[factor][itr,:,:,policy_i] = xn[policy_i][itr][factor]
+#     else:
+#         num_states, infer_len  = xn[0][0][0].shape
+#         xn_array = np.zeros( (num_itr, num_states, infer_len, num_policies) )
+#         for policy_i in range(num_policies):
+#             for itr in range(num_itr):
+#                 xn_array[itr,:,:,policy_i] = xn[policy_i][itr][0] 
+    
+#     return xn_array
diff --git a/pymdp/learning.py b/pymdp/learning.py
index ec334f68..1c21568a 100644
--- a/pymdp/learning.py
+++ b/pymdp/learning.py
@@ -57,6 +57,59 @@ def update_obs_likelihood_dirichlet(pA, A, obs, qs, lr=1.0, modalities="all"):
 
     return qA
 
+def update_obs_likelihood_dirichlet_factorized(pA, A, obs, qs, A_factor_list, lr=1.0, modalities="all"):
+    """ 
+    Update Dirichlet parameters of the observation likelihood distribution, in a case where the observation model is reduced (factorized) and only represents
+    the conditional dependencies between the observation modalities and particular hidden state factors (whose indices are specified in each modality-specific entry of ``A_factor_list``)
+
+    Parameters
+    -----------
+    pA: ``numpy.ndarray`` of dtype object
+        Prior Dirichlet parameters over observation model (same shape as ``A``)
+    A: ``numpy.ndarray`` of dtype object
+        Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of
+        stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store 
+        the probability of observation level ``i`` given hidden state levels ``j, k, ...``
+    obs: 1D ``numpy.ndarray``, ``numpy.ndarray`` of dtype object, ``int`` or ``tuple``
+        The observation (generated by the environment). If single modality, this can be a 1D ``numpy.ndarray``
+        (one-hot vector representation) or an ``int`` (observation index)
+        If multi-modality, this can be ``numpy.ndarray`` of dtype object whose entries are 1D one-hot vectors,
+        or a ``tuple`` (of ``int``)
+    qs: 1D ``numpy.ndarray`` or ``numpy.ndarray`` of dtype object, default None
+        Marginal posterior beliefs over hidden states at current timepoint.
+    A_factor_list: ``list`` of ``list`` of ``int``
+        List of lists, where each list with index `m` contains the indices of the hidden states that observation modality `m` depends on.
+    lr: float, default 1.0
+        Learning rate, scale of the Dirichlet pseudo-count update.
+    modalities: ``list``, default "all"
+        Indices (ranging from 0 to ``n_modalities - 1``) of the observation modalities to include 
+        in learning. Defaults to "all", meaning that modality-specific sub-arrays of ``pA``
+        are all updated using the corresponding observations.
+    
+    Returns
+    -----------
+    qA: ``numpy.ndarray`` of dtype object
+        Posterior Dirichlet parameters over observation model (same shape as ``A``), after having updated it with observations.
+    """
+
+    num_modalities = len(pA)
+    num_observations = [pA[modality].shape[0] for modality in range(num_modalities)]
+
+    obs_processed = utils.process_observation(obs, num_modalities, num_observations)
+    obs = utils.to_obj_array(obs_processed)
+
+    if modalities == "all":
+        modalities = list(range(num_modalities))
+
+    qA = copy.deepcopy(pA)
+        
+    for modality in modalities:
+        dfda = maths.spm_cross(obs[modality], qs[A_factor_list[modality]])
+        dfda = dfda * (A[modality] > 0).astype("float")
+        qA[modality] = qA[modality] + (lr * dfda)
+
+    return qA
+
 def update_state_likelihood_dirichlet(
     pB, B, actions, qs, qs_prev, lr=1.0, factors="all"
 ):
@@ -105,6 +158,57 @@ def update_state_likelihood_dirichlet(
 
     return qB
 
+def update_state_likelihood_dirichlet_interactions(
+    pB, B, actions, qs, qs_prev, B_factor_list, lr=1.0, factors="all"
+):
+    """
+    Update Dirichlet parameters of the transition distribution, in the case when 'interacting' hidden state factors are present, i.e.
+    the dynamics of a given hidden state factor `f` are no longer independent of the dynamics of other hidden state factors.
+
+    Parameters
+    -----------
+    pB: ``numpy.ndarray`` of dtype object
+        Prior Dirichlet parameters over transition model (same shape as ``B``)
+    B: ``numpy.ndarray`` of dtype object
+        Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.
+        Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability
+        of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.
+    actions: 1D ``numpy.ndarray``
+        A vector with length equal to the number of control factors, where each element contains the index of the action (for that control factor) performed at 
+        a given timestep.
+    qs: 1D ``numpy.ndarray`` or ``numpy.ndarray`` of dtype object
+        Marginal posterior beliefs over hidden states at current timepoint.
+    qs_prev: 1D ``numpy.ndarray`` or ``numpy.ndarray`` of dtype object
+        Marginal posterior beliefs over hidden states at previous timepoint.
+    B_factor_list: ``list`` of ``list`` of ``int``
+        A list of lists, where each element ``B_factor_list[f]`` is a list of indices of hidden state factors that that are needed to predict the dynamics of hidden state factor ``f``.
+    lr: float, default ``1.0``
+        Learning rate, scale of the Dirichlet pseudo-count update.
+    factors: ``list``, default "all"
+        Indices (ranging from 0 to ``n_factors - 1``) of the hidden state factors to include 
+        in learning. Defaults to "all", meaning that factor-specific sub-arrays of ``pB``
+        are all updated using the corresponding hidden state distributions and actions.
+
+    Returns
+    -----------
+    qB: ``numpy.ndarray`` of dtype object
+        Posterior Dirichlet parameters over transition model (same shape as ``B``), after having updated it with state beliefs and actions.
+    """
+
+    num_factors = len(pB)
+
+    qB = copy.deepcopy(pB)
+   
+    if factors == "all":
+        factors = list(range(num_factors))
+
+    for factor in factors:
+        dfdb = maths.spm_cross(qs[factor], qs_prev[B_factor_list[factor]])
+        dfdb *= (B[factor][...,int(actions[factor])] > 0).astype("float")
+        qB[factor][...,int(actions[factor])] += (lr*dfdb)
+
+    return qB
+
 def update_state_prior_dirichlet(
     pD, qs, lr=1.0, factors="all"
 ):
diff --git a/pymdp/maths.py b/pymdp/maths.py
index 27b163a8..1d5e9e4d 100644
--- a/pymdp/maths.py
+++ b/pymdp/maths.py
@@ -12,6 +12,7 @@
 from scipy import special
 from pymdp import utils
 from itertools import chain
+from opt_einsum import contract
 
 EPS_VAL = 1e-16 # global constant for use in spm_log() function
 
@@ -105,6 +106,28 @@ def spm_dot_classic(X, x, dims_to_omit=None):
 
     return Y
 
+def factor_dot_flex(M, xs, dims, keep_dims=None):
+    """ Dot product of a multidimensional array with `x`.
+    
+    Parameters
+    ----------
+    - `M` [numpy.ndarray] - tensor
+    - 'xs' [list of numpyr.ndarray] - list of tensors
+    - 'dims' [list of tuples] - list of dimensions of xs tensors in tensor M
+    - 'keep_dims' [tuple] - tuple of integers denoting dimesions to keep
+    Returns 
+    -------
+    - `Y` [1D numpy.ndarray] - the result of the dot product
+    """
+    all_dims = tuple(range(M.ndim))
+    matrix = [[xs[f], dims[f]] for f in range(len(xs))]
+    args = [M, all_dims]
+    for row in matrix:
+        args.extend(row)
+
+    args += [keep_dims]
+    return contract(*args, backend='numpy')
+
 def spm_dot_old(X, x, dims_to_omit=None, obs_mode=False):
     """ Dot product of a multidimensional array with `x`. The dimensions in `dims_to_omit` 
     will not be summed across during the dot product
@@ -205,12 +228,9 @@ def spm_cross(x, y=None, *args):
     if y is not None and utils.is_obj_array(y):
         y = spm_cross(*list(y))
 
-    reshape_dims = tuple(list(x.shape) + list(np.ones(y.ndim, dtype=int)))
-    A = x.reshape(reshape_dims)
-
-    reshape_dims = tuple(list(np.ones(x.ndim, dtype=int)) + list(y.shape))
-    B = y.reshape(reshape_dims)
-    z = np.squeeze(A * B)
+    A = np.expand_dims(x, tuple(range(-y.ndim, 0)))
+    B = np.expand_dims(y, tuple(range(x.ndim)))
+    z = A * B
 
     for x in args:
         z = spm_cross(z, x)
@@ -250,6 +270,23 @@ def get_joint_likelihood_seq(A, obs, num_states):
         ll_seq[t] = get_joint_likelihood(A, obs_t, num_states)
     return ll_seq
 
+def get_joint_likelihood_seq_by_modality(A, obs, num_states):
+    """
+    Returns joint likelihoods for each modality separately
+    """
+
+    ll_seq = utils.obj_array(len(obs))
+    n_modalities = len(A)
+
+    for t, obs_t in enumerate(obs):
+        likelihood = utils.obj_array(n_modalities)
+        obs_t_obj = utils.to_obj_array(obs_t)
+        for (m, A_m) in enumerate(A):
+            likelihood[m] = dot_likelihood(A_m, obs_t_obj[m])
+        ll_seq[t] = likelihood
+    
+    return ll_seq
+
 
 def spm_norm(A):
     """ 
@@ -372,6 +409,110 @@ def calc_free_energy(qs, prior, n_factors, likelihood=None):
         free_energy -= compute_accuracy(likelihood, qs)
     return free_energy
 
+def spm_calc_qo_entropy(A, x):
+    """ 
+    Function that just calculates the entropy part of the state information gain, using the same method used in 
+    spm_MDP_G.m in the original matlab code.
+
+    Parameters
+    ----------
+    A (numpy ndarray or array-object):
+        array assigning likelihoods of observations/outcomes under the various 
+        hidden state configurations
+    
+    x (numpy ndarray or array-object):
+        Categorical distribution presenting probabilities of hidden states 
+        (this can also be interpreted as the predictive density over hidden 
+        states/causes if you're calculating the expected Bayesian surprise)
+        
+    Returns
+    -------
+    H (float):
+        the entropy of the marginal distribution over observations/outcomes
+    """
+
+    num_modalities = len(A)
+
+    # Probability distribution over the hidden causes: i.e., Q(x)
+    qx = spm_cross(x)
+    qo = 0
+    idx = np.array(np.where(qx > np.exp(-16))).T
+
+    if utils.is_obj_array(A):
+        # Accumulate expectation of entropy: i.e., E_{Q(o, x)}[lnP(o|x)] = E_{P(o|x)Q(x)}[lnP(o|x)] = E_{Q(x)}[P(o|x)lnP(o|x)] = E_{Q(x)}[H[P(o|x)]]
+        for i in idx:
+            # Probability over outcomes for this combination of causes
+            po = np.ones(1)
+            for modality_idx, A_m in enumerate(A):
+                index_vector = [slice(0, A_m.shape[0])] + list(i)
+                po = spm_cross(po, A_m[tuple(index_vector)])
+            po = po.ravel()
+            qo += qx[tuple(i)] * po
+    else:
+        for i in idx:
+            po = np.ones(1)
+            index_vector = [slice(0, A.shape[0])] + list(i)
+            po = spm_cross(po, A[tuple(index_vector)])
+            po = po.ravel()
+            qo += qx[tuple(i)] * po
+   
+    # Compute entropy of expectations: i.e., -E_{Q(o)}[lnQ(o)]
+    H = - qo.dot(spm_log_single(qo))
+
+    return H
+
+def spm_calc_neg_ambig(A, x):
+    """
+    Function that just calculates the negativity ambiguity part of the state information gain, using the same method used in 
+    spm_MDP_G.m in the original matlab code.
+    
+    Parameters
+    ----------
+    A (numpy ndarray or array-object):
+        array assigning likelihoods of observations/outcomes under the various 
+        hidden state configurations
+    
+    x (numpy ndarray or array-object):
+        Categorical distribution presenting probabilities of hidden states 
+        (this can also be interpreted as the predictive density over hidden 
+        states/causes if you're calculating the expected Bayesian surprise)
+        
+    Returns
+    -------
+    G (float):
+        the negative ambiguity (negative entropy of the likelihood of observations given hidden states, expected under current posterior over hidden states)
+    """
+
+    num_modalities = len(A)
+
+    # Probability distribution over the hidden causes: i.e., Q(x)
+    qx = spm_cross(x)
+    G = 0
+    qo = 0
+    idx = np.array(np.where(qx > np.exp(-16))).T
+
+    if utils.is_obj_array(A):
+        # Accumulate expectation of entropy: i.e., E_{Q(o, x)}[lnP(o|x)] = E_{P(o|x)Q(x)}[lnP(o|x)] = E_{Q(x)}[P(o|x)lnP(o|x)] = E_{Q(x)}[H[P(o|x)]]
+        for i in idx:
+            # Probability over outcomes for this combination of causes
+            po = np.ones(1)
+            for modality_idx, A_m in enumerate(A):
+                index_vector = [slice(0, A_m.shape[0])] + list(i)
+                po = spm_cross(po, A_m[tuple(index_vector)])
+
+            po = po.ravel()
+            qo += qx[tuple(i)] * po
+            G += qx[tuple(i)] * po.dot(np.log(po + np.exp(-16)))
+    else:
+        for i in idx:
+            po = np.ones(1)
+            index_vector = [slice(0, A.shape[0])] + list(i)
+            po = spm_cross(po, A[tuple(index_vector)])
+            po = po.ravel()
+            qo += qx[tuple(i)] * po
+            G += qx[tuple(i)] * po.dot(np.log(po + np.exp(-16)))
+
+    return G
 
 def spm_MDP_G(A, x):
     """
@@ -406,14 +547,14 @@ def spm_MDP_G(A, x):
     idx = np.array(np.where(qx > np.exp(-16))).T
 
     if utils.is_obj_array(A):
-        # Accumulate expectation of entropy: i.e., E_{Q(o, s)}[lnP(o|x)]
+        # Accumulate expectation of entropy: i.e., E_{Q(o, x)}[lnP(o|x)] = E_{P(o|x)Q(x)}[lnP(o|x)] = E_{Q(x)}[P(o|x)lnP(o|x)] = E_{Q(x)}[H[P(o|x)]]
         for i in idx:
             # Probability over outcomes for this combination of causes
             po = np.ones(1)
             for modality_idx, A_m in enumerate(A):
                 index_vector = [slice(0, A_m.shape[0])] + list(i)
                 po = spm_cross(po, A_m[tuple(index_vector)])
-
+            
             po = po.ravel()
             qo += qx[tuple(i)] * po
             G += qx[tuple(i)] * po.dot(np.log(po + np.exp(-16)))
@@ -431,3 +572,37 @@ def spm_MDP_G(A, x):
 
     return G
 
+def kl_div(P,Q):
+    """
+    Parameters
+    ----------
+    P : Categorical probability distribution
+    Q : Categorical probability distribution
+
+    Returns
+    -------
+    The KL-divergence of P and Q
+
+    """
+    dkl = 0
+    for i in range(len(P)):
+        dkl += np.dot(P[i], np.log(P[i] + EPS_VAL) - np.log(Q[i] + EPS_VAL))
+    return(dkl)
+
+def entropy(A):
+    """
+    Compute the entropy term H of the likelihood matrix,
+    i.e. one entropy value per column
+    """
+    entropies = np.empty(len(A), dtype=object)
+    for i in range(len(A)):
+        if len(A[i].shape) > 2:
+            obs_dim = A[i].shape[0]
+            s_dim = A[i].size // obs_dim
+            A_merged = A[i].reshape(obs_dim, s_dim)
+        else:
+            A_merged = A[i]
+
+        H = - np.diag(np.matmul(A_merged.T, np.log(A_merged + EPS_VAL)))
+        entropies[i] = H.reshape(*A[i].shape[1:])
+    return entropies
\ No newline at end of file
diff --git a/pymdp/utils.py b/pymdp/utils.py
index 7b19ee56..b371f553 100644
--- a/pymdp/utils.py
+++ b/pymdp/utils.py
@@ -108,21 +108,27 @@ def onehot(value, num_values):
     arr[value] = 1.0
     return arr
 
-def random_A_matrix(num_obs, num_states):
+def random_A_matrix(num_obs, num_states, A_factor_list=None):
     if type(num_obs) is int:
         num_obs = [num_obs]
     if type(num_states) is int:
         num_states = [num_states]
     num_modalities = len(num_obs)
 
+    if A_factor_list is None:
+        num_factors = len(num_states)
+        A_factor_list = [list(range(num_factors))] * num_modalities
+
     A = obj_array(num_modalities)
     for modality, modality_obs in enumerate(num_obs):
-        modality_shape = [modality_obs] + num_states
+        # lagging_dimensions = [ns for i, ns in enumerate(num_states) if i in A_factor_list[modality]] # enforces sortedness of A_factor_list
+        lagging_dimensions = [num_states[idx] for idx in A_factor_list[modality]]
+        modality_shape = [modality_obs] + lagging_dimensions
         modality_dist = np.random.rand(*modality_shape)
         A[modality] = norm_dist(modality_dist)
     return A
 
-def random_B_matrix(num_states, num_controls):
+def random_B_matrix(num_states, num_controls, B_factor_list=None):
     if type(num_states) is int:
         num_states = [num_states]
     if type(num_controls) is int:
@@ -130,9 +136,14 @@ def random_B_matrix(num_states, num_controls):
     num_factors = len(num_states)
     assert len(num_controls) == len(num_states)
 
+    if B_factor_list is None:
+        B_factor_list = [[f] for f in range(num_factors)]
+
     B = obj_array(num_factors)
     for factor in range(num_factors):
-        factor_shape = (num_states[factor], num_states[factor], num_controls[factor])
+        lagging_shape = [ns for i, ns in enumerate(num_states) if i in B_factor_list[factor]]
+        factor_shape = [num_states[factor]] + lagging_shape + [num_controls[factor]]
+        # factor_shape = (num_states[factor], num_states[factor], num_controls[factor])
         factor_dist = np.random.rand(*factor_shape)
         B[factor] = norm_dist(factor_dist)
     return B
@@ -189,7 +200,7 @@ def dirichlet_like(template_categorical, scale = 1.0):
 
     return dirichlet_out
 
-def get_model_dimensions(A=None, B=None):
+def get_model_dimensions(A=None, B=None, factorized=False):
 
     if A is None and B is None:
         raise ValueError(
@@ -207,8 +218,13 @@ def get_model_dimensions(A=None, B=None):
         num_factors = len(num_states)
     else:
         if A is not None:
-            num_states = list(A[0].shape[1:]) if is_obj_array(A) else list(A.shape[1:])
-            num_factors = len(num_states)
+            if not factorized:
+                num_states = list(A[0].shape[1:]) if is_obj_array(A) else list(A.shape[1:])
+                num_factors = len(num_states)
+            else:
+                raise ValueError(
+                    "`A` array is factorized and  cannot be used to infer `num_states`"
+                )
         else:
             num_states, num_factors = None, None
     
