LSTMLayer_v2.py

import numpy as np
import theano
import theano.tensor as T
import lasagne
from lasagne import nonlinearities
from lasagne import init
from lasagne.utils import unroll_scan

from lasagne.layers.base import MergeLayer, Layer
from lasagne.layers.input import InputLayer
from lasagne.layers.dense import DenseLayer
from lasagne.layers.recurrent import *
from lasagne.layers import helper

__all__ = [
    "LSTMLayer_v2"
]


class LSTMLayer_v2(MergeLayer):
    r"""
    LSTMLayer_v2(incoming, num_units,
    ingate=lasagne.layers.Gate(), forgetgate=lasagne.layers.Gate(),
    cell=lasagne.layers.Gate(
    W_cell=None, nonlinearity=lasagne.nonlinearities.tanh),
    outgate=lasagne.layers.Gate(),
    nonlinearity=lasagne.nonlinearities.tanh,
    cell_init=lasagne.init.Constant(0.),
    hid_init=lasagne.init.Constant(0.), backwards=False, learn_init=False,
    peepholes=True, gradient_steps=-1, grad_clipping=0, unroll_scan=False,
    precompute_input=True, mask_input=None, only_return_final=False, **kwargs)
    A long short-term memory (LSTM) layer.
    Includes optional "peephole connections" and a forget gate.  Based on the
    definition in [1]_, which is the current common definition.  The output is
    computed by
    .. math ::
        i_t &= \sigma_i(x_t W_{xi} + h_{t-1} W_{hi}
               + w_{ci} \odot c_{t-1} + b_i)\\
        f_t &= \sigma_f(x_t W_{xf} + h_{t-1} W_{hf}
               + w_{cf} \odot c_{t-1} + b_f)\\
        c_t &= f_t \odot c_{t - 1}
               + i_t \odot \sigma_c(x_t W_{xc} + h_{t-1} W_{hc} + b_c)\\
        o_t &= \sigma_o(x_t W_{xo} + h_{t-1} W_{ho} + w_{co} \odot c_t + b_o)\\
        h_t &= o_t \odot \sigma_h(c_t)
    Parameters
    ----------
    incoming : a :class:`lasagne.layers.Layer` instance or a tuple
        The layer feeding into this layer, or the expected input shape.
    num_units : int
        Number of hidden/cell units in the layer.
    ingate : Gate
        Parameters for the input gate (:math:`i_t`): :math:`W_{xi}`,
        :math:`W_{hi}`, :math:`w_{ci}`, :math:`b_i`, and :math:`\sigma_i`.
    forgetgate : Gate
        Parameters for the forget gate (:math:`f_t`): :math:`W_{xf}`,
        :math:`W_{hf}`, :math:`w_{cf}`, :math:`b_f`, and :math:`\sigma_f`.
    cell : Gate
        Parameters for the cell computation (:math:`c_t`): :math:`W_{xc}`,
        :math:`W_{hc}`, :math:`b_c`, and :math:`\sigma_c`.
    outgate : Gate
        Parameters for the output gate (:math:`o_t`): :math:`W_{xo}`,
        :math:`W_{ho}`, :math:`w_{co}`, :math:`b_o`, and :math:`\sigma_o`.
    nonlinearity : callable or None
        The nonlinearity that is applied to the output (:math:`\sigma_h`). If
        None is provided, no nonlinearity will be applied.
    cell_init : callable, np.ndarray, theano.shared or :class:`Layer`
        Initializer for initial cell state (:math:`c_0`).
    hid_init : callable, np.ndarray, theano.shared or :class:`Layer`
        Initializer for initial hidden state (:math:`h_0`).
    backwards : bool
        If True, process the sequence backwards and then reverse the
        output again such that the output from the layer is always
        from :math:`x_1` to :math:`x_n`.
    learn_init : bool
        If True, initial hidden values are learned.
    peepholes : bool
        If True, the LSTM uses peephole connections.
        When False, `ingate.W_cell`, `forgetgate.W_cell` and
        `outgate.W_cell` are ignored.
    gradient_steps : int
        Number of timesteps to include in the backpropagated gradient.
        If -1, backpropagate through the entire sequence.
    grad_clipping : float
        If nonzero, the gradient messages are clipped to the given value during
        the backward pass.  See [1]_ (p. 6) for further explanation.
    unroll_scan : bool
        If True the recursion is unrolled instead of using scan. For some
        graphs this gives a significant speed up but it might also consume
        more memory. When `unroll_scan` is True, backpropagation always
        includes the full sequence, so `gradient_steps` must be set to -1 and
        the input sequence length must be known at compile time (i.e., cannot
        be given as None).
    precompute_input : bool
        If True, precompute input_to_hid before iterating through
        the sequence. This can result in a speedup at the expense of
        an increase in memory usage.
    mask_input : :class:`lasagne.layers.Layer`
        Layer which allows for a sequence mask to be input, for when sequences
        are of variable length.  Default `None`, which means no mask will be
        supplied (i.e. all sequences are of the same length).
    only_return_final : bool
        If True, only return the final sequential output (e.g. for tasks where
        a single target value for the entire sequence is desired).  In this
        case, Theano makes an optimization which saves memory.
    References
    ----------
    .. [1] Graves, Alex: "Generating sequences with recurrent neural networks."
           arXiv preprint arXiv:1308.0850 (2013).
    """
    def __init__(self, incoming, num_units,
                 ingate=Gate(),
                 forgetgate=Gate(),
                 cell=Gate(W_cell=None, nonlinearity=nonlinearities.tanh),
                 outgate=Gate(),
                 nonlinearity=nonlinearities.tanh,
                 cell_init=init.Constant(0.),
                 hid_init=init.Constant(0.),
                 backwards=False,
                 learn_init=False,
                 peepholes=True,
                 gradient_steps=-1,
                 grad_clipping=0,
                 unroll_scan=False,
                 precompute_input=True,
                 mask_input=None,
                 only_return_final=False,
                 **kwargs):