@@ -471,127 +487,6 @@ def construct_full_a(A_reduced, original_factor_idx, num_states):
     
     return A
 
-def create_A_matrix_stub(model_labels):
-
-    dimensions = get_model_dimensions_from_labels(model_labels)
-
-    obs_labels, state_labels = model_labels['observations'], model_labels['states']
-
-    state_combinations = pd.MultiIndex.from_product(list(state_labels.values()), names=list(state_labels.keys()))
-    num_rows = sum(dimensions.num_observations)
-
-    cell_values = np.zeros((num_rows, len(state_combinations)))
-
-    obs_combinations = []
-    for modality in obs_labels.keys():
-        levels_to_combine = [[modality]] + [obs_labels[modality]]
-        obs_combinations += list(itertools.product(*levels_to_combine))
-
-
-    obs_combinations = pd.MultiIndex.from_tuples(obs_combinations, names = ["Modality", "Level"])
-
-    A_matrix = pd.DataFrame(cell_values, index = obs_combinations, columns=state_combinations)
-
-    return A_matrix
-
-def create_B_matrix_stubs(model_labels):
-
-    dimensions = get_model_dimensions_from_labels(model_labels)
-
-    state_labels = model_labels['states']
-    action_labels = model_labels['actions']
-
-    B_matrices = {}
-
-    for f_idx, factor in enumerate(state_labels.keys()):
-
-        control_fac_name = list(action_labels)[f_idx]
-        factor_list = [state_labels[factor]] + [action_labels[control_fac_name]]
-
-        prev_state_action_combos = pd.MultiIndex.from_product(factor_list, names=[factor, list(action_labels.keys())[f_idx]])
-
-        num_state_action_combos = dimensions.num_states[f_idx] * dimensions.num_controls[f_idx]
-
-        num_rows = dimensions.num_states[f_idx]
-
-        cell_values = np.zeros((num_rows, num_state_action_combos))
-
-        next_state_list = state_labels[factor]
-        
-        B_matrix_f = pd.DataFrame(cell_values, index = next_state_list, columns=prev_state_action_combos)
-
-        B_matrices[factor] = B_matrix_f
-
-    return B_matrices
-
-def read_A_matrix(path, num_hidden_state_factors):
-    raw_table = pd.read_excel(path, header=None)
-    level_counts = {
-        "index": raw_table.iloc[0, :].dropna().index[0] + 1,
-        "header": raw_table.iloc[0, :].dropna().index[0] + num_hidden_state_factors - 1,
-    }
-    return pd.read_excel(
-        path,
-        index_col=list(range(level_counts["index"])),
-        header=list(range(level_counts["header"]))
-        ).astype(np.float64)
-
-def read_B_matrices(path):
-
-    all_sheets = pd.read_excel(path, sheet_name = None, header=None)
-
-    level_counts = {}
-    for sheet_name, raw_table in all_sheets.items():
-    
-        level_counts[sheet_name] = {
-            "index": raw_table.iloc[0, :].dropna().index[0]+1,
-            "header": raw_table.iloc[0, :].dropna().index[0]+2,
-        }
-
-    stub_dict = {}
-    for sheet_name, level_counts_sheet in level_counts.items():
-        sheet_f = pd.read_excel(
-            path,
-            sheet_name = sheet_name,
-            index_col=list(range(level_counts_sheet["index"])),
-            header=list(range(level_counts_sheet["header"]))
-            ).astype(np.float64)
-        stub_dict[sheet_name] = sheet_f
-        
-    return stub_dict
-
-def convert_A_stub_to_ndarray(A_stub, model_labels):
-    """
-    This function converts a multi-index pandas dataframe `A_stub` into an object array of different
-    A matrices, one per observation modality. 
-    """
-    dimensions = get_model_dimensions_from_labels(model_labels)
-
-    A = obj_array(dimensions.num_observation_modalities)
-
-    for g, modality_name in enumerate(model_labels['observations'].keys()):
-        A[g] = A_stub.loc[modality_name].to_numpy().reshape(dimensions.num_observations[g], *dimensions.num_states)
-        assert (A[g].sum(axis=0) == 1.0).all(), 'A matrix not normalized! Check your initialization....\n'
-
-    return A
-
-def convert_B_stubs_to_ndarray(B_stubs, model_labels):
-    """
-    This function converts a list of multi-index pandas dataframes `B_stubs` into an object array
-    of different B matrices, one per hidden state factor
-    """
-
-    dimensions  = get_model_dimensions_from_labels(model_labels)
-
-    B = obj_array(dimensions.num_control_factors)
-
-    for f, factor_name in enumerate(B_stubs.keys()):
-        
-        B[f] = B_stubs[factor_name].to_numpy().reshape(dimensions.num_states[f], dimensions.num_states[f], dimensions.num_controls[f])
-        assert (B[f].sum(axis=0) == 1.0).all(), 'B matrix not normalized! Check your initialization....\n'
-
-    return B
-
 # def build_belief_array(qx):
 
 #     """
diff --git a/requirements.txt b/requirements.txt
index d09a154b..de815d0c 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -7,7 +7,6 @@ nose>=1.3.7
 numpy>=1.19.5
 openpyxl>=3.0.7
 packaging>=20.8
-pandas>=1.2.4
 Pillow>=8.2.0
 pluggy>=0.13.1
 py>=1.10.0
@@ -24,3 +23,9 @@ xlsxwriter>=1.4.3
 sphinx-rtd-theme>=0.4
 myst-nb>=0.13.1
 autograd>=1.3
+jax>=0.3.4
+jaxlib>=0.3.4
+equinox>=0.9
+numpyro>=0.1
+arviz>=0.13
+optax>=0.1
\ No newline at end of file
diff --git a/setup.py b/setup.py
index f8378fba..03e2cbae 100644
--- a/setup.py
+++ b/setup.py
@@ -40,12 +40,19 @@
     'xlsxwriter>=1.4.3',
     'sphinx-rtd-theme>=0.4',
     'myst-nb>=0.13.1',
-    'autograd>=1.3'
+    'autograd>=1.3',
+    'jax>=0.3.4',
+    'jaxlib>=0.3.4',
+    'equinox>=0.9',
+    'numpyro>=0.1',
+    'arviz>=0.13',
+    'optax>=0.1'
     ],
     packages=[
         "pymdp",
         "pymdp.envs",
-        "pymdp.algos"
+        "pymdp.algos",
+        "pymdp.jax"
     ],
     include_package_data=True,
     keywords=[
diff --git a/test/test_SPM_validation.py b/test/test_SPM_validation.py
index 8c0bc136..ee386378 100644
--- a/test/test_SPM_validation.py
+++ b/test/test_SPM_validation.py
@@ -49,7 +49,7 @@ def test_active_inference_SPM_1a(self):
             q_pi, G= agent.infer_policies()
             action = agent.sample_action()
 
-            actions_python[t] = action
+            actions_python[t] = action.item()
 
             xn_python = build_xn_vn_array(xn_t)
             vn_python = build_xn_vn_array(vn_t)
diff --git a/test/test_agent.py b/test/test_agent.py
index ad3768ca..161bca56 100644
--- a/test/test_agent.py
+++ b/test/test_agent.py
@@ -164,7 +164,7 @@ def test_agent_infer_states(self):
 
         policies = control.construct_policies(num_states, num_controls, policy_len = planning_horizon)
 
-        qs_pi_validation, _ = inference.update_posterior_states_full(A, B, [o], policies, prior = agent.D, policy_sep_prior = False)
+        qs_pi_validation, _ = inference.update_posterior_states_full_factorized(A, agent.mb_dict, B, agent.B_factor_list, [o], policies, prior = agent.D, policy_sep_prior = False)
 
         for p_idx in range(len(policies)):
             for t in range(planning_horizon+backwards_horizon):
@@ -201,6 +201,98 @@ def test_mmp_active_inference(self):
         self.assertEqual(len(agent.prev_obs), T)
         self.assertEqual(len(agent.prev_actions), T)
 
+    def test_agent_with_A_learning_vanilla(self):
+        """ Unit test for updating prior Dirichlet parameters over likelihood model (pA) with the ``Agent`` class,
+        in the case that you're using "vanilla" inference mode.
+        """
+
+        # 3 x 3, 2-dimensional grid world
+        num_obs = [9]
+        num_states = [9]
+        num_controls = [4]
+
+        A = utils.obj_array_zeros([ [num_obs[0], num_states[0]] ])
+        A[0] = np.eye(num_obs[0])
+
+        pA = utils.dirichlet_like(A, scale=1.)
+
+        action_labels = ["LEFT", "DOWN", "RIGHT", "UP"]
+
+        # get some true transition dynamics
+        true_transition_matrix = generate_grid_world_transitions(action_labels, num_rows = 3, num_cols = 3)
+        B = utils.to_obj_array(true_transition_matrix)
+        
+        # instantiate the agent
+        learning_rate_pA = np.random.rand()
+        agent = Agent(A=A, B=B, pA=pA, inference_algo="VANILLA", action_selection="stochastic", lr_pA=learning_rate_pA)
+
+        # time horizon
+        T = 10
+        next_state = 0
+
+        for t in range(T):
+            
+            prev_state = next_state
+            o = [prev_state] 
+            qx = agent.infer_states(o)
+            agent.infer_policies()
+            agent.sample_action()
+
+            # sample the next state given the true transition dynamics and the sampled action
+            next_state = utils.sample(true_transition_matrix[:,prev_state,int(agent.action[0])])
+            
+            # compute the predicted update to the action-conditioned slice of qB
+            predicted_update = agent.pA[0] + learning_rate_pA*maths.spm_cross(utils.onehot(o[0], num_obs[0]), qx[0])
+            qA = agent.update_A(o) # update qA using the agent function
+
+            # check if the predicted update and the actual update are the same
+            self.assertTrue(np.allclose(predicted_update, qA[0]))
+    
+    def test_agent_with_A_learning_vanilla_factorized(self):
+        """ Unit test for updating prior Dirichlet parameters over likelihood model (pA) with the ``Agent`` class,
+        in the case that you're using "vanilla" inference mode. In this case, we encode sparse conditional dependencies by specifying
+        a non-all-to-all `A_factor_list`, that specifies the subset of hidden state factors that different modalities depend on.
+        """
+
+        num_obs = [5, 4, 3]
+        num_states = [9, 8, 2, 4]
+        num_controls = [2, 2, 1, 1]
+
+        A_factor_list = [[0, 1], [0, 2], [3]]
+
+        A = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_factor_list)
+        pA = utils.dirichlet_like(A, scale=1.)
+
+        B = utils.random_B_matrix(num_states, num_controls)
+        
+        # instantiate the agent
+        learning_rate_pA = np.random.rand()
+        agent = Agent(A=A, B=B, pA=pA, A_factor_list=A_factor_list, inference_algo="VANILLA", action_selection="stochastic", lr_pA=learning_rate_pA)
+
+        # time horizon
+        T = 10
+
+        obs_seq = []
+        for t in range(T):
+            obs_seq.append([np.random.randint(obs_dim) for obs_dim in num_obs])
+        
+        for t in range(T):
+            print(t)
+            
+            qx = agent.infer_states(obs_seq[t])
+            agent.infer_policies()
+            agent.sample_action()
+            
+            # compute the predicted update to the action-conditioned slice of qB
+            qA_valid = utils.obj_array_zeros([A_m.shape for A_m in A])
+            for m, pA_m in enumerate(agent.pA):
+                qA_valid[m] = pA_m + learning_rate_pA*maths.spm_cross(utils.onehot(obs_seq[t][m], num_obs[m]), qx[A_factor_list[m]])
+            qA_test = agent.update_A(obs_seq[t]) # update qA using the agent function
+
+            # check if the predicted update and the actual update are the same
+            for m, qA_valid_m in enumerate(qA_valid):
+                self.assertTrue(np.allclose(qA_valid_m, qA_test[m]))
+
     def test_agent_with_B_learning_vanilla(self):
         """ Unit test for updating prior Dirichlet parameters over transition model (pB) with the ``Agent`` class,
         in the case that you're using "vanilla" inference mode.
@@ -570,13 +662,150 @@ def test_agent_distributional_obs(self):
 
         policies = control.construct_policies(num_states, num_controls, policy_len = planning_horizon)
 
-        qs_pi_validation, _ = inference.update_posterior_states_full(A, B, [p_o], policies, prior = agent.D, policy_sep_prior = False)
+        qs_pi_validation, _ = inference.update_posterior_states_full_factorized(A, agent.mb_dict, B, agent.B_factor_list, [p_o], policies, prior = agent.D, policy_sep_prior = False)
 
         for p_idx in range(len(policies)):
             for t in range(planning_horizon+backwards_horizon):
                 for f in range(len(num_states)):
                     self.assertTrue(np.isclose(qs_pi_validation[p_idx][t][f], qs_pi_out[p_idx][t][f]).all())
 
+    def test_agent_with_factorized_inference(self):
+        """
+        Test that an instance of the `Agent` class can be initialized with a provided `A_factor_list` and run the factorized inference algorithm. Validate
+        against an equivalent `Agent` whose `A` matrix represents the full set of (redundant) conditional dependence relationships.
+        """
+
+        num_obs = [5, 4]
+        num_states = [2, 3]
+        num_controls = [2, 3]
+
+        A_factor_list = [ [0], [1] ]
+        A_reduced = utils.random_A_matrix(num_obs, num_states, A_factor_list)
+        B = utils.random_B_matrix(num_states, num_controls)
+
+        agent = Agent(A=A_reduced, B=B, A_factor_list=A_factor_list, inference_algo = "VANILLA")
+
+        obs = [np.random.randint(obs_dim) for obs_dim in num_obs]
+
+        qs_out = agent.infer_states(obs)
+
+        A_full = utils.initialize_empty_A(num_obs, num_states)
+        for m, A_m in enumerate(A_full):
+            other_factors = list(set(range(len(num_states))) - set(A_factor_list[m])) # list of the factors that modality `m` does not depend on
+
+            # broadcast or tile the reduced A matrix (`A_reduced`) along the dimensions of corresponding to `other_factors`
+            expanded_dims = [num_obs[m]] + [1 if f in other_factors else ns for (f, ns) in enumerate(num_states)]
+            tile_dims = [1] + [ns if f in other_factors else 1 for (f, ns) in enumerate(num_states)]
+            A_full[m] = np.tile(A_reduced[m].reshape(expanded_dims), tile_dims)
+        
+        agent = Agent(A=A_full, B=B, inference_algo = "VANILLA")
+        qs_validation = agent._infer_states_test(obs)
+
+        for qs_out_f, qs_val_f in zip(qs_out, qs_validation):
+            self.assertTrue(np.isclose(qs_out_f, qs_val_f).all())
+    
+    def test_agent_with_interactions_in_B(self):
+        """
+        Test that an instance of the `Agent` class can be initialized with a provided `B_factor_list` and run a time loop of active inferece
+        """
+
+        num_obs = [5, 4]
+        num_states = [2, 3]
+        num_controls = [2, 3]
+
+        A = utils.random_A_matrix(num_obs, num_states)
+        B = utils.random_B_matrix(num_states, num_controls)
+
+        agent_test = Agent(A=A, B=B, B_factor_list=[[0], [1]])
+        agent_val = Agent(A=A, B=B)
+
+        obs_seq = []
+        for t in range(5):
+            obs_seq.append([np.random.randint(obs_dim) for obs_dim in num_obs])
+        
+        for t in range(5):
+            qs_out = agent_test.infer_states(obs_seq[t])
+            qs_val = agent_val._infer_states_test(obs_seq[t])
+            for qs_out_f, qs_val_f in zip(qs_out, qs_val):
+                self.assertTrue(np.isclose(qs_out_f, qs_val_f).all())
+            
+            agent_test.infer_policies()
+            agent_val.infer_policies()
+
+            agent_test.sample_action()
+            agent_val.sample_action()
+    
+    def test_actinfloop_factorized(self):
+        """
+        Test that an instance of the `Agent` class can be initialized and run
+        with the fully-factorized generative model functions (including policy inference)
+        """
+
+        num_obs = [5, 4, 4]
+        num_states = [2, 3, 5]
+        num_controls = [2, 3, 2]
+
+        A_factor_list = [[0], [0, 1], [0, 1, 2]]
+        B_factor_list = [[0], [0, 1], [1, 2]]
+        A = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_factor_list)
+        B = utils.random_B_matrix(num_states, num_controls, B_factor_list=B_factor_list)
+
+        agent = Agent(A=A, B=B, A_factor_list=A_factor_list, B_factor_list=B_factor_list, inference_algo="VANILLA")
+
+        obs_seq = []
+        for t in range(5):
+            obs_seq.append([np.random.randint(obs_dim) for obs_dim in num_obs])
+        
+        for t in range(5):
+            qs_out = agent.infer_states(obs_seq[t])
+            agent.infer_policies()
+            agent.sample_action()
+
+        """ Test to make sure it works even when generative model sparsity is not taken advantage of """
+        A = utils.random_A_matrix(num_obs, num_states)
+        B = utils.random_B_matrix(num_states, num_controls)
+
+        agent = Agent(A=A, B=B, inference_algo="VANILLA")
+
+        obs_seq = []
+        for t in range(5):
+            obs_seq.append([np.random.randint(obs_dim) for obs_dim in num_obs])
+        
+        for t in range(5):
+            qs_out = agent.infer_states(obs_seq[t])
+            agent.infer_policies()
+            agent.sample_action()
+        
+        """ Test with pA and pB learning & information gain """
+
+        num_obs = [5, 4, 4]
+        num_states = [2, 3, 5]
+        num_controls = [2, 3, 2]
+
+        A_factor_list = [[0], [0, 1], [0, 1, 2]]
+        B_factor_list = [[0], [0, 1], [1, 2]]
+        A = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_factor_list)
+        B = utils.random_B_matrix(num_states, num_controls, B_factor_list=B_factor_list)
+        pA = utils.dirichlet_like(A)
+        pB = utils.dirichlet_like(B)
+
+        agent = Agent(A=A, pA=pA, B=B, pB=pB, save_belief_hist=True, use_param_info_gain=True, A_factor_list=A_factor_list, B_factor_list=B_factor_list, inference_algo="VANILLA")
+
+        obs_seq = []
+        for t in range(5):
+            obs_seq.append([np.random.randint(obs_dim) for obs_dim in num_obs])
+        
+        for t in range(5):
+            qs_out = agent.infer_states(obs_seq[t])
+            agent.infer_policies()
+            agent.sample_action()
+            agent.update_A(obs_seq[t])
+            if t > 0:
+                agent.update_B(qs_prev = agent.qs_hist[-2]) # need to have `save_belief_hist=True` for this to work
+
+
+        
+
 
         
 
diff --git a/test/test_agent_jax.py b/test/test_agent_jax.py
new file mode 100644
index 00000000..ad3d85d8
--- /dev/null
+++ b/test/test_agent_jax.py
@@ -0,0 +1,71 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+""" Unit Tests
+__author__: Dimitrije Markovic, Conor Heins
+"""
+
+import os
+import unittest
+
+import numpy as np
+import jax.numpy as jnp
+from jax import vmap, nn, random
+import jax.tree_util as jtu
+
+from pymdp.jax.maths import compute_log_likelihood_single_modality
+from pymdp.jax.utils import norm_dist
+from equinox import Module
+from typing import Any, List
+
+class TestAgentJax(unittest.TestCase):
+
+    def test_vmappable_agent_methods(self):
+
+        dim, N = 5, 10
+        sampling_key = random.PRNGKey(1)
+
+        class BasicAgent(Module):
+            A: jnp.ndarray
+            B: jnp.ndarray 
+            qs: jnp.ndarray
+
+            def __init__(self, A, B, qs=None):
+                self.A = A
+                self.B = B
+                self.qs = jnp.ones((N, dim))/dim if qs is None else qs
+            
+            @vmap
+            def infer_states(self, obs):
+                qs = nn.softmax(compute_log_likelihood_single_modality(obs, self.A))
+                return qs, BasicAgent(self.A, self.B, qs=qs)
+
+        A_key, B_key, obs_key, test_key = random.split(sampling_key, 4)
+
+        all_A = vmap(norm_dist)(random.uniform(A_key, shape = (N, dim, dim)))
+        all_B = vmap(norm_dist)(random.uniform(B_key, shape = (N, dim, dim)))
+        all_obs = vmap(nn.one_hot, (0, None))(random.choice(obs_key, dim, shape = (N,)), dim)
+
+        my_agent = BasicAgent(all_A, all_B)
+
+        all_qs, my_agent = my_agent.infer_states(all_obs)
+
+        assert all_qs.shape == my_agent.qs.shape
+        self.assertTrue(jnp.allclose(all_qs, my_agent.qs))
+
+        # validate that the method broadcasted properly
+        for id_to_check in range(N):
+            validation_qs = nn.softmax(compute_log_likelihood_single_modality(all_obs[id_to_check], all_A[id_to_check]))
+            self.assertTrue(jnp.allclose(validation_qs, all_qs[id_to_check]))
+
+if __name__ == "__main__":
+    unittest.main()       
+
+
+
+
+
+
+
+
+    
diff --git a/test/test_control.py b/test/test_control.py
index abd5ea89..14b09938 100644
--- a/test/test_control.py
+++ b/test/test_control.py
@@ -99,6 +99,118 @@ def test_get_expected_states(self):
                     else:
                         self.assertTrue((qs_pi[p_idx][t_idx][factor_idx] == B[factor_idx][:,:,policies[p_idx][t_idx,factor_idx]].dot(qs_pi[p_idx][t_idx-1][factor_idx])).all())
 
+    def test_get_expected_states_interactions_single_factor(self):
+        """
+        Test the new version of `get_expected_states` that includes `B` array inter-factor dependencies, in case a of trivial single factor
+        """
+        
+        num_states = [3]
+        num_controls = [3]
+
+        B_factor_list = [[0]]
+
+        qs = utils.random_single_categorical(num_states)
+        B = utils.random_B_matrix(num_states, num_controls, B_factor_list=B_factor_list)
+
+        policies = control.construct_policies(num_states, num_controls, policy_len=1)
+
+        qs_pi_0 = control.get_expected_states_interactions(qs, B, B_factor_list, policies[0])
+
+        self.assertTrue(np.allclose(qs_pi_0[0][0], B[0][:,:,policies[0][0,0]].dot(qs[0])))
+
+    def test_get_expected_states_interactions_multi_factor(self):
+        """
+        Test the new version of `get_expected_states` that includes `B` array inter-factor dependencies, 
+        in the case where there are two hidden state factors: one that depends on itself and another that depends on both itself and the other factor.
+        """
+        
+        num_states = [3, 4]
+        num_controls = [3, 2]
+
+        B_factor_list = [[0], [0, 1]]
+
+        qs = utils.random_single_categorical(num_states)
+        B = utils.random_B_matrix(num_states, num_controls, B_factor_list=B_factor_list)
+
+        policies = control.construct_policies(num_states, num_controls, policy_len=1)
+
+        qs_pi_0 = control.get_expected_states_interactions(qs, B, B_factor_list, policies[0])
+
+        self.assertTrue(np.allclose(qs_pi_0[0][0], B[0][:,:,policies[0][0,0]].dot(qs[0])))
+
+        qs_next_validation = (B[1][..., policies[0][0,1]] * maths.spm_cross(qs)[None,...]).sum(axis=(1,2)) # how to compute equivalent of `spm_dot(B[...,past_action], qs)`
+        self.assertTrue(np.allclose(qs_pi_0[0][1], qs_next_validation))
+    
+    def test_get_expected_states_interactions_multi_factor_independent(self):
+        """
+        Test the new version of `get_expected_states` that includes `B` array inter-factor dependencies, 
+        in the case where there are multiple hidden state factors, but they all only depend on themselves
+        """
+        
+        num_states = [3, 4, 5, 6]
+        num_controls = [1, 2, 5, 3]
+
+        B_factor_list = [[f] for f in range(len(num_states))] # each factor only depends on itself
+
+        qs = utils.random_single_categorical(num_states)
+        B = utils.random_B_matrix(num_states, num_controls)
+
+        policies = control.construct_policies(num_states, num_controls, policy_len=1)
+
+        qs_pi_0 = control.get_expected_states_interactions(qs, B, B_factor_list, policies[0])
+
+        qs_pi_0_validation = control.get_expected_states(qs, B, policies[0])
+
+        for qs_f, qs_val_f in zip(qs_pi_0[0], qs_pi_0_validation[0]):
+            self.assertTrue(np.allclose(qs_f, qs_val_f))
+
+    def test_get_expected_obs_factorized(self):
+        """
+        Test the new version of `get_expected_obs` that includes sparse dependencies of `A` array on hidden state factors (not all observation modalities depend on all hidden state factors)
+        """
+
+        """ Case 1, where all modalities depend on all hidden state factors """
+
+        num_states = [3, 4]
+        num_obs = [3, 4]
+
+        A_factor_list = [[0, 1], [0, 1]]
+
+        qs = utils.random_single_categorical(num_states)
+        A = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_factor_list)
+
+        qo_test = control.get_expected_obs_factorized([qs], A, A_factor_list) # need to wrap `qs` in list because `get_expected_obs_factorized` expects a list of `qs` (representing multiple timesteps)
+        qo_val = control.get_expected_obs([qs], A) # need to wrap `qs` in list because `get_expected_obs` expects a list of `qs` (representing multiple timesteps)
+
+        for qo_m, qo_val_m in zip(qo_test[0], qo_val[0]): # need to extract first index of `qo_test` and `qo_val` because `get_expected_obs_factorized` returns a list of `qo` (representing multiple timesteps)
+            self.assertTrue(np.allclose(qo_m, qo_val_m))
+        
+        """ Case 2, where some modalities depend on some hidden state factors """
+
+        num_states = [3, 4]
+        num_obs = [3, 4]
+
+        A_factor_list = [[0], [0, 1]]
+
+        qs = utils.random_single_categorical(num_states)
+        A_reduced = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_factor_list)
+
+        qo_test = control.get_expected_obs_factorized([qs], A_reduced, A_factor_list) # need to wrap `qs` in list because `get_expected_obs_factorized` expects a list of `qs` (representing multiple timesteps)
+
+        A_full = utils.initialize_empty_A(num_obs, num_states)
+        for m, A_m in enumerate(A_full):
+            other_factors = list(set(range(len(num_states))) - set(A_factor_list[m])) # list of the factors that modality `m` does not depend on
+
+            # broadcast or tile the reduced A matrix (`A_reduced`) along the dimensions of corresponding to `other_factors`
+            expanded_dims = [num_obs[m]] + [1 if f in other_factors else ns for (f, ns) in enumerate(num_states)]
+            tile_dims = [1] + [ns if f in other_factors else 1 for (f, ns) in enumerate(num_states)]
+            A_full[m] = np.tile(A_reduced[m].reshape(expanded_dims), tile_dims)
+        
+        qo_val = control.get_expected_obs([qs], A_full) # need to wrap `qs` in list because `get_expected_obs` expects a list of `qs` (representing multiple timesteps)
+        
+        for qo_m, qo_val_m in zip(qo_test[0], qo_val[0]): # need to extract first index of `qo_test` and `qo_val` because `get_expected_obs_factorized` returns a list of `qo` (representing multiple timesteps)
+            self.assertTrue(np.allclose(qo_m, qo_val_m))
+
     def test_get_expected_states_and_obs(self):
         """
         Tests the refactored (Categorical-less) versions of `get_expected_states` and `get_expected_obs` together
@@ -351,9 +463,109 @@ def test_state_info_gain(self):
             qs_pi = control.get_expected_states(qs, B, policy)
             state_info_gains[idx] += control.calc_states_info_gain(A, qs_pi)
         self.assertGreater(state_info_gains[1], state_info_gains[0])
+
+    def test_state_info_gain_factorized(self):
+        """ 
+        Unit test the `calc_states_info_gain_factorized` function by qualitatively checking that in the T-Maze (contextual bandit)
+        example, the state info gain is higher for the policy that leads to visiting the cue, which is higher than state info gain
+        for visiting the bandit arm, which in turn is higher than the state info gain for the policy that leads to staying in the start state.
+        """
+
+        num_states = [2, 3]  
+        num_obs = [3, 3, 3]
+        num_controls = [1, 3]
+
+        A_factor_list = [[0, 1], [0, 1], [1]] 
+        
+        A = utils.obj_array(len(num_obs))
+        for m, obs in enumerate(num_obs):
+            lagging_dimensions = [ns for i, ns in enumerate(num_states) if i in A_factor_list[m]]
+            modality_shape = [obs] + lagging_dimensions
+            A[m] = np.zeros(modality_shape)
+            if m == 0:
+                A[m][:, :, 0] = np.ones( (num_obs[m], num_states[0]) ) / num_obs[m]
+                A[m][:, :, 1] = np.ones( (num_obs[m], num_states[0]) ) / num_obs[m]
+                A[m][:, :, 2] = np.array([[0.9, 0.1], [0.0, 0.0], [0.1, 0.9]]) # cue statistics
+            if m == 1:
+                A[m][2, :, 0] = np.ones(num_states[0])
+                A[m][0:2, :, 1] = np.array([[0.6, 0.4], [0.6, 0.4]]) # bandit statistics (mapping between reward-state (first hidden state factor) and rewards (Good vs Bad))
+                A[m][2, :, 2] = np.ones(num_states[0])
+            if m == 2:
+                A[m] = np.eye(obs)
+
+        qs_start = utils.obj_array_uniform(num_states)
+        qs_start[1] = np.array([1., 0., 0.]) # agent believes it's in the start state
+
+        state_info_gain_visit_start = 0.
+        for m, A_m in enumerate(A):
+            if len(A_factor_list[m]) == 1:
+                qs_that_matter = utils.to_obj_array(qs_start[A_factor_list[m]])
+            else:
+                qs_that_matter = qs_start[A_factor_list[m]]
+            state_info_gain_visit_start += control.calc_states_info_gain(A_m, [qs_that_matter])
+
+        qs_arm = utils.obj_array_uniform(num_states)
+        qs_arm[1] = np.array([0., 1., 0.]) # agent believes it's in the arm-visiting state
+
+        state_info_gain_visit_arm = 0.
+        for m, A_m in enumerate(A):
+            if len(A_factor_list[m]) == 1:
+                qs_that_matter = utils.to_obj_array(qs_arm[A_factor_list[m]])
+            else:
+                qs_that_matter = qs_arm[A_factor_list[m]]
+            state_info_gain_visit_arm += control.calc_states_info_gain(A_m, [qs_that_matter])
+
+        qs_cue = utils.obj_array_uniform(num_states)
+        qs_cue[1] = np.array([0., 0., 1.]) # agent believes it's in the cue-visiting state
+
+        state_info_gain_visit_cue = 0.
+        for m, A_m in enumerate(A):
+            if len(A_factor_list[m]) == 1:
+                qs_that_matter = utils.to_obj_array(qs_cue[A_factor_list[m]])
+            else:
+                qs_that_matter = qs_cue[A_factor_list[m]]
+            state_info_gain_visit_cue += control.calc_states_info_gain(A_m, [qs_that_matter])
+        
+        self.assertGreater(state_info_gain_visit_arm, state_info_gain_visit_start)
+        self.assertGreater(state_info_gain_visit_cue, state_info_gain_visit_arm)
+
+    # def test_neg_ambiguity_modality_sum(self):
+    #     """
+    #     Test that the negativity ambiguity function is the same when computed using the full (unfactorized) joint distribution over observations and hidden state factors vs. when computed for each modality separately and summed together.
+    #     """
+
+    #     num_states = [10, 20, 10, 10]
+    #     num_obs = [2, 25, 10, 8]
+
+    #     qs = utils.random_single_categorical(num_states)
+    #     A = utils.random_A_matrix(num_obs, num_states)
+
+    #     neg_ambig_full = maths.spm_calc_neg_ambig(A, qs) # need to wrap `qs` in a list because the function expects a list of policy-conditioned posterior beliefs (corresponding to each timestep)
+    #     neg_ambig_by_modality = 0.
+    #     for m, A_m in enumerate(A):
+    #         neg_ambig_by_modality += maths.spm_calc_neg_ambig(A_m, qs)
+        
+    #     self.assertEqual(neg_ambig_full, neg_ambig_by_modality)
     
-    def test_pA_info_gain(self):
+    # def test_entropy_modality_sum(self):
+    #     """
+    #     Test that the negativity ambiguity function is the same when computed using the full (unfactorized) joint distribution over observations and hidden state factors vs. when computed for each modality separately and summed together.
+    #     """
+
+    #     num_states = [10, 20, 10, 10]
+    #     num_obs = [2, 25, 10, 8]
 
+    #     qs = utils.random_single_categorical(num_states)
+    #     A = utils.random_A_matrix(num_obs, num_states)
+
+    #     H_full = maths.spm_calc_qo_entropy(A, qs) # need to wrap `qs` in a list because the function expects a list of policy-conditioned posterior beliefs (corresponding to each timestep)
+    #     H_by_modality = 0.
+    #     for m, A_m in enumerate(A):
+    #         H_by_modality += maths.spm_calc_qo_entropy(A_m, qs)
+        
+    #     self.assertEqual(H_full, H_by_modality)
+
+    def test_pA_info_gain(self):
         """
         Test the pA_info_gain function. Demonstrates operation
         by manipulating shape of the Dirichlet priors over likelihood parameters
@@ -392,9 +604,18 @@ def test_pA_info_gain(self):
         for idx, policy in enumerate(policies):
             qs_pi = control.get_expected_states(qs, B, policy)
             qo_pi = control.get_expected_obs(qs_pi, A)
-            pA_info_gains[idx] += control.calc_pA_info_gain(pA, qo_pi, qs_pi)
+            pA_info_gains[idx] += control.calc_pA_info_gain(pA, qo_pi, qs_pi).item()
 
         self.assertGreater(pA_info_gains[1], pA_info_gains[0])
+
+        """ Test the factorized version of the pA_info_gain function. """
+        pA_info_gains_fac = np.zeros(len(policies))
+        for idx, policy in enumerate(policies):
+            qs_pi = control.get_expected_states(qs, B, policy)
+            qo_pi = control.get_expected_obs_factorized(qs_pi, A, A_factor_list=[[0]])
+            pA_info_gains_fac[idx] += control.calc_pA_info_gain_factorized(pA, qo_pi, qs_pi, A_factor_list=[[0]]).item()
+
+        self.assertTrue(np.allclose(pA_info_gains_fac,  pA_info_gains))  
     
     def test_pB_info_gain(self):
         """
@@ -432,6 +653,13 @@ def test_pB_info_gain(self):
             pB_info_gains[idx] += control.calc_pB_info_gain(pB, qs_pi, qs, policy)
         self.assertGreater(pB_info_gains[1], pB_info_gains[0])
 
+        B_factor_list = [[0]]
+        pB_info_gains_interactions = np.zeros(len(policies))
+        for idx, policy in enumerate(policies):
+            qs_pi = control.get_expected_states_interactions(qs, B, B_factor_list, policy)
+            pB_info_gains_interactions[idx] += control.calc_pB_info_gain_interactions(pB, qs_pi, qs, B_factor_list, policy)
+        self.assertTrue(np.allclose(pB_info_gains_interactions, pB_info_gains))
+
     def test_update_posterior_policies_utility(self):
         """
         Tests the refactored (Categorical-less) version of `update_posterior_policies`, using only the expected utility component of the expected free energy
@@ -479,7 +707,7 @@ def test_update_posterior_policies_utility(self):
             qo_pi = control.get_expected_obs(qs_pi, A)
 
             lnC = maths.spm_log_single(maths.softmax(C[modality_idx][:, np.newaxis]))
-            efe_valid[idx] += qo_pi[t_idx][modality_idx].dot(lnC)
+            efe_valid[idx] += qo_pi[t_idx][modality_idx].dot(lnC).item()
         
         q_pi_valid = maths.softmax(efe_valid * 16.0)
 
@@ -527,7 +755,7 @@ def test_update_posterior_policies_utility(self):
 
             for modality_idx in range(len(A)):
                 lnC = maths.spm_log_single(maths.softmax(C[modality_idx][:, np.newaxis]))
-                efe_valid[idx] += qo_pi[t_idx][modality_idx].dot(lnC)
+                efe_valid[idx] += qo_pi[t_idx][modality_idx].dot(lnC).item()
         
         q_pi_valid = maths.softmax(efe_valid * 16.0)
 
@@ -574,7 +802,7 @@ def test_update_posterior_policies_utility(self):
             for t_idx in range(3):
                 for modality_idx in range(len(A)):
                     lnC = maths.spm_log_single(maths.softmax(C[modality_idx][:, np.newaxis]))
-                    efe_valid[idx] += qo_pi[t_idx][modality_idx].dot(lnC)
+                    efe_valid[idx] += qo_pi[t_idx][modality_idx].dot(lnC).item()
         
         q_pi_valid = maths.softmax(efe_valid * 16.0)
 
@@ -627,7 +855,7 @@ def test_temporal_C_matrix(self):
             for t_idx in range(3):
                 for modality_idx in range(len(A)):
                     lnC = maths.spm_log_single(maths.softmax(C[modality_idx][:, np.newaxis]))
-                    efe_valid[idx] += qo_pi[t_idx][modality_idx].dot(lnC)
+                    efe_valid[idx] += qo_pi[t_idx][modality_idx].dot(lnC).item()
 
         q_pi_valid = maths.softmax(efe_valid * 16.0)
 
@@ -677,7 +905,7 @@ def test_temporal_C_matrix(self):
             for t_idx in range(3):
                 for modality_idx in range(len(A)):
                     lnC = maths.spm_log_single(maths.softmax(C[modality_idx][:, t_idx]))
-                    efe_valid[idx] += qo_pi[t_idx][modality_idx].dot(lnC)
+                    efe_valid[idx] += qo_pi[t_idx][modality_idx].dot(lnC).item()
 
         q_pi_valid = maths.softmax(efe_valid * 16.0)
 