        # This layer inherits from a MergeLayer, because it can have four
        # inputs - the layer input, the mask, the initial hidden state and the
        # inital cell state. We will just provide the layer input as incomings,
        # unless a mask input, inital hidden state or initial cell state was
        # provided.
        incomings = [incoming]
        self.mask_incoming_index = -1
        self.hid_init_incoming_index = -1
        self.cell_init_incoming_index = -1
        if mask_input is not None:
            incomings.append(mask_input)
            self.mask_incoming_index = len(incomings)-1
        if isinstance(hid_init, Layer):
            incomings.append(hid_init)
            self.hid_init_incoming_index = len(incomings)-1
        if isinstance(cell_init, Layer):
            incomings.append(cell_init)
            self.cell_init_incoming_index = len(incomings)-1

        # Initialize parent layer
        super(LSTMLayer_v2, self).__init__(incomings, **kwargs)

        # If the provided nonlinearity is None, make it linear
        if nonlinearity is None:
            self.nonlinearity = nonlinearities.identity
        else:
            self.nonlinearity = nonlinearity

        self.learn_init = learn_init
        self.num_units = num_units
        self.backwards = backwards
        self.peepholes = peepholes
        self.gradient_steps = gradient_steps
        self.grad_clipping = grad_clipping
        self.unroll_scan = unroll_scan
        self.precompute_input = precompute_input
        self.only_return_final = only_return_final

        if unroll_scan and gradient_steps != -1:
            raise ValueError(
                "Gradient steps must be -1 when unroll_scan is true.")

        # Retrieve the dimensionality of the incoming layer
        input_shape = self.input_shapes[0]

        if unroll_scan and input_shape[1] is None:
            raise ValueError("Input sequence length cannot be specified as "
                             "None when unroll_scan is True")

        num_inputs = np.prod(input_shape[2:])

        def add_gate_params(gate, gate_name):
            """ Convenience function for adding layer parameters from a Gate
            instance. """
            return (self.add_param(gate.W_in, (num_inputs, num_units),
                                   name="W_in_to_{}".format(gate_name)),
                    self.add_param(gate.W_hid, (num_units, num_units),
                                   name="W_hid_to_{}".format(gate_name)),
                    self.add_param(gate.b, (num_units,),
                                   name="b_{}".format(gate_name),
                                   regularizable=False),
                    gate.nonlinearity)

        # Add in parameters from the supplied Gate instances
        (self.W_in_to_ingate, self.W_hid_to_ingate, self.b_ingate,
         self.nonlinearity_ingate) = add_gate_params(ingate, 'ingate')

        (self.W_in_to_forgetgate, self.W_hid_to_forgetgate, self.b_forgetgate,
         self.nonlinearity_forgetgate) = add_gate_params(forgetgate,
                                                         'forgetgate')

        (self.W_in_to_cell, self.W_hid_to_cell, self.b_cell,
         self.nonlinearity_cell) = add_gate_params(cell, 'cell')

        (self.W_in_to_outgate, self.W_hid_to_outgate, self.b_outgate,
         self.nonlinearity_outgate) = add_gate_params(outgate, 'outgate')

        # If peephole (cell to gate) connections were enabled, initialize
        # peephole connections.  These are elementwise products with the cell
        # state, so they are represented as vectors.
        if self.peepholes:
            self.W_cell_to_ingate = self.add_param(
                ingate.W_cell, (num_units, ), name="W_cell_to_ingate")

            self.W_cell_to_forgetgate = self.add_param(
                forgetgate.W_cell, (num_units, ), name="W_cell_to_forgetgate")

            self.W_cell_to_outgate = self.add_param(
                outgate.W_cell, (num_units, ), name="W_cell_to_outgate")

        # Setup initial values for the cell and the hidden units
        if isinstance(cell_init, Layer):
            self.cell_init = cell_init
        else:
            self.cell_init = self.add_param(
                cell_init, (1, num_units), name="cell_init",
                trainable=learn_init, regularizable=False)

        if isinstance(hid_init, Layer):
            self.hid_init = hid_init
        else:
            self.hid_init = self.add_param(
                hid_init, (1, self.num_units), name="hid_init",
                trainable=learn_init, regularizable=False)

    def get_output_shape_for(self, input_shapes):
        # The shape of the input to this layer will be the first element
        # of input_shapes, whether or not a mask input is being used.
        input_shape = input_shapes[0]
        # When only_return_final is true, the second (sequence step) dimension
        # will be flattened
        if self.only_return_final:
            return input_shape[0], self.num_units
        # Otherwise, the shape will be (n_batch, n_steps, num_units)
        else:
            return input_shape[0], input_shape[1], self.num_units

    def get_output_for(self, inputs, **kwargs):
        """
        Compute this layer's output function given a symbolic input variable
        Parameters
        ----------
        inputs : list of theano.TensorType
            `inputs[0]` should always be the symbolic input variable.  When
            this layer has a mask input (i.e. was instantiated with
            `mask_input != None`, indicating that the lengths of sequences in
            each batch vary), `inputs` should have length 2, where `inputs[1]`
            is the `mask`.  The `mask` should be supplied as a Theano variable
            denoting whether each time step in each sequence in the batch is
            part of the sequence or not.  `mask` should be a matrix of shape
            ``(n_batch, n_time_steps)`` where ``mask[i, j] = 1`` when ``j <=
            (length of sequence i)`` and ``mask[i, j] = 0`` when ``j > (length
            of sequence i)``. When the hidden state of this layer is to be
            pre-filled (i.e. was set to a :class:`Layer` instance) `inputs`
            should have length at least 2, and `inputs[-1]` is the hidden state
            to prefill with. When the cell state of this layer is to be
            pre-filled (i.e. was set to a :class:`Layer` instance) `inputs`
            should have length at least 2, and `inputs[-1]` is the hidden state
            to prefill with. When both the cell state and the hidden state are
            being pre-filled `inputs[-2]` is the hidden state, while
            `inputs[-1]` is the cell state.
        Returns
        -------
        layer_output : theano.TensorType
            Symbolic output variable.
        """
        # Retrieve the layer input
        input = inputs[0]
        # Retrieve the mask when it is supplied
        mask = None
        hid_init = None
        cell_init = None
        if self.mask_incoming_index > 0:
            mask = inputs[self.mask_incoming_index]
        if self.hid_init_incoming_index > 0:
            hid_init = inputs[self.hid_init_incoming_index]
        if self.cell_init_incoming_index > 0:
            cell_init = inputs[self.cell_init_incoming_index]

        # Treat all dimensions after the second as flattened feature dimensions
        if input.ndim > 3:
            input = T.flatten(input, 3)

        # Because scan iterates over the first dimension we dimshuffle to
        # (n_time_steps, n_batch, n_features)
        input = input.dimshuffle(1, 0, 2)
        seq_len, num_batch, _ = input.shape

        # Stack input weight matrices into a (num_inputs, 4*num_units)
        # matrix, which speeds up computation
        W_in_stacked = T.concatenate(
            [self.W_in_to_ingate, self.W_in_to_forgetgate,
             self.W_in_to_cell, self.W_in_to_outgate], axis=1)

        # Same for hidden weight matrices
        W_hid_stacked = T.concatenate(
            [self.W_hid_to_ingate, self.W_hid_to_forgetgate,
             self.W_hid_to_cell, self.W_hid_to_outgate], axis=1)