@@ -730,7 +958,7 @@ def test_temporal_C_matrix(self):
                         lnC = maths.spm_log_single(maths.softmax(C[modality_idx][:, t_idx]))
                     elif modality_idx == 1:
                         lnC = maths.spm_log_single(maths.softmax(C[modality_idx][:, np.newaxis]))
-                    efe_valid[idx] += qo_pi[t_idx][modality_idx].dot(lnC)
+                    efe_valid[idx] += qo_pi[t_idx][modality_idx].dot(lnC).item()
         
         q_pi_valid = maths.softmax(efe_valid * 16.0)
 
@@ -915,7 +1143,7 @@ def test_update_posterior_policies_pA_infogain(self):
             qs_pi = control.get_expected_states(qs, B, policy)
             qo_pi = control.get_expected_obs(qs_pi, A)
             
-            efe_valid[idx] += control.calc_pA_info_gain(pA, qo_pi, qs_pi)
+            efe_valid[idx] += control.calc_pA_info_gain(pA, qo_pi, qs_pi).item()
         
         q_pi_valid = maths.softmax(efe_valid * 16.0)
 
@@ -960,7 +1188,7 @@ def test_update_posterior_policies_pA_infogain(self):
             qs_pi = control.get_expected_states(qs, B, policy)
             qo_pi = control.get_expected_obs(qs_pi, A)
             
-            efe_valid[idx] += control.calc_pA_info_gain(pA, qo_pi, qs_pi)
+            efe_valid[idx] += control.calc_pA_info_gain(pA, qo_pi, qs_pi).item()
         
         q_pi_valid = maths.softmax(efe_valid * 16.0)
 
@@ -1003,7 +1231,7 @@ def test_update_posterior_policies_pA_infogain(self):
             qs_pi = control.get_expected_states(qs, B, policy)
             qo_pi = control.get_expected_obs(qs_pi, A)
 
-            efe_valid[idx] += control.calc_pA_info_gain(pA, qo_pi, qs_pi)
+            efe_valid[idx] += control.calc_pA_info_gain(pA, qo_pi, qs_pi).item()
     
         q_pi_valid = maths.softmax(efe_valid * 16.0)
 
@@ -1146,6 +1374,43 @@ def test_update_posterior_policies_pB_infogain(self):
 
         self.assertTrue(np.allclose(efe, efe_valid))
         self.assertTrue(np.allclose(q_pi, q_pi_valid))
+    
+    def test_update_posterior_policies_factorized(self):
+        """ 
+        Test new update_posterior_policies_factorized function, just to make sure it runs through and outputs correct shapes
+        """
+
+        num_obs = [3, 3]
+        num_states = [3, 2]
+        num_controls = [3, 2]
+
+        A_factor_list = [[0, 1], [1]]
+        B_factor_list = [[0], [0, 1]]
+
+        qs = utils.random_single_categorical(num_states)
+        A = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_factor_list)
+        B = utils.random_B_matrix(num_states, num_controls, B_factor_list=B_factor_list)
+        C = utils.obj_array_zeros(num_obs)
+
+        policies = control.construct_policies(num_states, num_controls, policy_len=1)
+
+        q_pi, efe = control.update_posterior_policies_factorized(
+            qs,
+            A,
+            B,
+            C,
+            A_factor_list,
+            B_factor_list,
+            policies,
+            use_utility = True,
+            use_states_info_gain = True,
+            gamma=16.0
+        )
+
+        self.assertEqual(len(q_pi), len(policies))
+        self.assertEqual(len(efe), len(policies))
+
+        chosen_action = control.sample_action(q_pi, policies, num_controls, action_selection="deterministic")
 
     def test_sample_action(self):
         """
diff --git a/test/test_control_jax.py b/test/test_control_jax.py
new file mode 100644
index 00000000..75de6912
--- /dev/null
+++ b/test/test_control_jax.py
@@ -0,0 +1,144 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+""" Unit Tests
+__author__: Dimitrije Markovic, Conor Heins
+"""
+
+import os
+import unittest
+import pytest
+
+import numpy as np
+import jax.numpy as jnp
+import jax.random as jr
+import jax.tree_util as jtu
+
+import pymdp.jax.control as ctl_jax
+import pymdp.control as ctl_np
+
+from pymdp.jax.maths import factor_dot
+from pymdp import utils
+
+cfg = {"source_key": 0, "num_models": 4}
+
+def generate_model_params():
+    """
+    Generate random model dimensions
+    """
+    rng_keys = jr.split(jr.PRNGKey(cfg["source_key"]), cfg["num_models"])
+    num_factors_list = [ jr.randint(key, (1,), 1, 10)[0].item() for key in rng_keys ]
+    num_states_list = [ jr.randint(key, (nf,), 1, 5).tolist() for nf, key in zip(num_factors_list, rng_keys) ]
+
+    rng_keys = jr.split(rng_keys[-1], cfg["num_models"])
+    num_modalities_list = [ jr.randint(key, (1,), 1, 10)[0].item() for key in rng_keys ]
+    num_obs_list = [ jr.randint(key, (nm,), 1, 5).tolist() for nm, key in zip(num_modalities_list, rng_keys) ]
+
+    rng_keys = jr.split(rng_keys[-1], cfg["num_models"])
+    A_deps_list = []
+    for nf, nm, model_key in zip(num_factors_list, num_modalities_list, rng_keys):
+        keys_model_i = jr.split(model_key, nm)
+        A_deps_model_i = [jr.randint(key, (nm,), 0, nf).tolist() for key in keys_model_i]
+        A_deps_list.append(A_deps_model_i)
+    
+    return {'nf_list': num_factors_list, 
+            'ns_list': num_states_list, 
+            'nm_list': num_modalities_list, 
+            'no_list': num_obs_list, 
+            'A_deps_list': A_deps_list}
+
+class TestControlJax(unittest.TestCase):
+
+    def test_get_expected_obs_factorized(self):
+        """
+        Tests the jax-ified version of computations of expected observations under some hidden states and policy
+        """
+        gm_params = generate_model_params()
+        num_factors_list, num_states_list, num_modalities_list, num_obs_list, A_deps_list = gm_params['nf_list'], gm_params['ns_list'], gm_params['nm_list'], gm_params['no_list'], gm_params['A_deps_list']
+        for (num_states, num_obs, A_deps) in zip(num_states_list, num_obs_list, A_deps_list):
+            
+            qs_numpy = utils.random_single_categorical(num_states)
+            qs_jax = list(qs_numpy)
+
+            A_np = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_deps)
+            A_jax = jtu.tree_map(lambda x: jnp.array(x), list(A_np))   
+
+            qo_test = ctl_jax.compute_expected_obs(qs_jax, A_jax, A_deps) 
+            qo_validation = ctl_np.get_expected_obs_factorized([qs_numpy], A_np, A_deps) # need to wrap `qs` in list because `get_expected_obs_factorized` expects a list of `qs` (representing multiple timesteps)
+
+            for qo_m, qo_val_m in zip(qo_test, qo_validation[0]): # need to extract first index of `qo_validation` because `get_expected_obs_factorized` returns a list of `qo` (representing multiple timesteps)
+                self.assertTrue(np.allclose(qo_m, qo_val_m))
+
+    def test_info_gain_factorized(self):
+        """ 
+        Unit test the `calc_states_info_gain_factorized` function by qualitatively checking that in the T-Maze (contextual bandit)
+        example, the state info gain is higher for the policy that leads to visiting the cue, which is higher than state info gain
+        for visiting the bandit arm, which in turn is higher than the state info gain for the policy that leads to staying in the start state.
+        """
+
+        num_states = [2, 3]  
+        num_obs = [3, 3, 3]
+
+        A_dependencies = [[0, 1], [0, 1], [1]] 
+        A = []
+        for m, obs in enumerate(num_obs):
+            lagging_dimensions = [ns for i, ns in enumerate(num_states) if i in A_dependencies[m]]
+            modality_shape = [obs] + lagging_dimensions
+            A.append(np.zeros(modality_shape))
+            if m == 0:
+                A[m][:, :, 0] = np.ones( (num_obs[m], num_states[0]) ) / num_obs[m]
+                A[m][:, :, 1] = np.ones( (num_obs[m], num_states[0]) ) / num_obs[m]
+                A[m][:, :, 2] = np.array([[0.9, 0.1], [0.0, 0.0], [0.1, 0.9]]) # cue statistics
+            if m == 1:
+                A[m][2, :, 0] = np.ones(num_states[0])
+                A[m][0:2, :, 1] = np.array([[0.6, 0.4], [0.6, 0.4]]) # bandit statistics (mapping between reward-state (first hidden state factor) and rewards (Good vs Bad))
+                A[m][2, :, 2] = np.ones(num_states[0])
+            if m == 2:
+                A[m] = np.eye(obs)
+
+        qs_start = list(utils.obj_array_uniform(num_states))
+        qs_start[1] = np.array([1., 0., 0.]) # agent believes it's in the start state
+
+        A = [jnp.array(A_m) for A_m in A]
+        qs_start = [jnp.array(qs) for qs in qs_start]
+        qo_start = ctl_jax.compute_expected_obs(qs_start, A, A_dependencies)
+        
+        start_info_gain = ctl_jax.compute_info_gain(qs_start, qo_start, A, A_dependencies)
+
+        qs_arm = list(utils.obj_array_uniform(num_states))
+        qs_arm[1] = np.array([0., 1., 0.]) # agent believes it's in the arm-visiting state
+        qs_arm = [jnp.array(qs) for qs in qs_arm]
+        qo_arm = ctl_jax.compute_expected_obs(qs_arm, A, A_dependencies)
+        
+        arm_info_gain = ctl_jax.compute_info_gain(qs_arm, qo_arm, A, A_dependencies)
+        
+        qs_cue = utils.obj_array_uniform(num_states)
+        qs_cue[1] = np.array([0., 0., 1.]) # agent believes it's in the cue-visiting state
+        qs_cue = [jnp.array(qs) for qs in qs_cue]
+        
+        qo_cue = ctl_jax.compute_expected_obs(qs_cue, A, A_dependencies)
+        cue_info_gain = ctl_jax.compute_info_gain(qs_cue, qo_cue, A, A_dependencies)
+        
+        self.assertGreater(arm_info_gain, start_info_gain)
+        self.assertGreater(cue_info_gain, arm_info_gain)
+
+        gm_params = generate_model_params()
+        num_factors_list, num_states_list, num_modalities_list, num_obs_list, A_deps_list = gm_params['nf_list'], gm_params['ns_list'], gm_params['nm_list'], gm_params['no_list'], gm_params['A_deps_list']
+        for (num_states, num_obs, A_deps) in zip(num_states_list, num_obs_list, A_deps_list):
+
+            qs_numpy = utils.random_single_categorical(num_states)
+            qs_jax = list(qs_numpy)
+
+            A_np = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_deps)
+            A_jax = jtu.tree_map(lambda x: jnp.array(x), list(A_np))   
+
+            qo = ctl_jax.compute_expected_obs(qs_jax, A_jax, A_deps)
+
+            info_gain = ctl_jax.compute_info_gain(qs_jax, qo, A_jax, A_deps)
+            info_gain_validation = ctl_np.calc_states_info_gain_factorized(A_np, [qs_numpy],  A_deps)
+
+            self.assertTrue(np.allclose(info_gain, info_gain_validation, atol=1e-5))
+    
+
+if __name__ == "__main__":
+    unittest.main()
\ No newline at end of file
diff --git a/test/test_demos.py b/test/test_demos.py
index 35d98c79..d29d3eb4 100644
--- a/test/test_demos.py
+++ b/test/test_demos.py
@@ -69,18 +69,18 @@ def test_tmaze_demo(self):
 
         '''test plotting of the observation likelihood (just plot one slice)'''
         A_gp = env.get_likelihood_dist()
-        plot_likelihood(A_gp[1][:,:,0],'Reward Right')
+        # plot_likelihood(A_gp[1][:,:,0],'Reward Right')
 
         '''test plotting of the transition likelihood (just plot one slice)'''
         B_gp = env.get_transition_dist()
-        plot_likelihood(B_gp[1][:,:,0],'Reward Condition Transitions')
+        # plot_likelihood(B_gp[1][:,:,0],'Reward Condition Transitions')
 
         A_gm = copy.deepcopy(A_gp) # make a copy of the true observation likelihood to initialize the observation model
         B_gm = copy.deepcopy(B_gp)# make a copy of the true transition likelihood to initialize the transition model
         
         control_fac_idx = [0]
         agent = Agent(A=A_gm, B=B_gm, control_fac_idx=control_fac_idx)
-        plot_beliefs(agent.D[0],"Beliefs about initial location")
+        # plot_beliefs(agent.D[0],"Beliefs about initial location")
 
         agent.C[1][1] = 3.0 # they like reward
         agent.C[1][2] = -3.0 # they don't like loss
@@ -115,7 +115,7 @@ def test_tmaze_demo(self):
                     self.assertEqual(obs[2], 1) # this tests that the cue observation is 'Cue Left' in case of 'Reward on Left' condition
 
             
-        plot_beliefs(qx[1],"Final posterior beliefs about reward condition")
+        # plot_beliefs(qx[1],"Final posterior beliefs about reward condition")
     
     def test_tmaze_learning_demo(self):
         """
@@ -206,7 +206,7 @@ def test_gridworld_genmodel_construction(self):
 
         labels = [state_mapping[i] for i in range(A.shape[1])]
 
-        plot_likelihood(A)
+        # plot_likelihood(A)
 
         P = {}
         dim = 3
@@ -240,18 +240,18 @@ def test_gridworld_genmodel_construction(self):
         
         self.assertTrue(B.shape[0] == 9)
 
-        fig, axes = plt.subplots(2,3, figsize = (15,8))
-        a = list(actions.keys())
-        count = 0
-        for i in range(dim-1):
-            for j in range(dim):
-                if count >= 5:
-                    break 
-                g = sns.heatmap(B[:,:,count], cmap = "OrRd", linewidth = 2.5, cbar = False, ax = axes[i,j], xticklabels=labels, yticklabels=labels)
-                g.set_title(a[count])
-                count +=1 
-        fig.delaxes(axes.flatten()[5])
-        plt.tight_layout()
+        # fig, axes = plt.subplots(2,3, figsize = (15,8))
+        # a = list(actions.keys())
+        # count = 0
+        # for i in range(dim-1):
+        #     for j in range(dim):
+        #         if count >= 5:
+        #             break 
+        #         g = sns.heatmap(B[:,:,count], cmap = "OrRd", linewidth = 2.5, cbar = False, ax = axes[i,j], xticklabels=labels, yticklabels=labels)
+        #         g.set_title(a[count])
+        #         count +=1 
+        # fig.delaxes(axes.flatten()[5])
+        # plt.tight_layout()
     
     def test_gridworld_activeinference(self):
         """
@@ -266,38 +266,38 @@ def test_gridworld_activeinference(self):
        
         labels = [state_mapping[i] for i in range(A.shape[1])]
        
-        def plot_empirical_prior(B):
-            fig, axes = plt.subplots(3,2, figsize=(8, 10))
-            actions = ['UP', 'RIGHT', 'DOWN', 'LEFT', 'STAY']
-            count = 0
-            for i in range(3):
-                for j in range(2):
-                    if count >= 5:
-                        break
+        # def plot_empirical_prior(B):
+        #     fig, axes = plt.subplots(3,2, figsize=(8, 10))
+        #     actions = ['UP', 'RIGHT', 'DOWN', 'LEFT', 'STAY']
+        #     count = 0
+        #     for i in range(3):
+        #         for j in range(2):
+        #             if count >= 5:
+        #                 break
                         
-                    g = sns.heatmap(B[:,:,count], cmap="OrRd", linewidth=2.5, cbar=False, ax=axes[i,j])
+        #             g = sns.heatmap(B[:,:,count], cmap="OrRd", linewidth=2.5, cbar=False, ax=axes[i,j])
 
-                    g.set_title(actions[count])
-                    count += 1
-            fig.delaxes(axes.flatten()[5])
-            plt.tight_layout()
+        #             g.set_title(actions[count])
+        #             count += 1
+        #     fig.delaxes(axes.flatten()[5])
+        #     plt.tight_layout()
             
-        def plot_transition(B):
-            fig, axes = plt.subplots(2,3, figsize = (15,8))
-            a = list(actions.keys())
-            count = 0
-            for i in range(dim-1):
-                for j in range(dim):
-                    if count >= 5:
-                        break 
-                    g = sns.heatmap(B[:,:,count], cmap = "OrRd", linewidth = 2.5, cbar = False, ax = axes[i,j], xticklabels=labels, yticklabels=labels)
-                    g.set_title(a[count])
-                    count +=1 
-            fig.delaxes(axes.flatten()[5])
-            plt.tight_layout()
+        # def plot_transition(B):
+        #     fig, axes = plt.subplots(2,3, figsize = (15,8))
+        #     a = list(actions.keys())
+        #     count = 0
+        #     for i in range(dim-1):
+        #         for j in range(dim):
+        #             if count >= 5:
+        #                 break 
+        #             g = sns.heatmap(B[:,:,count], cmap = "OrRd", linewidth = 2.5, cbar = False, ax = axes[i,j], xticklabels=labels, yticklabels=labels)
+        #             g.set_title(a[count])
+        #             count +=1 
+        #     fig.delaxes(axes.flatten()[5])
+        #     plt.tight_layout()
         
         A = np.eye(9)
-        plot_likelihood(A)
+        # plot_likelihood(A)
 
         P = {}
         dim = 3
@@ -330,7 +330,7 @@ def plot_transition(B):
                 ns = int(P[s][a])
                 B[ns, s, a] = 1
 
-        plot_transition(B)
+        # plot_transition(B)
         
         class GridWorldEnv():
     
@@ -362,18 +362,18 @@ def compute_free_energy(q,A, B):
         def softmax(x):
             return np.exp(x) / np.sum(np.exp(x))
 
-        def perform_inference(likelihood, prior):
-            return softmax(log_stable(likelihood) + log_stable(prior))
+        # def perform_inference(likelihood, prior):
+        #     return softmax(log_stable(likelihood) + log_stable(prior))
         
         Qs = np.ones(9) * 1/9
-        plot_beliefs(Qs)
+        # plot_beliefs(Qs)
 
         REWARD_LOCATION = 7
         reward_state = state_mapping[REWARD_LOCATION]
 
         C = np.zeros(num_states)
         C[REWARD_LOCATION] = 1. 
-        plot_beliefs(C)
+        # plot_beliefs(C)
 
         def evaluate_policy(policy, Qs, A, B, C):
             # initialize expected free energy at 0
@@ -383,7 +383,7 @@ def evaluate_policy(policy, Qs, A, B, C):
             for t in range(len(policy)):
 
                 # get action entailed by the policy at timestep `t`
-                u = int(policy[t])
+                u = int(policy[t].item())
 
                 # work out expected state, given the action
                 Qs_pi = B[:,:,u].dot(Qs)
@@ -424,7 +424,7 @@ def infer_action(Qs, A, B, C, n_actions, policies):
             # sum probabilites of control states or actions 
             for i, policy in enumerate(policies):
                 # control state specified by policy
-                u = int(policy[0])
+                u = int(policy[0].item())
                 # add probability of policy
                 Qu[u] += Q_pi[i]
 
@@ -466,7 +466,7 @@ def infer_action(Qs, A, B, C, n_actions, policies):
 
             Qs = maths.softmax(log_stable(likelihood) + log_stable(prior))
             