        # Stack biases into a (4*num_units) vector
        b_stacked = T.concatenate(
            [self.b_ingate, self.b_forgetgate,
             self.b_cell, self.b_outgate], axis=0)

        if self.precompute_input:
            # Because the input is given for all time steps, we can
            # precompute_input the inputs dot weight matrices before scanning.
            # W_in_stacked is (n_features, 4*num_units). input is then
            # (n_time_steps, n_batch, 4*num_units).
            input = T.dot(input, W_in_stacked) + b_stacked

        # At each call to scan, input_n will be (n_time_steps, 4*num_units).
        # We define a slicing function that extract the input to each LSTM gate
        def slice_w(x, n):
            return x[:, n*self.num_units:(n+1)*self.num_units]

        # Create single recurrent computation step function
        # input_n is the n'th vector of the input
        def step(input_n, cell_previous, hid_previous, *args):
            if not self.precompute_input:
                input_n = T.dot(input_n, W_in_stacked) + b_stacked

            # Calculate gates pre-activations and slice
            gates = input_n + T.dot(hid_previous, W_hid_stacked)

            # Clip gradients
            if self.grad_clipping:
                gates = theano.gradient.grad_clip(
                    gates, -self.grad_clipping, self.grad_clipping)

            # Extract the pre-activation gate values
            ingate = slice_w(gates, 0)
            forgetgate = slice_w(gates, 1)
            cell_input = slice_w(gates, 2)
            outgate = slice_w(gates, 3)

            if self.peepholes:
                # Compute peephole connections
                ingate += cell_previous*self.W_cell_to_ingate
                forgetgate += cell_previous*self.W_cell_to_forgetgate

            # Apply nonlinearities
            ingate = self.nonlinearity_ingate(ingate)
            forgetgate = self.nonlinearity_forgetgate(forgetgate)
            cell_input = self.nonlinearity_cell(cell_input)

            # Compute new cell value
            cell = forgetgate*cell_previous + ingate*cell_input

            if self.peepholes:
                outgate += cell*self.W_cell_to_outgate
            outgate = self.nonlinearity_outgate(outgate)

            # Compute new hidden unit activation
            hid = outgate*self.nonlinearity(cell)
            return [cell, hid]

        def step_masked(input_n, mask_n, cell_previous, hid_previous, *args):
            cell, hid = step(input_n, cell_previous, hid_previous, *args)

            # Skip over any input with mask 0 by copying the previous
            # hidden state; proceed normally for any input with mask 1.
            cell = T.switch(mask_n, cell, cell_previous)
            hid = T.switch(mask_n, hid, hid_previous)

            return [cell, hid]

        if mask is not None:
            # mask is given as (batch_size, seq_len). Because scan iterates
            # over first dimension, we dimshuffle to (seq_len, batch_size) and
            # add a broadcastable dimension
            mask = mask.dimshuffle(1, 0, 'x')
            sequences = [input, mask]
            step_fun = step_masked
        else:
            sequences = input
            step_fun = step

        ones = T.ones((num_batch, 1))
        if not isinstance(self.cell_init, Layer):
            # Dot against a 1s vector to repeat to shape (num_batch, num_units)
            cell_init = T.dot(ones, self.cell_init)

        if not isinstance(self.hid_init, Layer):
            # Dot against a 1s vector to repeat to shape (num_batch, num_units)
            hid_init = T.dot(ones, self.hid_init)

        # The hidden-to-hidden weight matrix is always used in step
        non_seqs = [W_hid_stacked]
        # The "peephole" weight matrices are only used when self.peepholes=True
        if self.peepholes:
            non_seqs += [self.W_cell_to_ingate,
                         self.W_cell_to_forgetgate,
                         self.W_cell_to_outgate]

        # When we aren't precomputing the input outside of scan, we need to
        # provide the input weights and biases to the step function
        if not self.precompute_input:
            non_seqs += [W_in_stacked, b_stacked]

        if self.unroll_scan:
            # Retrieve the dimensionality of the incoming layer
            input_shape = self.input_shapes[0]
            # Explicitly unroll the recurrence instead of using scan
            cell_out, hid_out = unroll_scan(
                fn=step_fun,
                sequences=sequences,
                outputs_info=[cell_init, hid_init],
                go_backwards=self.backwards,
                non_sequences=non_seqs,
                n_steps=input_shape[1])
        else:
            # Scan op iterates over first dimension of input and repeatedly
            # applies the step function
            cell_out, hid_out = theano.scan(
                fn=step_fun,
                sequences=sequences,
                outputs_info=[cell_init, hid_init],
                go_backwards=self.backwards,
                truncate_gradient=self.gradient_steps,
                non_sequences=non_seqs,
                strict=True)[0]

        # When it is requested that we only return the final sequence step,
        # we need to slice it out immediately after scan is applied
        if self.only_return_final:
            hid_out = hid_out[-1]
        else:
            # dimshuffle back to (n_batch, n_time_steps, n_features))
            hid_out = hid_out.dimshuffle(1, 0, 2)

            # if scan is backward reverse the output
            if self.backwards:
                hid_out = hid_out[:, ::-1]

        return hid_out
        
    def get_hid_cell_for(self, inputs, **kwargs):
        """
        Compute this layer's hidden and cell states given a symbolic input variable
        Parameters
        ----------
        inputs : list of theano.TensorType
            `inputs[0]` should always be the symbolic input variable.  When
            this layer has a mask input (i.e. was instantiated with
            `mask_input != None`, indicating that the lengths of sequences in
            each batch vary), `inputs` should have length 2, where `inputs[1]`
            is the `mask`.  The `mask` should be supplied as a Theano variable
            denoting whether each time step in each sequence in the batch is
            part of the sequence or not.  `mask` should be a matrix of shape
            ``(n_batch, n_time_steps)`` where ``mask[i, j] = 1`` when ``j <=
            (length of sequence i)`` and ``mask[i, j] = 0`` when ``j > (length
            of sequence i)``. When the hidden state of this layer is to be
            pre-filled (i.e. was set to a :class:`Layer` instance) `inputs`
            should have length at least 2, and `inputs[-1]` is the hidden state
            to prefill with. When the cell state of this layer is to be
            pre-filled (i.e. was set to a :class:`Layer` instance) `inputs`
            should have length at least 2, and `inputs[-1]` is the hidden state
            to prefill with. When both the cell state and the hidden state are
            being pre-filled `inputs[-2]` is the hidden state, while
            `inputs[-1]` is the cell state.
        Returns
        -------
        layer_output : theano.TensorType
            Symbolic output variable.
        """
        # Retrieve the layer input
        input = inputs[0]
        # Retrieve the mask when it is supplied
        mask = None
        hid_init = None
        cell_init = None
        if self.mask_incoming_index > 0:
            mask = inputs[self.mask_incoming_index]
        if self.hid_init_incoming_index > 0:
            hid_init = inputs[self.hid_init_incoming_index]
        if self.cell_init_incoming_index > 0:
            cell_init = inputs[self.cell_init_incoming_index]

        # Treat all dimensions after the second as flattened feature dimensions
        if input.ndim > 3:
            input = T.flatten(input, 3)

        # Because scan iterates over the first dimension we dimshuffle to
        # (n_time_steps, n_batch, n_features)
        input = input.dimshuffle(1, 0, 2)
        seq_len, num_batch, _ = input.shape

        # Stack input weight matrices into a (num_inputs, 4*num_units)
        # matrix, which speeds up computation
        W_in_stacked = T.concatenate(
            [self.W_in_to_ingate, self.W_in_to_forgetgate,
             self.W_in_to_cell, self.W_in_to_outgate], axis=1)

        # Same for hidden weight matrices
        W_hid_stacked = T.concatenate(
            [self.W_hid_to_ingate, self.W_hid_to_forgetgate,
             self.W_hid_to_cell, self.W_hid_to_outgate], axis=1)

        # Stack biases into a (4*num_units) vector
        b_stacked = T.concatenate(
            [self.b_ingate, self.b_forgetgate,
             self.b_cell, self.b_outgate], axis=0)

        if self.precompute_input:
            # Because the input is given for all time steps, we can
            # precompute_input the inputs dot weight matrices before scanning.
            # W_in_stacked is (n_features, 4*num_units). input is then
            # (n_time_steps, n_batch, 4*num_units).
            input = T.dot(input, W_in_stacked) + b_stacked

        # At each call to scan, input_n will be (n_time_steps, 4*num_units).
        # We define a slicing function that extract the input to each LSTM gate
        def slice_w(x, n):
            return x[:, n*self.num_units:(n+1)*self.num_units]