-            plot_beliefs(Qs, "Beliefs (Qs) at time {}".format(t))
+            # plot_beliefs(Qs, "Beliefs (Qs) at time {}".format(t))
 
         # self.assertEqual(np.argmax(Qs), REWARD_LOCATION) # @NOTE: This is not always true due to stochastic samplign!!!
         self.assertEqual(Qs.shape[0], B.shape[0])
diff --git a/test/test_fpi.py b/test/test_fpi.py
new file mode 100644
index 00000000..d60f944e
--- /dev/null
+++ b/test/test_fpi.py
@@ -0,0 +1,203 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+""" Unit Tests for factorized version of variational fixed point iteration (FPI or "Vanilla FPI")
+__author__: Conor Heins
+"""
+
+import os
+import unittest
+
+import numpy as np
+
+from pymdp import utils, maths
+from pymdp.algos import run_vanilla_fpi, run_vanilla_fpi_factorized
+
+class TestFPI(unittest.TestCase):
+
+    def test_factorized_fpi_one_factor_one_modality(self):
+        """
+        Test the sparsified version of `run_vanilla_fpi`, named `run_vanilla_fpi_factorized`
+        with single hidden state factor and single observation modality.
+        """
+
+        num_states = [3]
+        num_obs = [3]       
+
+        prior = utils.random_single_categorical(num_states)
+
+        A = utils.to_obj_array(maths.softmax(np.eye(num_states[0]) * 0.1))
+
+        obs_idx = np.random.choice(num_obs[0])
+        obs = utils.onehot(obs_idx, num_obs[0])
+
+        mb_dict = {'A_factor_list': [[0]],
+                    'A_modality_list': [[0]]}
+
+        qs_out = run_vanilla_fpi_factorized(A, obs, num_obs, num_states, mb_dict, prior=prior)[0]
+        qs_validation_1 = run_vanilla_fpi(A, obs, num_obs, num_states, prior=prior)[0]
+        qs_validation_2 = maths.softmax(maths.spm_log_single(A[0][obs_idx,:]) + maths.spm_log_single(prior[0]))
+
+        self.assertTrue(np.isclose(qs_validation_1, qs_out).all())
+        self.assertTrue(np.isclose(qs_validation_2, qs_out).all())
+    
+    def test_factorized_fpi_one_factor_multi_modality(self):
+        """
+        Test the sparsified version of `run_vanilla_fpi`, named `run_vanilla_fpi_factorized`
+        with single hidden state factor and multiple observation modalities.
+        """
+
+        num_states = [3]
+        num_obs = [3, 2]
+
+        prior = utils.random_single_categorical(num_states)
+
+        A = utils.random_A_matrix(num_obs, num_states)
+
+        obs = utils.obj_array(len(num_obs))
+        for m, obs_dim in enumerate(num_obs):
+            obs[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+        mb_dict = {'A_factor_list': [[0], [0]],
+                    'A_modality_list': [[0, 1]]}
+        
+        qs_out = run_vanilla_fpi_factorized(A, obs, num_obs, num_states, mb_dict, prior=prior)[0]
+        qs_validation = run_vanilla_fpi(A, obs, num_obs, num_states, prior=prior)[0]
+
+        self.assertTrue(np.isclose(qs_validation, qs_out).all())
+    
+    def test_factorized_fpi_multi_factor_one_modality(self):
+        """
+        Test the sparsified version of `run_vanilla_fpi`, named `run_vanilla_fpi_factorized`
+        with multiple hidden state factors and one observation modality.
+        """
+
+        num_states = [4, 5]
+        num_obs = [3]
+
+        prior = utils.random_single_categorical(num_states)
+
+        A = utils.random_A_matrix(num_obs, num_states)
+
+        obs_idx = np.random.choice(num_obs[0])
+        obs = utils.onehot(obs_idx, num_obs[0])
+
+        mb_dict = {'A_factor_list': [[0, 1]],
+                    'A_modality_list': [[0], [0]]}
+        
+        qs_out = run_vanilla_fpi_factorized(A, obs, num_obs, num_states, mb_dict, prior=prior)
+        qs_validation = run_vanilla_fpi(A, obs, num_obs, num_states, prior=prior)
+
+        for qs_f_val, qs_f_out in zip(qs_validation, qs_out):
+            self.assertTrue(np.isclose(qs_f_val, qs_f_out).all())
+    
+    def test_factorized_fpi_multi_factor_multi_modality(self):
+        """
+        Test the sparsified version of `run_vanilla_fpi`, named `run_vanilla_fpi_factorized`
+        with multiple hidden state factors and multiple observation modalities.
+        """
+
+        num_states = [3, 4]
+        num_obs = [3, 3, 5]
+
+        prior = utils.random_single_categorical(num_states)
+
+        A = utils.random_A_matrix(num_obs, num_states)
+
+        obs = utils.obj_array(len(num_obs))
+        for m, obs_dim in enumerate(num_obs):
+            obs[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+        mb_dict = {'A_factor_list': [[0, 1], [0, 1], [0, 1]],
+                    'A_modality_list': [[0, 1, 2], [0, 1, 2]]}
+        
+        qs_out = run_vanilla_fpi_factorized(A, obs, num_obs, num_states, mb_dict, prior=prior)
+        qs_validation = run_vanilla_fpi(A, obs, num_obs, num_states, prior=prior)
+
+        for qs_f_val, qs_f_out in zip(qs_validation, qs_out):
+            self.assertTrue(np.isclose(qs_f_val, qs_f_out).all())
+
+        # test it also without computing VFE (i.e. with `compute_vfe=False`)
+        qs_out = run_vanilla_fpi_factorized(A, obs, num_obs, num_states, mb_dict, prior=prior, compute_vfe=False)
+        qs_validation = run_vanilla_fpi(A, obs, num_obs, num_states, prior=prior, compute_vfe=False)
+
+        for qs_f_val, qs_f_out in zip(qs_validation, qs_out):
+            self.assertTrue(np.isclose(qs_f_val, qs_f_out).all())
+
+    def test_factorized_fpi_multi_factor_multi_modality_with_condind(self):
+        """
+        Test the sparsified version of `run_vanilla_fpi`, named `run_vanilla_fpi_factorized`
+        with multiple hidden state factors and multiple observation modalities, where some modalities only depend on some factors.
+        """
+
+        num_states = [3, 4]
+        num_obs = [3, 3, 5]
+
+        prior = utils.random_single_categorical(num_states)
+
+        obs = utils.obj_array(len(num_obs))
+        for m, obs_dim in enumerate(num_obs):
+            obs[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+        mb_dict = {'A_factor_list': [[0], [1], [0, 1]],
+                    'A_modality_list': [[0, 2], [1, 2]]}
+
+        A_reduced = utils.random_A_matrix(num_obs, num_states, A_factor_list=mb_dict['A_factor_list'])
+        
+        qs_out = run_vanilla_fpi_factorized(A_reduced, obs, num_obs, num_states, mb_dict, prior=prior)
+
+        A_full = utils.initialize_empty_A(num_obs, num_states)
+        for m, A_m in enumerate(A_full):
+            other_factors = list(set(range(len(num_states))) - set(mb_dict['A_factor_list'][m])) # list of the factors that modality `m` does not depend on
+
+            # broadcast or tile the reduced A matrix (`A_reduced`) along the dimensions of corresponding to `other_factors`
+            expanded_dims = [num_obs[m]] + [1 if f in other_factors else ns for (f, ns) in enumerate(num_states)]
+            tile_dims = [1] + [ns if f in other_factors else 1 for (f, ns) in enumerate(num_states)]
+            A_full[m] = np.tile(A_reduced[m].reshape(expanded_dims), tile_dims)
+
+        qs_validation = run_vanilla_fpi(A_full, obs, num_obs, num_states, prior=prior)
+
+        for qs_f_val, qs_f_out in zip(qs_validation, qs_out):
+            self.assertTrue(np.isclose(qs_f_val, qs_f_out).all())
+    
+    def test_factorized_fpi_multi_factor_single_modality_with_condind(self):
+        """
+        Test the sparsified version of `run_vanilla_fpi`, named `run_vanilla_fpi_factorized`
+        with multiple hidden state factors and one observation modality, where the modality only depend on some factors.
+        """
+
+        num_states = [3, 4]
+        num_obs = [3]
+
+        prior = utils.random_single_categorical(num_states)
+
+        obs = utils.obj_array(len(num_obs))
+        for m, obs_dim in enumerate(num_obs):
+            obs[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+        mb_dict = {'A_factor_list': [[0]],
+                    'A_modality_list': [[0], []]}
+
+        A_reduced = utils.random_A_matrix(num_obs, num_states, A_factor_list=mb_dict['A_factor_list'])
+        
+        qs_out = run_vanilla_fpi_factorized(A_reduced, obs, num_obs, num_states, mb_dict, prior=prior)
+
+        A_full = utils.initialize_empty_A(num_obs, num_states)
+        for m, A_m in enumerate(A_full):
+            other_factors = list(set(range(len(num_states))) - set(mb_dict['A_factor_list'][m])) # list of the factors that modality `m` does not depend on
+
+            # broadcast or tile the reduced A matrix (`A_reduced`) along the dimensions of corresponding to `other_factors`
+            expanded_dims = [num_obs[m]] + [1 if f in other_factors else ns for (f, ns) in enumerate(num_states)]
+            tile_dims = [1] + [ns if f in other_factors else 1 for (f, ns) in enumerate(num_states)]
+            A_full[m] = np.tile(A_reduced[m].reshape(expanded_dims), tile_dims)
+
+        qs_validation = run_vanilla_fpi(A_full, obs, num_obs, num_states, prior=prior)
+
+        for qs_f_val, qs_f_out in zip(qs_validation, qs_out):
+            self.assertTrue(np.isclose(qs_f_val, qs_f_out).all())
+        
+        self.assertTrue(np.isclose(qs_out[1], prior[1]).all())
+
+
+if __name__ == "__main__":
+    unittest.main()
\ No newline at end of file
diff --git a/test/test_inference.py b/test/test_inference.py
index c84a958a..6528ab6d 100644
--- a/test/test_inference.py
+++ b/test/test_inference.py
@@ -108,6 +108,106 @@ def test_update_posterior_states(self):
         for factor in range(len(num_states)):
             self.assertTrue(np.isclose(qs_out1[factor], qs_out2[factor]).all())
 
+    def test_update_posterior_states_factorized_single_factor(self):
+        """
+        Tests the version of `update_posterior_states` where an `mb_dict` is provided as an argument to factorize
+        the fixed-point iteration (FPI) algorithm. Single factor version.
+        """
+        num_states = [3]
+        num_obs = [3]       
+
+        prior = utils.random_single_categorical(num_states)
+
+        A = utils.to_obj_array(maths.softmax(np.eye(num_states[0]) * 0.1))
+
+        obs_idx = 1
+        obs = utils.onehot(obs_idx, num_obs[0])
+
+        mb_dict = {'A_factor_list': [[0]],
+                    'A_modality_list': [[0]]}
+
+        qs_out = inference.update_posterior_states_factorized(A, obs, num_obs, num_states, mb_dict, prior=prior)
+        qs_validation =  maths.softmax(maths.spm_log_single(A[0][obs_idx,:]) + maths.spm_log_single(prior[0]))
+
+        self.assertTrue(np.isclose(qs_validation, qs_out[0]).all())
+
+        '''Try single modality inference where the observation is passed in as an int'''
+        qs_out_2 = inference.update_posterior_states_factorized(A, obs_idx, num_obs, num_states, mb_dict, prior=prior)
+        self.assertTrue(np.isclose(qs_out_2[0], qs_out[0]).all())
+
+        '''Try single modality inference where the observation is a one-hot stored in an object array'''
+        qs_out_3 = inference.update_posterior_states_factorized(A, utils.to_obj_array(obs),num_obs, num_states, mb_dict, prior=prior)
+        self.assertTrue(np.isclose(qs_out_3[0], qs_out[0]).all())
+
+    def test_update_posterior_states_factorized(self):
+        """
+        Tests the version of `update_posterior_states` where an `mb_dict` is provided as an argument to factorize
+        the fixed-point iteration (FPI) algorithm.
+        """
+
+        num_states = [3, 4]
+        num_obs = [3, 3, 5]
+
+        prior = utils.random_single_categorical(num_states)
+
+        obs_index_tuple = tuple([np.random.randint(obs_dim) for obs_dim in num_obs])
+
+        mb_dict = {'A_factor_list': [[0], [1], [0, 1]],
+                    'A_modality_list': [[0, 2], [1, 2]]}
+        
+        A_reduced = utils.random_A_matrix(num_obs, num_states, A_factor_list=mb_dict['A_factor_list'])
+
+        qs_out = inference.update_posterior_states_factorized(A_reduced, obs_index_tuple, num_obs, num_states, mb_dict, prior=prior)
+
+        A_full = utils.initialize_empty_A(num_obs, num_states)
+        for m, A_m in enumerate(A_full):
+            other_factors = list(set(range(len(num_states))) - set(mb_dict['A_factor_list'][m])) # list of the factors that modality `m` does not depend on
+
+            # broadcast or tile the reduced A matrix (`A_reduced`) along the dimensions of corresponding to `other_factors`
+            expanded_dims = [num_obs[m]] + [1 if f in other_factors else ns for (f, ns) in enumerate(num_states)]
+            tile_dims = [1] + [ns if f in other_factors else 1 for (f, ns) in enumerate(num_states)]
+            A_full[m] = np.tile(A_reduced[m].reshape(expanded_dims), tile_dims)
+        
+        qs_validation = inference.update_posterior_states(A_full, obs_index_tuple, prior=prior)
+
+        for qs_f_val, qs_f_out in zip(qs_validation, qs_out):
+            self.assertTrue(np.isclose(qs_f_val, qs_f_out).all())
+    
+    def test_update_posterior_states_factorized_noVFE_compute(self):
+        """
+        Tests the version of `update_posterior_states` where an `mb_dict` is provided as an argument to factorize
+        the fixed-point iteration (FPI) algorithm.
+
+        In this version, we always run the total number of iterations because we don't compute the variational free energy over the course of convergence/optimization.
+        """
+
+        num_states = [3, 4]
+        num_obs = [3, 3, 5]
+
+        prior = utils.random_single_categorical(num_states)
+
+        obs_index_tuple = tuple([np.random.randint(obs_dim) for obs_dim in num_obs])
+
+        mb_dict = {'A_factor_list': [[0], [1], [0, 1]],
+                    'A_modality_list': [[0, 2], [1, 2]]}
+        
+        A_reduced = utils.random_A_matrix(num_obs, num_states, A_factor_list=mb_dict['A_factor_list'])
+
+        qs_out = inference.update_posterior_states_factorized(A_reduced, obs_index_tuple, num_obs, num_states, mb_dict, prior=prior, compute_vfe=False)
+
+        A_full = utils.initialize_empty_A(num_obs, num_states)
+        for m, A_m in enumerate(A_full):
+            other_factors = list(set(range(len(num_states))) - set(mb_dict['A_factor_list'][m])) # list of the factors that modality `m` does not depend on
+
+            # broadcast or tile the reduced A matrix (`A_reduced`) along the dimensions of corresponding to `other_factors`
+            expanded_dims = [num_obs[m]] + [1 if f in other_factors else ns for (f, ns) in enumerate(num_states)]
+            tile_dims = [1] + [ns if f in other_factors else 1 for (f, ns) in enumerate(num_states)]
+            A_full[m] = np.tile(A_reduced[m].reshape(expanded_dims), tile_dims)
+        
+        qs_validation = inference.update_posterior_states(A_full, obs_index_tuple, prior=prior, compute_vfe=False)
+
+        for qs_f_val, qs_f_out in zip(qs_validation, qs_out):
+            self.assertTrue(np.isclose(qs_f_val, qs_f_out).all())
     