        # Create single recurrent computation step function
        # input_n is the n'th vector of the input
        def step(input_n, cell_previous, hid_previous, *args):
            if not self.precompute_input:
                input_n = T.dot(input_n, W_in_stacked) + b_stacked

            # Calculate gates pre-activations and slice
            gates = input_n + T.dot(hid_previous, W_hid_stacked)

            # Clip gradients
            if self.grad_clipping:
                gates = theano.gradient.grad_clip(
                    gates, -self.grad_clipping, self.grad_clipping)

            # Extract the pre-activation gate values
            ingate = slice_w(gates, 0)
            forgetgate = slice_w(gates, 1)
            cell_input = slice_w(gates, 2)
            outgate = slice_w(gates, 3)

            if self.peepholes:
                # Compute peephole connections
                ingate += cell_previous*self.W_cell_to_ingate
                forgetgate += cell_previous*self.W_cell_to_forgetgate

            # Apply nonlinearities
            ingate = self.nonlinearity_ingate(ingate)
            forgetgate = self.nonlinearity_forgetgate(forgetgate)
            cell_input = self.nonlinearity_cell(cell_input)

            # Compute new cell value
            cell = forgetgate*cell_previous + ingate*cell_input

            if self.peepholes:
                outgate += cell*self.W_cell_to_outgate
            outgate = self.nonlinearity_outgate(outgate)

            # Compute new hidden unit activation
            hid = outgate*self.nonlinearity(cell)
            return [cell, hid]

        def step_masked(input_n, mask_n, cell_previous, hid_previous, *args):
            cell, hid = step(input_n, cell_previous, hid_previous, *args)

            # Skip over any input with mask 0 by copying the previous
            # hidden state; proceed normally for any input with mask 1.
            cell = T.switch(mask_n, cell, cell_previous)
            hid = T.switch(mask_n, hid, hid_previous)

            return [cell, hid]

        if mask is not None:
            # mask is given as (batch_size, seq_len). Because scan iterates
            # over first dimension, we dimshuffle to (seq_len, batch_size) and
            # add a broadcastable dimension
            mask = mask.dimshuffle(1, 0, 'x')
            sequences = [input, mask]
            step_fun = step_masked
        else:
            sequences = input
            step_fun = step

        ones = T.ones((num_batch, 1))
        if not isinstance(self.cell_init, Layer):
            # Dot against a 1s vector to repeat to shape (num_batch, num_units)
            cell_init = T.dot(ones, self.cell_init)

        if not isinstance(self.hid_init, Layer):
            # Dot against a 1s vector to repeat to shape (num_batch, num_units)
            hid_init = T.dot(ones, self.hid_init)

        # The hidden-to-hidden weight matrix is always used in step
        non_seqs = [W_hid_stacked]
        # The "peephole" weight matrices are only used when self.peepholes=True
        if self.peepholes:
            non_seqs += [self.W_cell_to_ingate,
                         self.W_cell_to_forgetgate,
                         self.W_cell_to_outgate]

        # When we aren't precomputing the input outside of scan, we need to
        # provide the input weights and biases to the step function
        if not self.precompute_input:
            non_seqs += [W_in_stacked, b_stacked]

        if self.unroll_scan:
            # Retrieve the dimensionality of the incoming layer
            input_shape = self.input_shapes[0]
            # Explicitly unroll the recurrence instead of using scan
            cell_out, hid_out = unroll_scan(
                fn=step_fun,
                sequences=sequences,
                outputs_info=[cell_init, hid_init],
                go_backwards=self.backwards,
                non_sequences=non_seqs,
                n_steps=input_shape[1])
        else:
            # Scan op iterates over first dimension of input and repeatedly
            # applies the step function
            cell_out, hid_out = theano.scan(
                fn=step_fun,
                sequences=sequences,
                outputs_info=[cell_init, hid_init],
                go_backwards=self.backwards,
                truncate_gradient=self.gradient_steps,
                non_sequences=non_seqs,
                strict=True)[0]

        # When it is requested that we only return the final sequence step,
        # we need to slice it out immediately after scan is applied
        if self.only_return_final:
            hid_out = hid_out[-1]
        else:
            # dimshuffle back to (n_batch, n_time_steps, n_features))
            hid_out = hid_out.dimshuffle(1, 0, 2)
            cell_out = cell_out.dimshuffle(1, 0, 2)

            # if scan is backward reverse the output
            if self.backwards:
                hid_out = hid_out[:, ::-1]
                cell_out = cell_out[:, ::-1]

        return hid_out, cell_out