 
 if __name__ == "__main__":
diff --git a/test/test_inference_jax.py b/test/test_inference_jax.py
new file mode 100644
index 00000000..e426c870
--- /dev/null
+++ b/test/test_inference_jax.py
@@ -0,0 +1,234 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+""" Unit Tests
+__author__: Dimitrije Markovic, Conor Heins
+"""
+
+import os
+import unittest
+
+import numpy as np
+import jax.numpy as jnp
+
+from pymdp.jax.algos import run_vanilla_fpi as fpi_jax
+from pymdp.algos import run_vanilla_fpi as fpi_numpy
+from pymdp import utils, maths
+
+class TestInferenceJax(unittest.TestCase):
+
+    def test_fixed_point_iteration_singlestate_singleobs(self):
+        """
+        Tests the jax-ified version of mean-field fixed-point iteration against the original numpy version.
+        In this version there is one hidden state factor and one observation modality
+        """
+
+        num_states_list = [
+                            [1],
+                            [5],
+                            [10]
+        ]
+
+        num_obs_list = [
+                        [5],
+                        [1],
+                        [2]
+        ]
+
+        for (num_states, num_obs) in zip(num_states_list, num_obs_list):
+
+            # numpy version
+            prior = utils.random_single_categorical(num_states)
+            A = utils.random_A_matrix(num_obs, num_states)
+
+            obs = utils.obj_array(len(num_obs))
+            for m, obs_dim in enumerate(num_obs):
+                obs[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+            qs_numpy = fpi_numpy(A, obs, num_obs, num_states, prior=prior, num_iter=16, dF=1.0, dF_tol=-1.0) # set dF_tol to negative number so numpy version of FPI never stops early due to convergence
+
+            # jax version
+            prior = [jnp.array(prior_f) for prior_f in prior]
+            A = [jnp.array(a_m) for a_m in A]
+            obs = [jnp.array(o_m) for o_m in obs]
+
+            qs_jax = fpi_jax(A, obs, prior, num_iter=16)
+
+            for f, _ in enumerate(qs_jax):
+                self.assertTrue(np.allclose(qs_numpy[f], qs_jax[f]))
+    
+    def test_fixed_point_iteration_singlestate_multiobs(self):
+        """
+        Tests the jax-ified version of mean-field fixed-point iteration against the original numpy version.
+        In this version there is one hidden state factor and multiple observation modalities
+        """
+
+        num_states_list = [
+                            [1],
+                            [5],
+                            [10]
+        ]
+
+        num_obs_list = [
+                        [5, 2],
+                        [1, 8, 9],
+                        [2, 2, 2]
+        ]
+
+        for (num_states, num_obs) in zip(num_states_list, num_obs_list):
+
+            # numpy version
+            prior = utils.random_single_categorical(num_states)
+            A = utils.random_A_matrix(num_obs, num_states)
+
+            obs = utils.obj_array(len(num_obs))
+            for m, obs_dim in enumerate(num_obs):
+                obs[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+            qs_numpy = fpi_numpy(A, obs, num_obs, num_states, prior=prior, num_iter=16, dF=1.0, dF_tol=-1.0) # set dF_tol to negative number so numpy version of FPI never stops early due to convergence
+
+            # jax version
+            prior = [jnp.array(prior_f) for prior_f in prior]
+            A = [jnp.array(a_m) for a_m in A]
+            obs = [jnp.array(o_m) for o_m in obs]
+
+            qs_jax = fpi_jax(A, obs, prior, num_iter=16)
+
+            for f, _ in enumerate(qs_jax):
+                self.assertTrue(np.allclose(qs_numpy[f], qs_jax[f]))
+    
+    def test_fixed_point_iteration_multistate_singleobs(self):
+        """
+        Tests the jax-ified version of mean-field fixed-point iteration against the original numpy version.
+        In this version there are multiple hidden state factors and a single observation modality
+        """
+
+        num_states_list = [
+                            [1, 10, 2],
+                            [5, 5, 10, 2],
+                            [10, 2]
+        ]
+
+        num_obs_list = [
+                        [5],
+                        [1],
+                        [10]
+        ]
+
+        for (num_states, num_obs) in zip(num_states_list, num_obs_list):
+
+            # numpy version
+            prior = utils.random_single_categorical(num_states)
+            A = utils.random_A_matrix(num_obs, num_states)
+
+            obs = utils.obj_array(len(num_obs))
+            for m, obs_dim in enumerate(num_obs):
+                obs[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+            qs_numpy = fpi_numpy(A, obs, num_obs, num_states, prior=prior, num_iter=16, dF=1.0, dF_tol=-1.0) # set dF_tol to negative number so numpy version of FPI never stops early due to convergence
+
+            # jax version
+            prior = [jnp.array(prior_f) for prior_f in prior]
+            A = [jnp.array(a_m) for a_m in A]
+            obs = [jnp.array(o_m) for o_m in obs]
+
+            qs_jax = fpi_jax(A, obs, prior, num_iter=16)
+
+            for f, _ in enumerate(qs_jax):
+                self.assertTrue(np.allclose(qs_numpy[f], qs_jax[f]))
+
+
+    def test_fixed_point_iteration_multistate_multiobs(self):
+        """
+        Tests the jax-ified version of mean-field fixed-point iteration against the original numpy version.
+        In this version there are multiple hidden state factors and multiple observation modalities
+        """
+
+        ''' Start by creating a collection of random generative models with different 
+        cardinalities and dimensionalities of hidden state factors and observation modalities'''
+
+        num_states_list = [ 
+                         [2, 2, 5],
+                         [2, 2, 2],
+                         [4, 4]
+        ]
+
+        num_obs_list = [
+                        [5, 10],
+                        [4, 3, 2],
+                        [5, 10, 6]
+        ]
+
+        for (num_states, num_obs) in zip(num_states_list, num_obs_list):
+
+            # numpy version
+            prior = utils.random_single_categorical(num_states)
+            A = utils.random_A_matrix(num_obs, num_states)
+
+            obs = utils.obj_array(len(num_obs))
+            for m, obs_dim in enumerate(num_obs):
+                obs[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+            qs_numpy = fpi_numpy(A, obs, num_obs, num_states, prior=prior, num_iter=16, dF=1.0, dF_tol=-1.0) # set dF_tol to negative number so numpy version of FPI never stops early due to convergence
+
+            # jax version
+            prior = [jnp.array(prior_f) for prior_f in prior]
+            A = [jnp.array(a_m) for a_m in A]
+            obs = [jnp.array(o_m) for o_m in obs]
+
+            qs_jax = fpi_jax(A, obs, prior, num_iter=16)
+
+            for f, _ in enumerate(qs_jax):
+                self.assertTrue(np.allclose(qs_numpy[f], qs_jax[f]))
+    
+    def test_fixed_point_iteration_index_observations(self):
+        """
+        Tests the jax-ified version of mean-field fixed-point iteration against the original NumPy version.
+        In this version there are multiple hidden state factors and multiple observation modalities.
+
+        Test the jax version with index-based observations (not one-hots)
+        """
+
+        ''' Start by creating a collection of random generative models with different 
+        cardinalities and dimensionalities of hidden state factors and observation modalities'''
+
+        num_states_list = [ 
+                         [2, 2, 5],
+                         [2, 2, 2],
+                         [4, 4]
+        ]
+
+        num_obs_list = [
+                        [5, 10],
+                        [4, 3, 2],
+                        [5, 10, 6]
+        ]
+
+        for (num_states, num_obs) in zip(num_states_list, num_obs_list):
+
+            # numpy version
+            prior = utils.random_single_categorical(num_states)
+            A = utils.random_A_matrix(num_obs, num_states)
+
+            obs = utils.obj_array(len(num_obs))
+            for m, obs_dim in enumerate(num_obs):
+                obs[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+            qs_numpy = fpi_numpy(A, obs, num_obs, num_states, prior=prior, num_iter=16, dF=1.0, dF_tol=-1.0) # set dF_tol to negative number so numpy version of FPI never stops early due to convergence
+
+            obs_idx = []
+            for ob in obs:
+                obs_idx.append(np.where(ob)[0][0])
+            
+            # jax version
+            prior = [jnp.array(prior_f) for prior_f in prior]
+            A = [jnp.array(a_m) for a_m in A]
+            # obs = [jnp.array(o_m) for o_m in obs]
+
+            qs_jax = fpi_jax(A, obs_idx, prior, num_iter=16, distr_obs=False)
+
+            for f, _ in enumerate(qs_jax):
+                self.assertTrue(np.allclose(qs_numpy[f], qs_jax[f]))
+
+if __name__ == "__main__":
+    unittest.main()
\ No newline at end of file
diff --git a/test/test_learning.py b/test/test_learning.py
index a849c982..c839704c 100644
--- a/test/test_learning.py
+++ b/test/test_learning.py
@@ -249,7 +249,53 @@ def test_update_pA_diff_observation_formats(self):
             pA, A, observation_onehot, qs, lr=l_rate, modalities=modalities_to_update)
         
         self.assertTrue(np.allclose(pA_updated_1[0], pA_updated_2[0]))
+    
+    def test_update_pA_factorized(self):
+        """
+        Test for `learning.update_obs_likelihood_dirichlet_factorized`, which is the learning function updating prior Dirichlet parameters over the sensory likelihood (pA) 
+        in the case that the generative model is sparse and only some modalities depend on some hidden state factors
+        """
+
+        """ Test version with sparse conditional dependency graph (taking advantage of `A_factor_list` argument) """
+        num_states = [2, 6, 5]
+        num_obs = [3, 4, 5]
+        A_factor_list = [[0], [1, 2], [0, 2]]
+
+        qs = utils.random_single_categorical(num_states)
+        A = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_factor_list)
+        pA = utils.dirichlet_like(A, scale=1.0)
+        observation = [np.random.randint(obs_dim) for obs_dim in num_obs]
+        pA_updated_test = learning.update_obs_likelihood_dirichlet_factorized(
+            pA, A, observation, qs, A_factor_list
+            )
 
+        for modality, obs_dim in enumerate(num_obs):
+            update = maths.spm_cross(utils.onehot(observation[modality], obs_dim), qs[A_factor_list[modality]])
+            pA_updated_valid_m = pA[modality] +  update
+            self.assertTrue(np.allclose(pA_updated_test[modality], pA_updated_valid_m))
+
+        """ Test version with full conditional dependency graph (not taking advantage of `A_factor_list` argument, but including it anyway) """
+        num_states = [2, 6, 5]
+        num_obs = [3, 4, 5]
+        A_factor_list = len(num_obs) * [[0, 1, 2]]
+        qs = utils.random_single_categorical(num_states)
+        A = utils.random_A_matrix(num_obs, num_states)
+
+        modalities_to_update = [0, 2]
+        learning_rate = np.random.rand() # sample some positive learning rate
+
+        pA = utils.dirichlet_like(A, scale=1.0)
+        observation = [np.random.randint(obs_dim) for obs_dim in num_obs]
+        pA_updated_test = learning.update_obs_likelihood_dirichlet_factorized(
+            pA, A, observation, qs, A_factor_list, lr=learning_rate, modalities=modalities_to_update
+            )
+
+        pA_updated_valid = learning.update_obs_likelihood_dirichlet(
+            pA, A, observation, qs, lr=learning_rate, modalities=modalities_to_update
+            )
+
+        for modality, obs_dim in enumerate(num_obs):
+            self.assertTrue(np.allclose(pA_updated_test[modality], pA_updated_valid[modality]))
 
     def test_update_pB_single_factor_no_actions(self):
         """
@@ -552,6 +598,70 @@ def test_update_pB_multi_factor_some_controllable_some_factors(self):
                 )
             self.assertTrue(np.all(pB_updated[factor] == validation_pB[factor]))
     
+    def test_update_pB_interactions(self):
+        """
+        Test for `learning.update_state_likelihood_dirichlet_factorized`, which is the learning function updating prior Dirichlet parameters over the transition likelihood (pB) 
+        in the case that there are allowable interactions between hidden state factors, i.e. the dynamics of factor `f` may depend on more than just its control factor and its own state.
+        """
+
+        """ Test version with interactions """
+        num_states = [3, 4, 5]
+        num_controls = [2, 1, 1]
+        B_factor_list= [[0, 1], [0,1,2], [1, 2]]
+        factors_to_update = [0, 1]
+
+        qs_prev = utils.random_single_categorical(num_states)
+        qs = utils.random_single_categorical(num_states)
+
+        B = utils.random_B_matrix(num_states, num_controls, B_factor_list=B_factor_list)
+        pB = utils.dirichlet_like(B, scale=1.)
+        l_rate = np.random.rand() # sample some positive learning rate
+
+        action = np.array([np.random.randint(c_dim) for c_dim in num_controls])
+
+        pB_updated_test = learning.update_state_likelihood_dirichlet_interactions(
+            pB, B, action, qs, qs_prev, B_factor_list, lr=l_rate, factors=factors_to_update
+        )
+
+        pB_updated_valid = utils.dirichlet_like(B, scale=1.)
+
+        for factor, action_i in enumerate(action):
+            
+            if factor in factors_to_update:
+                pB_updated_valid[factor][...,action_i] += (
+                    l_rate
+                    * maths.spm_cross(qs[factor], qs_prev[B_factor_list[factor]])
+                    * (B[factor][...,action_i] > 0)
+                )
+            self.assertTrue(np.all(pB_updated_test[factor] == pB_updated_valid[factor]))
+
+        """ Test version without interactions, but still use the factorized version to test it against the non-interacting version `update_state_likelihood_dirichlet` """
+        num_states = [3, 4, 5]
+        num_controls = [2, 1, 1]
+        B_factor_list= [[0], [1], [2]]
+        factors_to_update = [0, 1]
+
+        qs_prev = utils.random_single_categorical(num_states)
+        qs = utils.random_single_categorical(num_states)
+
+        B = utils.random_B_matrix(num_states, num_controls, B_factor_list=B_factor_list)
+        pB = utils.dirichlet_like(B, scale=1.)
+        l_rate = np.random.rand() # sample some positive learning rate
+
+        action = np.array([np.random.randint(c_dim) for c_dim in num_controls])
+
+        pB_updated_test = learning.update_state_likelihood_dirichlet_interactions(
+            pB, B, action, qs, qs_prev, B_factor_list, lr=l_rate, factors=factors_to_update
+        )
+
+        pB_updated_valid = learning.update_state_likelihood_dirichlet(
+            pB, B, action, qs, qs_prev, lr=l_rate, factors=factors_to_update
+        )
+
+        for factor, action_i in enumerate(action):
+            self.assertTrue(np.allclose(pB_updated_test[factor], pB_updated_valid[factor]))
+
+
     def test_update_pD(self):
         """
         Test updating prior Dirichlet parameters over initial hidden states (pD). 
diff --git a/test/test_learning_jax.py b/test/test_learning_jax.py
new file mode 100644
index 00000000..cdb3b86c
--- /dev/null
+++ b/test/test_learning_jax.py
@@ -0,0 +1,139 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+""" Unit Tests
+__author__: Dimitrije Markovic, Conor Heins
+"""
+
+import os
+import unittest
+
+import numpy as np
+import jax.numpy as jnp
+import jax.tree_util as jtu
+
+from pymdp.learning import update_obs_likelihood_dirichlet as update_pA_numpy
+from pymdp.learning import update_obs_likelihood_dirichlet_factorized as update_pA_numpy_factorized
+from pymdp.jax.learning import update_obs_likelihood_dirichlet as update_pA_jax
+from pymdp import utils, maths
+
+class TestLearningJax(unittest.TestCase):
+
+    def test_update_observation_likelihood_fullyconnected(self):
+        """
+        Testing JAX-ified version of updating Dirichlet posterior over observation likelihood parameters (qA is posterior, pA is prior, and A is expectation
+        of likelihood wrt to current posterior over A, i.e. $A = E_{Q(A)}[P(o|s,A)]$.
+
+        This is the so-called 'fully-connected' version where all hidden state factors drive each modality (i.e. A_dependencies is a list of lists of hidden state factors)
+        """
+
+        num_obs_list = [ [5], 
+                        [10, 3, 2], 
+                        [2, 4, 4, 2],
+                        [10]
+                        ]
+        num_states_list = [ [2,3,4], 
+                        [2], 
+                        [4,5],
+                        [3] 
+                        ]
+
+        A_dependencies_list = [ [ [0,1,2] ],
+                                [ [0], [0], [0] ],
+                                [ [0,1], [0,1], [0,1], [0,1] ],
+                                [ [0] ]
+                                ]
+
+        for (num_obs, num_states, A_dependencies) in zip(num_obs_list, num_states_list, A_dependencies_list):
+            # create numpy arrays to test numpy version of learning
+
+            # create A matrix initialization (expected initial value of P(o|s, A)) and prior over A (pA)
+            A_np = utils.random_A_matrix(num_obs, num_states)
+            pA_np = utils.dirichlet_like(A_np, scale = 3.0)
+
+            # create random observations 
+            obs_np = utils.obj_array(len(num_obs))
+            for m, obs_dim in enumerate(num_obs):
+                obs_np[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+            # create random state posterior
+            qs_np = utils.random_single_categorical(num_states)
+
+            l_rate = 1.0
+
+            # run numpy version of learning
+            qA_np_test = update_pA_numpy(pA_np, A_np, obs_np, qs_np, lr=l_rate)
+
+            pA_jax = jtu.tree_map(lambda x: jnp.array(x), list(pA_np))
+            obs_jax = jtu.tree_map(lambda x: jnp.array(x)[None], list(obs_np))
+            qs_jax = jtu.tree_map(lambda x: jnp.array(x)[None], list(qs_np))
+
+            qA_jax_test = update_pA_jax(pA_jax, obs_jax, qs_jax, A_dependencies, lr=l_rate)
+
+            for modality, obs_dim in enumerate(num_obs):
+                self.assertTrue(np.allclose(qA_jax_test[modality], qA_np_test[modality]))
+
+    def test_update_observation_likelihood_factorized(self):
+        """
+        Testing JAX-ified version of updating Dirichlet posterior over observation likelihood parameters (qA is posterior, pA is prior, and A is expectation
+        of likelihood wrt to current posterior over A, i.e. $A = E_{Q(A)}[P(o|s,A)]$.
+
+        This is the factorized version where only some hidden state factors drive each modality (i.e. A_dependencies is a list of lists of hidden state factors)
+        """
+
+        num_obs_list = [ [5], 
+                        [10, 3, 2], 
+                        [2, 4, 4, 2],
+                        [10]
+                        ]
+        num_states_list = [ [2,3,4], 
+                        [2, 5, 2], 
+                        [4,5],
+                        [3] 
+                        ]
+
+        A_dependencies_list = [ [ [0,1] ],
+                                [ [0, 1], [1], [1, 2] ],
+                                [ [0,1], [0], [0,1], [1] ],
+                                [ [0] ]
+                                ]
+
+        for (num_obs, num_states, A_dependencies) in zip(num_obs_list, num_states_list, A_dependencies_list):
+            # create numpy arrays to test numpy version of learning
+
+            # create A matrix initialization (expected initial value of P(o|s, A)) and prior over A (pA)
+            A_np = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_dependencies)
+            pA_np = utils.dirichlet_like(A_np, scale = 3.0)
+
+            # create random observations 
+            obs_np = utils.obj_array(len(num_obs))
+            for m, obs_dim in enumerate(num_obs):
+                obs_np[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+            # create random state posterior
+            qs_np = utils.random_single_categorical(num_states)
+
+            l_rate = 1.0
+
+            # run numpy version of learning
+            qA_np_test = update_pA_numpy_factorized(pA_np, A_np, obs_np, qs_np, A_dependencies, lr=l_rate)
+
+            pA_jax = jtu.tree_map(lambda x: jnp.array(x), list(pA_np))
+            obs_jax = jtu.tree_map(lambda x: jnp.array(x)[None], list(obs_np))
+            qs_jax = jtu.tree_map(lambda x: jnp.array(x)[None], list(qs_np))
+
+            qA_jax_test = update_pA_jax(pA_jax, obs_jax, qs_jax, A_dependencies, lr=l_rate)
+
+            for modality, obs_dim in enumerate(num_obs):
+                self.assertTrue(np.allclose(qA_jax_test[modality],qA_np_test[modality]))
+
+if __name__ == "__main__":
+    unittest.main()
+
+
+
+
+
+
+
+
diff --git a/test/test_message_passing_jax.py b/test/test_message_passing_jax.py
new file mode 100644
index 00000000..b27be336
--- /dev/null
+++ b/test/test_message_passing_jax.py
@@ -0,0 +1,698 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+""" Unit Tests
+__author__: Dimitrije Markovic, Conor Heins
+"""
+
+import os
+import unittest
+from functools import partial
+
+import numpy as np
+import jax.numpy as jnp
+import jax.tree_util as jtu
+from jax import vmap, nn
+from jax import random as jr
+
+from pymdp.jax.algos import run_vanilla_fpi as fpi_jax
+from pymdp.jax.algos import run_factorized_fpi as fpi_jax_factorized
+from pymdp.jax.algos import update_variational_filtering as ovf_jax
+from pymdp.algos import run_vanilla_fpi as fpi_numpy
+from pymdp.algos import run_mmp as mmp_numpy
+from pymdp.jax.algos import run_mmp as mmp_jax
+from pymdp.jax.algos import run_vmp as vmp_jax
+from pymdp import utils, maths
+
+from typing import Any, List, Dict
+
+
+def make_model_configs(source_seed=0, num_models=4) -> Dict:
+    rng_keys = jr.split(jr.PRNGKey(source_seed), num_models)
+    num_factors_list = [ jr.randint(key, (1,), 1, 7)[0].item() for key in rng_keys ] # list of total numbers of hidden state factors per model
+    num_states_list = [ jr.randint(key, (nf,), 2, 5).tolist() for nf, key in zip(num_factors_list, rng_keys) ]
+    num_controls_list = [ jr.randint(key, (nf,), 1, 3).tolist() for nf, key in zip(num_factors_list, rng_keys) ]
+
+    rng_keys = jr.split(rng_keys[-1], num_models)
+    num_modalities_list = [ jr.randint(key, (1,), 1, 10)[0].item() for key in rng_keys ]
+    num_obs_list = [ jr.randint(key, (nm,), 1, 5).tolist() for nm, key in zip(num_modalities_list, rng_keys) ]
+
+    rng_keys = jr.split(rng_keys[-1], num_models)
+    A_deps_list, B_deps_list = [], []
+    for nf, nm, model_key in zip(num_factors_list, num_modalities_list, rng_keys):
+        modality_keys_model_i = jr.split(model_key, nm)
+        num_f_per_modality = [jr.randint(key, shape=(), minval=1, maxval=nf+1).item() for key in modality_keys_model_i] # this is the number of factors that each modality depends on
+        A_deps_model_i = [sorted(jr.choice(key, a=nf, shape=(num_f_m,), replace=False).tolist()) for key, num_f_m in zip(modality_keys_model_i, num_f_per_modality)]
+        A_deps_list.append(A_deps_model_i)
+
+        factor_keys_model_i = jr.split(modality_keys_model_i[-1], nf)
+        num_f_per_factor = [jr.randint(key, shape=(), minval=1, maxval=nf+1).item() for key in factor_keys_model_i] # this is the number of factors that each factor depends on
+        B_deps_model_i = [sorted(jr.choice(key, a=nf, shape=(num_f_f,), replace=False).tolist()) for key, num_f_f in zip(factor_keys_model_i, num_f_per_factor)]
+        B_deps_list.append(B_deps_model_i)
+
+    return {'nf_list': num_factors_list, 
+            'ns_list': num_states_list, 
+            'nc_list': num_controls_list,
+            'nm_list': num_modalities_list, 
+            'no_list': num_obs_list, 
+            'A_deps_list': A_deps_list,
+            'B_deps_list': B_deps_list
+        }
+
+def make_A_full(A_reduced: List[np.ndarray], A_dependencies: List[List[int]], num_obs: List[int], num_states: List[int]) -> np.ndarray:
+    """ 
+    Given a reduced A matrix, `A_reduced`, and a list of dependencies between hidden state factors and observation modalities, `A_dependencies`,
+    return a full A matrix, `A_full`, where `A_full[m]` is the full A matrix for modality `m`. This means all redundant conditional independencies
+    between observation modalities `m` and all hidden state factors (i.e. `range(len(num_states))`) are represented as lagging dimensions in `A_full`.
+    """
+    A_full = utils.initialize_empty_A(num_obs, num_states) # initialize the full likelihood tensor (ALL modalities might depend on ALL factors)
+    all_factors = range(len(num_states)) # indices of all hidden state factors
+    for m, A_m in enumerate(A_full):
+
+        # Step 1. Extract the list of the factors that modality `m` does NOT depend on
+        non_dependent_factors = list(set(all_factors) - set(A_dependencies[m])) 
+
+        # Step 2. broadcast or tile the reduced A matrix (`A_reduced`) along the dimensions of corresponding to `non_dependent_factors`, to give it the full shape of `(num_obs[m], *num_states)`
+        expanded_dims = [num_obs[m]] + [1 if f in non_dependent_factors else ns for (f, ns) in enumerate(num_states)]
+        tile_dims = [1] + [ns if f in non_dependent_factors else 1 for (f, ns) in enumerate(num_states)]
+        A_full[m] = np.tile(A_reduced[m].reshape(expanded_dims), tile_dims)
+    
+    return A_full
+                
+class TestMessagePassing(unittest.TestCase):
+
+    def test_fixed_point_iteration(self):
+        cfg = {'source_seed': 0,
+                'num_models': 4
+            }
+        gm_params = make_model_configs(**cfg)
+        num_states_list, num_obs_list = gm_params['ns_list'], gm_params['no_list']
+
+        for (num_states, num_obs) in zip(num_states_list, num_obs_list):
+
+            # numpy version
+            prior = utils.random_single_categorical(num_states)
+            A = utils.random_A_matrix(num_obs, num_states)
+
+            obs = utils.obj_array(len(num_obs))
+            for m, obs_dim in enumerate(num_obs):
+                obs[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+            qs_numpy = fpi_numpy(A, obs, num_obs, num_states, prior=prior, num_iter=16, dF=1.0, dF_tol=-1.0) # set dF_tol to negative number so numpy version of FPI never stops early due to convergence
+
+            # jax version
+            prior = [jnp.array(prior_f) for prior_f in prior]
+            A = [jnp.array(a_m) for a_m in A]
+            obs = [jnp.array(o_m) for o_m in obs]
+
+            qs_jax = fpi_jax(A, obs, prior, num_iter=16)
+
+            for f, _ in enumerate(qs_jax):
+                self.assertTrue(np.allclose(qs_numpy[f], qs_jax[f]))
+
+
+    def test_fixed_point_iteration_factorized_fullyconnected(self):
+        """
+        Test the factorized version of `run_vanilla_fpi`, named `run_factorized_fpi`
+        with multiple hidden state factors and multiple observation modalities.
+        """
+        cfg = {'source_seed': 1,
+                'num_models': 4
+            }
+        gm_params = make_model_configs(**cfg)
+        num_states_list, num_obs_list = gm_params['ns_list'], gm_params['no_list']
+
+        for (num_states, num_obs) in zip(num_states_list, num_obs_list):
+
+            # initialize arrays in numpy version
+            prior = utils.random_single_categorical(num_states)
+            A = utils.random_A_matrix(num_obs, num_states)
+
+            obs = utils.obj_array(len(num_obs))
+            for m, obs_dim in enumerate(num_obs):
+                obs[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+            # jax version
+            prior = [jnp.array(prior_f) for prior_f in prior]
+            A = [jnp.array(a_m) for a_m in A]
+            obs = [jnp.array(o_m) for o_m in obs]
+
+            factor_lists = len(num_obs) * [list(range(len(num_states)))]
+
+            qs_jax = fpi_jax(A, obs, prior, num_iter=16)
+            qs_jax_factorized = fpi_jax_factorized(A, obs, prior, factor_lists, num_iter=16)
+
+            for f, _ in enumerate(qs_jax):
+                self.assertTrue(np.allclose(qs_jax[f], qs_jax_factorized[f], atol=1e-6))
+
+    def test_fixed_point_iteration_factorized_sparsegraph(self):
+        """
+        Test the factorized version of `run_vanilla_fpi`, named `run_factorized_fpi`
+        with multiple hidden state factors and multiple observation modalities, and with sparse conditional dependence relationships between hidden states
+        and observation modalities
+        """
+        cfg = {'source_seed': 3,
+                'num_models': 4
+            }
+        gm_params = make_model_configs(**cfg)
+
+        num_states_list, num_obs_list, A_dependencies_list = gm_params['ns_list'], gm_params['no_list'], gm_params['A_deps_list']
+
+        for (num_states, num_obs, a_deps_i) in zip(num_states_list, num_obs_list, A_dependencies_list):
+            
+            prior = utils.random_single_categorical(num_states)
+
+            obs = utils.obj_array(len(num_obs))
+            for m, obs_dim in enumerate(num_obs):
+                obs[m] = utils.onehot(np.random.randint(obs_dim), obs_dim)
+
+            A_reduced = utils.random_A_matrix(num_obs, num_states, A_factor_list=a_deps_i)
+
+            # jax version
+            prior_jax = [jnp.array(prior_f) for prior_f in prior]
+            A_reduced_jax = [jnp.array(a_m) for a_m in A_reduced]
+            obs_jax = [jnp.array(o_m) for o_m in obs]
+
+            qs_out = fpi_jax_factorized(A_reduced_jax, obs_jax, prior_jax, a_deps_i, num_iter=16)
+
+            # create the full A matrix, where all hidden state factors are represented in the lagging dimensions of each sub-A array
+            A_full = make_A_full(A_reduced, a_deps_i, num_obs, num_states)
+           
+            # jax version
+            A_full_jax = [jnp.array(a_m) for a_m in A_full]
+
+            qs_validation = fpi_jax(A_full_jax, obs_jax, prior_jax, num_iter=16)
+
+            for qs_f_val, qs_f_out in zip(qs_validation, qs_out):
+                self.assertTrue(np.allclose(qs_f_val, qs_f_out))
+
+    def test_marginal_message_passing(self):
+
+        cfg = {'source_seed': 5,
+                'num_models': 4
+            }
+        gm_params = make_model_configs(**cfg)
+
+        num_states_list, num_obs_list, num_controls_list, A_dependencies_list, B_dependencies_list = gm_params['ns_list'], gm_params['no_list'], gm_params['nc_list'], \
+                                                                                                     gm_params['A_deps_list'], gm_params['B_deps_list']
+
+        batch_size = 10
+        n_timesteps = 4
+
+        for num_states, num_obs, num_controls, A_deps, B_deps in zip(num_states_list, num_obs_list, num_controls_list, A_dependencies_list, B_dependencies_list):
+
+            # create a version of a_deps_i where each sub-list is sorted
+            prior = [jr.dirichlet(key, alpha=jnp.ones((ns,)), shape=(batch_size,)) for ns, key in zip(num_states, jr.split(jr.PRNGKey(0), len(num_states)))] 
+
+            obs = [jr.categorical(key, logits=jnp.zeros(no), shape=(n_timesteps,batch_size)) for no, key in zip(num_obs, jr.split(jr.PRNGKey(1), len(num_obs)))]
+            obs = jtu.tree_map(lambda x, no: nn.one_hot(x, num_classes=no), obs, num_obs)
+
+            A_sub_shapes = [ [ns for f, ns in enumerate(num_states) if f in a_deps_i] for a_deps_i in A_deps ]
+            A_sampling_keys = jr.split(jr.PRNGKey(2), len(num_obs))
+            A = [jr.dirichlet(key, alpha=jnp.ones(no) / no, shape=factor_shapes) for no, factor_shapes, key in zip(num_obs, A_sub_shapes, A_sampling_keys)]
+            A = jtu.tree_map(lambda a: jnp.moveaxis(a, -1, 0), A) # move observations into leading dimensions
+            A = jtu.tree_map(lambda a: jnp.broadcast_to(a, (batch_size,) + a.shape), A)
+
+            B_sub_shapes = [ [ns for f, ns in enumerate(num_states) if f in b_deps_i] + [nc] for nc, b_deps_i in zip(num_controls, B_deps) ]
+            B_sampling_keys = jr.split(jr.PRNGKey(3), len(num_states))
+            B = [jr.dirichlet(key, alpha=jnp.ones(ns) / ns, shape=factor_shapes) for ns, factor_shapes, key in zip(num_states, B_sub_shapes, B_sampling_keys)]
+            B = jtu.tree_map(lambda b: jnp.moveaxis(b, -2, -1), B) # move u_t to the rightmost axis of the array
+            B = jtu.tree_map(lambda b: jnp.moveaxis(b, -2, 0), B) # s_t+1 to the leading dimension of the array
+            B = jtu.tree_map(lambda b: jnp.broadcast_to(b, (batch_size,) + b.shape), B)
+
+            # # create a policy-dependent sequence of B matrices, but now we store the sequence dimension (action indices) in the first dimension (0th dimension is still batch dimension)
+            policy = []
+            key = jr.PRNGKey(11)
+            for nc in num_controls:
+                key, k = jr.split(key)
+                policy.append( jr.choice(k, jnp.arange(nc), shape=(n_timesteps - 1, 1)) )
+            
+            policy = jnp.concatenate(policy, -1)
+            nf = len(B)
+            actions_tree = [policy[:, i] for i in range(nf)]
+            B_seq = jtu.tree_map(lambda b, a_idx: jnp.moveaxis(b[..., a_idx], -1, 0), B, actions_tree)
+
+            mmp = vmap(
+                partial(mmp_jax, num_iter=16, tau=1.0),
+                in_axes=(0, 1, 1, 0, None, None)
+            )
+            qs_out = mmp(A, B_seq, obs, prior, A_deps, B_deps)
+
+            self.assertTrue(qs_out[0].shape[0] == obs[0].shape[1])
+
+    # def test_variational_message_passing(self):
+
+    #     num_states = [3]
+    #     num_obs = [3]
+
+    #     A = [ jnp.broadcast_to(jnp.array([[0.5, 0.5, 0.], 
+    #                                     [0.0,  0.0,  1.], 
+    #                                     [0.5, 0.5, 0.]]
+    #                                 ), (2, 3, 3) )]
+
+    #     # create two B matrices, one for each action
+    #     B_1 = jnp.broadcast_to(jnp.array([[0.0, 0.75, 0.0],
+    #                                     [0.0, 0.25, 1.0],
+    #                                     [1.0, 0.0, 0.0]]
+    #                 ), (2, 3, 3))
+        
+    #     B_2 = jnp.broadcast_to(jnp.array([[0.0, 0.25, 0.0],
+    #                                     [0.0, 0.75, 0.0],
+    #                                     [1.0, 0.0, 1.0]]
+    #                 ), (2, 3, 3))
+        
+    #     B = [jnp.stack([B_1, B_2], axis=-1)]
+
+    #     # create a policy-dependent sequence of B matrices
+
+    #     policy = jnp.array([0, 1, 0])
+    #     B_policy = jtu.tree_map(lambda b: b[..., policy].transpose(0, 3, 1, 2), B)
+
+    #     # for the single modality, a sequence over time of observations (one hot vectors)
+    #     obs = [
+    #             jnp.broadcast_to(jnp.array([[1., 0., 0.], 
+    #                                         [0., 1., 0.], 
+    #                                         [0., 0., 1.],
+    #                                         [1., 0., 0.]])[:, None], (4, 2, 3) )
+    #                             ]
+
+    #     prior = [jnp.ones((2, 3)) / 3.]
+
+    #     A_dependencies = [list(range(len(num_states))) for _ in range(len(num_obs))]
+    #     qs_out = vmp_jax(A, B_policy, obs, prior, A_dependencies, num_iter=16, tau=1.)
+
+    #     self.assertTrue(qs_out[0].shape[0] == obs[0].shape[0])
+    
+    # def test_vmap_variational_message_passing_across_policies(self):
+
+    #     num_states = [3, 2]
+    #     num_obs = [3]
+
+    #     A_tensor = jnp.stack([jnp.array([[0.5, 0.5, 0.], 
+    #                                     [0.0,  0.0,  1.], 
+    #                                     [0.5, 0.5, 0.]]
+    #                                 ), jnp.array([[1./3, 1./3, 1./3], 
+    #                                               [1./3, 1./3, 1./3], 
+    #                                               [1./3, 1./3, 1./3]]
+    #                                 )], axis=-1)
+
+    #     A = [ jnp.broadcast_to(A_tensor, (2, 3, 3, 2)) ]
+
+    #     # create two B matrices, one for each action
+    #     B_1 = jnp.broadcast_to(jnp.array([[0.0, 0.75, 0.0],
+    #                                     [0.0, 0.25, 1.0],
+    #                                     [1.0, 0.0, 0.0]]
+    #                 ), (2, 3, 3))
+        
+    #     B_2 = jnp.broadcast_to(jnp.array([[0.0, 0.25, 0.0],
+    #                                     [0.0, 0.75, 0.0],
+    #                                     [1.0, 0.0, 1.0]]
+    #                 ), (2, 3, 3))
+        
+    #     B_uncontrollable = jnp.expand_dims(
+    #         jnp.broadcast_to(
+    #             jnp.array([[1.0, 0.0], [0.0, 1.0]]), (2, 2, 2)
+    #         ), 
+    #         -1
+    #     )
+
+    #     B = [jnp.stack([B_1, B_2], axis=-1), B_uncontrollable]
+
+    #     # create a policy-dependent sequence of B matrices
+
+    #     policy_1 = jnp.array([ [0, 0],
+    #                            [1, 0],
+    #                            [1, 0] ]
+    #                         )
+
+    #     policy_2 = jnp.array([ [1, 0],
+    #                            [1, 0],
+    #                            [1, 0] ]
+    #                         )
+        
+    #     policy_3 = jnp.array([ [1, 0],
+    #                            [0, 0],
+    #                            [1, 0] ]
+    #                         )
+        
+    #     all_policies = [policy_1, policy_2, policy_3]
+    #     all_policies = list(jnp.stack(all_policies).transpose(2, 0, 1)) # `n_factors` lists, each with matrix of shape `(n_policies, n_time_steps)`
+
+    #     # for the single modality, a sequence over time of observations (one hot vectors)
+    #     obs = [jnp.broadcast_to(jnp.array([[1., 0., 0.], 
+    #                                        [0., 1., 0.], 
+    #                                        [0., 0., 1.],
+    #                                        [1., 0., 0.]])[:, None], (4, 2, 3) )]
+
+    #     prior = [jnp.ones((2, 3)) / 3., jnp.ones((2, 2)) / 2.]
+
+    #     A_dependencies = [list(range(len(num_states))) for _ in range(len(num_obs))]
+
+    #     ### First do VMP
+    #     def test(action_sequence):
+    #         B_policy = jtu.tree_map(lambda b, a_idx: b[..., a_idx].transpose(0, 3, 1, 2), B, action_sequence)            
+    #         return vmp_jax(A, B_policy, obs, prior, A_dependencies, num_iter=16, tau=1.)
+    #     qs_out = vmap(test)(all_policies)
+    #     self.assertTrue(qs_out[0].shape[1] == obs[0].shape[0])
+
+    #     ### Then do MMP
+    #     def test(action_sequence):
+    #         B_policy = jtu.tree_map(lambda b, a_idx: b[..., a_idx].transpose(0, 3, 1, 2), B, action_sequence)
+    #         return mmp_jax(A, B_policy, obs, prior, A_dependencies, num_iter=16, tau=1.)
+    #     qs_out = vmap(test)(all_policies)
+    #     self.assertTrue(qs_out[0].shape[1] == obs[0].shape[0])
+    
+    # def test_variational_message_passing_multiple_modalities_factors(self):
+
+    #     num_states_list = [ 
+    #                      [2, 2, 5],
+    #                      [2, 2, 2],
+    #                      [4, 4]
+    #     ]
+
+    #     num_controls_list = [
+    #                         [2, 1, 3],
+    #                         [2, 1, 2],
+    #                         [1, 3]
+    #     ]
+
+    #     num_obs_list = [
+    #                     [5, 10],
+    #                     [4, 3, 2],
+    #                     [5, 2, 6, 3]
+    #     ]
+
+    #     batch_dim, T = 2, 4 # batch dimension (e.g. number of agents, parallel realizations, etc.) and time steps
+    #     n_policies = 3
+
+    #     for (num_states, num_controls, num_obs) in zip(num_states_list, num_controls_list, num_obs_list):
+
+    #         # initialize arrays in numpy
+    #         A_numpy = utils.random_A_matrix(num_obs, num_states)
+    #         B_numpy = utils.random_B_matrix(num_states, num_controls)
+
+    #         A = []
+    #         for mod_i in range(len(num_obs)):
+    #             broadcast_shape = (batch_dim,) + tuple(A_numpy[mod_i].shape)
+    #             A.append(jnp.broadcast_to(A_numpy[mod_i], broadcast_shape))
+            
+    #         B = []
+    #         for fac_i in range(len(num_states)):
+    #             broadcast_shape = (batch_dim,) + tuple(B_numpy[fac_i].shape)
+    #             B.append(jnp.broadcast_to(B_numpy[fac_i], broadcast_shape))
+
+    #         prior_numpy = utils.random_single_categorical(num_states)
+    #         prior = []
+    #         for fac_i in range(len(num_states)):
+    #             broadcast_shape = (batch_dim,) + tuple(prior_numpy[fac_i].shape)
+    #             prior.append(jnp.broadcast_to(prior_numpy[fac_i], broadcast_shape))
+
+    #         # initialization observation sequences in jax
+    #         obs_seq = []
+    #         for n_obs in num_obs:
+    #             obs_ints = np.random.randint(0, high=n_obs, size=(T,1))
+    #             obs_array_mod_i = jnp.broadcast_to(nn.one_hot(obs_ints, num_classes=n_obs), (T, batch_dim, n_obs))
+    #             obs_seq.append(obs_array_mod_i)
+
+    #         # create random policies
+    #         policies = []
+    #         for n_controls in num_controls:
+    #             policies.append(jnp.array(np.random.randint(0, high=n_controls, size=(n_policies, T-1))))
+            
+    #         A_dependencies = [list(range(len(num_states))) for _ in range(len(num_obs))]
+    #         ### First do VMP
+    #         def test(action_sequence):
+    #             B_policy = jtu.tree_map(lambda b, a_idx: b[..., a_idx].transpose(0, 3, 1, 2), B, action_sequence)            
+    #             return vmp_jax(A, B_policy, obs_seq, prior, A_dependencies, num_iter=16, tau=1.)
+    #         qs_out = vmap(test)(policies)
+    #         self.assertTrue(qs_out[0].shape[1] == obs_seq[0].shape[0])
+
+    #         ### Then do MMP
+    #         def test(action_sequence):
+    #             B_policy = jtu.tree_map(lambda b, a_idx: b[..., a_idx].transpose(0, 3, 1, 2), B, action_sequence)
+    #             return mmp_jax(A, B_policy, obs_seq, prior, A_dependencies, num_iter=16, tau=1.)
+    #         qs_out = vmap(test)(policies)
+    #         self.assertTrue(qs_out[0].shape[1] == obs_seq[0].shape[0])
+    
+    # def test_A_dependencies_variational_message_passing(self):
+    #     """ Test variational message passing with A dependencies """
+
+    #     num_states_list = [ 
+    #                      [2, 2, 5],
+    #                      [2, 2, 2],
+    #                      [4, 4]
+    #     ]
+
+    #     num_controls_list = [
+    #                         [2, 1, 3],
+    #                         [2, 1, 2],
+    #                         [1, 3]
+    #     ]
+
+    #     num_obs_list = [
+    #                     [5, 10],
+    #                     [4, 3, 2],
+    #                     [5, 2, 6, 3]
+    #     ]
+
+    #     A_dependencies_list = [
+    #                         [[0, 1], [1,2]],
+    #                         [[0], [1], [2]],
+    #                         [[0,1], [1], [0], [1]]
+    #     ]
+
+    #     batch_dim, T = 13, 4 # batch dimension (e.g. number of agents, parallel realizations, etc.) and time steps
+    #     n_policies = 3
+
+    #     for (num_states, A_dependencies, num_controls, num_obs) in zip(num_states_list, A_dependencies_list, num_controls_list, num_obs_list):
+            
+    #         A_reduced_numpy = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_dependencies)
+    #         A_reduced = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_dim,) + x.shape), list(A_reduced_numpy))
+          
+    #         A_full_numpy = []
+    #         for m, no in enumerate(num_obs):
+    #             other_factors = list(set(range(len(num_states))) - set(A_dependencies[m])) # list of the factors that modality `m` does not depend on
+
+    #             # broadcast or tile the reduced A matrix (`A_reduced`) along the dimensions of corresponding to `other_factors`
+    #             expanded_dims = [no] + [1 if f in other_factors else ns for (f, ns) in enumerate(num_states)]
+    #             tile_dims = [1] + [ns if f in other_factors else 1 for (f, ns) in enumerate(num_states)]
+    #             A_full_numpy.append(np.tile(A_reduced_numpy[m].reshape(expanded_dims), tile_dims))
+            
+    #         A_full = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_dim,) + x.shape), list(A_full_numpy))
+
+    #         B_numpy = utils.random_B_matrix(num_states, num_controls)
+    #         B = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_dim,) + x.shape), list(B_numpy))
+
+    #         prior_numpy = utils.random_single_categorical(num_states)
+    #         prior = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_dim,) + x.shape), list(prior_numpy))
+          
+    #         # initialization observation sequences in jax
+    #         obs_seq = []
+    #         for n_obs in num_obs:
+    #             obs_ints = np.random.randint(0, high=n_obs, size=(T,1))
+    #             obs_array_mod_i = jnp.broadcast_to(nn.one_hot(obs_ints, num_classes=n_obs), (T, batch_dim, n_obs))
+    #             obs_seq.append(obs_array_mod_i)
+
+    #         # create random policies
+    #         policies = []
+    #         for n_controls in num_controls:
+    #             policies.append(jnp.array(np.random.randint(0, high=n_controls, size=(n_policies, T-1))))
+
+    #          ### First do VMP
+    #         def test_full(action_sequence):
+    #             B_policy = jtu.tree_map(lambda b, a_idx: b[..., a_idx].transpose(0, 3, 1, 2), B, action_sequence)
+    #             dependencies_fully_connected = [list(range(len(num_states))) for _ in range(len(num_obs))]
+    #             return vmp_jax(A_full, B_policy, obs_seq, prior, dependencies_fully_connected, num_iter=16, tau=1.)
+            
+    #         def test_sparse(action_sequence):
+    #             B_policy = jtu.tree_map(lambda b, a_idx: b[..., a_idx].transpose(0, 3, 1, 2), B, action_sequence)
+    #             return vmp_jax(A_reduced, B_policy, obs_seq, prior, A_dependencies, num_iter=16, tau=1)
+
+    #         qs_full = vmap(test_full)(policies)
+    #         qs_reduced = vmap(test_sparse)(policies)
+
+    #         for f in range(len(qs_full)):
+    #             self.assertTrue(jnp.allclose(qs_full[f], qs_reduced[f]))
+
+    # def test_B_dependencies_variational_message_passing(self):
+    #     """ Test variational message passing with B dependencies """
+
+    #     num_states_list = [ 
+    #                      [2, 2, 5],
+    #                      [2, 2, 2],
+    #                      [4, 4]
+    #     ]
+
+    #     num_controls_list = [
+    #                         [2, 1, 3],
+    #                         [2, 1, 2],
+    #                         [1, 3]
+    #     ]
+
+    #     num_obs_list = [
+    #                     [5, 10],
+    #                     [4, 3, 2],
+    #                     [5, 2, 6, 3]
+    #     ]
+
+    #     A_dependencies_list = [
+    #                         [[0, 1], [1,2]],
+    #                         [[0], [1], [2]],
+    #                         [[0,1], [1], [0], [1]]
+    #     ]
+
+    #     batch_dim, T = 13, 4 # batch dimension (e.g. number of agents, parallel realizations, etc.) and time steps
+    #     n_policies = 3
+
+    #     for (num_states, A_dependencies, num_controls, num_obs) in zip(num_states_list, A_dependencies_list, num_controls_list, num_obs_list):
+            
+    #         A_reduced_numpy = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_dependencies)
+    #         A_reduced = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_dim,) + x.shape), list(A_reduced_numpy))
+          
+    #         A_full_numpy = []
+    #         for m, no in enumerate(num_obs):
+    #             other_factors = list(set(range(len(num_states))) - set(A_dependencies[m])) # list of the factors that modality `m` does not depend on
+
+    #             # broadcast or tile the reduced A matrix (`A_reduced`) along the dimensions of corresponding to `other_factors`
+    #             expanded_dims = [no] + [1 if f in other_factors else ns for (f, ns) in enumerate(num_states)]
+    #             tile_dims = [1] + [ns if f in other_factors else 1 for (f, ns) in enumerate(num_states)]
+    #             A_full_numpy.append(np.tile(A_reduced_numpy[m].reshape(expanded_dims), tile_dims))
+            
+    #         A_full = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_dim,) + x.shape), list(A_full_numpy))
+
+    #         B_numpy = utils.random_B_matrix(num_states, num_controls)
+    #         B = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_dim,) + x.shape), list(B_numpy))
+
+    #         prior_numpy = utils.random_single_categorical(num_states)
+    #         prior = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_dim,) + x.shape), list(prior_numpy))
+          
+    #         # initialization observation sequences in jax
+    #         obs_seq = []
+    #         for n_obs in num_obs:
+    #             obs_ints = np.random.randint(0, high=n_obs, size=(T,1))
+    #             obs_array_mod_i = jnp.broadcast_to(nn.one_hot(obs_ints, num_classes=n_obs), (T, batch_dim, n_obs))
+    #             obs_seq.append(obs_array_mod_i)
+
+    #         # create random policies
+    #         policies = []
+    #         for n_controls in num_controls:
+    #             policies.append(jnp.array(np.random.randint(0, high=n_controls, size=(n_policies, T-1))))
+
+    #          ### First do VMP
+    #         def test_full(action_sequence):
+    #             B_policy = jtu.tree_map(lambda b, a_idx: b[..., a_idx].transpose(0, 3, 1, 2), B, action_sequence)
+    #             dependencies_fully_connected = [list(range(len(num_states))) for _ in range(len(num_obs))]
+    #             return vmp_jax(A_full, B_policy, obs_seq, prior, dependencies_fully_connected, num_iter=16, tau=1.)
+            
+    #         def test_sparse(action_sequence):
+    #             B_policy = jtu.tree_map(lambda b, a_idx: b[..., a_idx].transpose(0, 3, 1, 2), B, action_sequence)
+    #             return vmp_jax(A_reduced, B_policy, obs_seq, prior, A_dependencies, num_iter=16, tau=1)
+
+    #         qs_full = vmap(test_full)(policies)
+    #         qs_reduced = vmap(test_sparse)(policies)
+
+    #         for f in range(len(qs_full)):
+    #             self.assertTrue(jnp.allclose(qs_full[f], qs_reduced[f]))
+    
+    # def test_online_variational_filtering(self):
+    #     """ Unit test for @dimarkov's implementation of online variational filtering, also where it's conditional on actions (vmapped across policies) """
+
+    #     num_states_list = [ 
+    #                 [2, 2, 5],
+    #                 [2, 2, 2],
+    #                 [4, 4]
+    #     ]
+
+    #     num_controls_list = [
+    #                         [2, 1, 3],
+    #                         [2, 1, 2],
+    #                         [1, 3]
+    #     ]
+
+    #     num_obs_list = [
+    #                     [5, 10],
+    #                     [4, 3, 2],
+    #                     [5, 2, 6, 3]
+    #     ]
+
+    #     A_dependencies_list = [
+    #                         [[0, 1], [1, 2]],
+    #                         [[0], [1], [2]],
+    #                         [[0,1], [1], [0], [1]],
+    #     ]
+
+    #     batch_dim, T = 13, 4 # batch dimension (e.g. number of agents, parallel realizations, etc.) and time steps
+    #     n_policies = 3
+
+    #     for (num_states, A_dependencies, num_controls, num_obs) in zip(num_states_list, A_dependencies_list, num_controls_list, num_obs_list):
+            
+    #         A_reduced_numpy = utils.random_A_matrix(num_obs, num_states, A_factor_list=A_dependencies)
+    #         A_reduced = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_dim,) + x.shape), list(A_reduced_numpy))
+                
+    #         A_full_numpy = []
+    #         for m, no in enumerate(num_obs):
+    #             other_factors = list(set(range(len(num_states))) - set(A_dependencies[m])) # list of the factors that modality `m` does not depend on
+
+    #             # broadcast or tile the reduced A matrix (`A_reduced`) along the dimensions of corresponding to `other_factors`
+    #             expanded_dims = [no] + [1 if f in other_factors else ns for (f, ns) in enumerate(num_states)]
+    #             tile_dims = [1] + [ns if f in other_factors else 1 for (f, ns) in enumerate(num_states)]
+    #             A_full_numpy.append(np.tile(A_reduced_numpy[m].reshape(expanded_dims), tile_dims))
+            
+    #         A_full = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_dim,) + x.shape), list(A_full_numpy))
+
+    #         B_numpy = utils.random_B_matrix(num_states, num_controls)
+    #         B = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_dim,) + x.shape), list(B_numpy))
+
+    #         prior_numpy = utils.random_single_categorical(num_states)
+    #         prior = jtu.tree_map(lambda x: jnp.broadcast_to(x, (batch_dim,) + x.shape), list(prior_numpy))
+                
+    #         # initialization observation sequences in jax
+    #         obs_seq = []
+    #         for n_obs in num_obs:
+    #             obs_ints = np.random.randint(0, high=n_obs, size=(T,1))
+    #             obs_array_mod_i = jnp.broadcast_to(nn.one_hot(obs_ints, num_classes=n_obs), (T, batch_dim, n_obs))
+    #             obs_seq.append(obs_array_mod_i)
+
+    #         # create random policies
+    #         policies = []
+    #         for n_controls in num_controls:
+    #             policies.append(jnp.array(np.random.randint(0, high=n_controls, size=(n_policies, T-1))))
+
+    #         def test_sparse(action_sequence):
+    #             B_policy = jtu.tree_map(lambda b, a_idx: b[..., a_idx].transpose(3, 0, 1, 2), B, action_sequence)
+    #             qs, ps, qss = ovf_jax(obs_seq, A_reduced, B_policy, prior, A_dependencies)
+    #             return qs, ps, qss
+
+    #         qs_pi_sparse, ps_pi_sparse, qss_pi_sparse = vmap(test_sparse)(policies)
+
+    #         for f, (qs, ps, qss) in enumerate(zip(qs_pi_sparse, ps_pi_sparse, qss_pi_sparse)):
+    #             self.assertTrue(qs.shape == (n_policies, batch_dim, num_states[f]))
+    #             self.assertTrue(ps.shape == (n_policies, batch_dim, num_states[f]))
+    #             self.assertTrue(qss.shape == (n_policies, T, batch_dim, num_states[f], num_states[f]))
+
+    #             #Note: qs/ps are of dimension [n_policies x num_agents x dim_state_f] * num_factors
+    #             #Note: qss is of dimension [n_policies x time_steps x num_agents x dim_state_f x dim_state_f] * num_factors
+            
+    #         def test_full(action_sequence):
+    #             B_policy = jtu.tree_map(lambda b, a_idx: b[..., a_idx].transpose(3, 0, 1, 2), B, action_sequence)
+    #             dependencies_fully_connected = [list(range(len(num_states))) for _ in range(len(num_obs))]
+    #             qs, ps, qss = ovf_jax(obs_seq, A_full, B_policy, prior, dependencies_fully_connected)
+    #             return qs, ps, qss
+
+    #         qs_pi_full, ps_pi_full, qss_pi_full = vmap(test_full)(policies)
+
+    #         # test that the sparse and fully connected versions of OVF give the same results
+    #         for (qs_sparse, ps_sparse, qss_sparse, qs_full, ps_full, qss_full) in zip(qs_pi_sparse, ps_pi_sparse, qss_pi_sparse, qs_pi_full, ps_pi_full, qss_pi_full):
+    #             self.assertTrue(np.allclose(qs_sparse, qs_full))
+    #             self.assertTrue(np.allclose(ps_sparse, ps_full))
+    #             self.assertTrue(np.allclose(qss_sparse, qss_full))
+
+if __name__ == "__main__":
+    unittest.main()
+
+
+
+
+
+
+    
diff --git a/test/test_wrappers.py b/test/test_wrappers.py
index 254d902b..cf405e56 100644
--- a/test/test_wrappers.py
+++ b/test/test_wrappers.py
@@ -1,16 +1,7 @@
 import os
 import unittest
 from pathlib import Path
-
-import pandas as pd
-from pandas.testing import assert_frame_equal
-
-from pymdp.utils import Dimensions, get_model_dimensions_from_labels, create_A_matrix_stub, read_A_matrix, create_B_matrix_stubs, read_B_matrices
-
-tmp_path = Path('tmp_dir')
-
-if not os.path.isdir(tmp_path):
-    os.mkdir(tmp_path)
+from pymdp.utils import Dimensions, get_model_dimensions_from_labels
 
 class TestWrappers(unittest.TestCase):
 
@@ -62,88 +53,6 @@ def test_get_model_dimensions_from_labels(self):
         self.assertEqual(want.num_state_factors, got.num_state_factors)
         self.assertEqual(want.num_controls, got.num_controls)
         self.assertEqual(want.num_control_factors, got.num_control_factors)
-
-    def test_A_matrix_stub(self):
-        """
-        This tests the construction of a 2-modality, 2-hidden state factor pandas MultiIndex dataframe using 
-        the `model_labels` dictionary, which contains the modality- and factor-specific levels, labeled with string
-        identifiers.
-
-        Note: actions are ignored when creating an A matrix stub
-        """
-
-        model_labels = {
-            "observations": {
-                "grass_observation": [
-                    "wet",
-                    "dry"            
-                    ],
-                "weather_observation": [
-                    "clear",
-                    "rainy",
-                    "cloudy"
-                ]
-            },
-            "states": {
-                "weather_state": ["raining", "clear"],
-                "sprinkler_state": ["on", "off"],
-            },
-            "actions": {
-                "actions": ["something", "nothing"],
-            }
-        }
-
-        num_hidden_state_factors = len(model_labels["states"])
-        
-        expected_A_matrix_stub = create_A_matrix_stub(model_labels)
-    
-        temporary_file_path = (tmp_path / "A_matrix_stub.xlsx").resolve()
-        expected_A_matrix_stub.to_excel(temporary_file_path)
-        actual_A_matrix_stub = read_A_matrix(temporary_file_path, num_hidden_state_factors)
-
-        os.remove(temporary_file_path)
-
-        frames_are_equal = assert_frame_equal(expected_A_matrix_stub, actual_A_matrix_stub) is None
-        self.assertTrue(frames_are_equal)
-    
-    def test_B_matrix_stub(self):
-        """
-        This tests the construction of a 1-modality, 2-hidden state factor, 2 control factor pandas MultiIndex dataframe using 
-        the `model_labels` dictionary, which contains the hidden-state-factor- and control-factor-specific levels, labeled with string
-        identifiers
-        """
-
-        model_labels = {
-            "observations": {
-                "reward outcome": [
-                    "win",
-                    "loss"            
-                    ]
-            },
-            "states": {
-                "location": ["start", "arm1", "arm2"],
-                "bandit_state": ["high_rew", "low_rew"]
-            },
-            "actions": {
-                "arm_play": ["play_arm1", "play_arm2"],
-                "bandit_state_control": ["null"]
-            }
-        }
-        
-        B_stubs = create_B_matrix_stubs(model_labels)
-    
-        xls_path = (tmp_path / "B_matrix_stubs.xlsx").resolve()
-
-        with pd.ExcelWriter(xls_path) as writer:
-            for factor_name, B_stub_f in B_stubs.items():
-                B_stub_f.to_excel(writer,'%s' % factor_name)
-
-        read_in_B_stubs = read_B_matrices(xls_path)
-
-        os.remove(xls_path)
-
-        all_stub_compares = [assert_frame_equal(stub_og, stub_read_in) for stub_og, stub_read_in in zip(*[B_stubs.values(), read_in_B_stubs.values()])]
-        self.assertTrue(all(stub_compare is None for stub_compare in all_stub_compares))
        
 if __name__ == "__main__":
     unittest.main()