README.md

Installation • Releases • Contributing • Features

MatterIx is a simple deep learning framework built to understand the fundamental concepts of autodiff, optimizers and loss functions from a first principle basis. It provide features such as automatic differentiation (autodiff), optimizers, loss functions and basic modules to create your own neural networks.

Feature	Description	Function/Specs
Autodiff	Allows to compute gradients for tensors.	First-order derivative
Loss functions	Provides a metric to evaluate the model or function	Mean squared error (MSE), Root mean squared error (RMSE)
Optimizers	Updates the parameters of a model for a specific optimization problem	Stochastic gradient descent (SGD)
Activation functions	It basically decides whether a neuron should be activated or not. Activation function is a non-linear transformation which applied to the output before passing it to the next layer	Sigmoid, tanh, ReLU
Module	Serves as a base class to design your own neural networks	NIL

The core value of matterix is that it is a distilled version of pytorch so it is easier to understand what is happening under the hood.

Installation

a. Install it from github

# Install either with option-1 or option-2

# Option-1 (Preferred)
pip install git+https://github.com/SiddeshSambasivam/MatterIx.git#egg=MatterIx

# Option-2
git clone https://github.com/SiddeshSambasivam/MatterIx.git

python setup.py install

(or)

b. Install from PyPI

# Install directly from PyPI repository
pip install --upgrade matterix

Features

1. Autodiff

Gradients are computed using reverse-mode autodiff. All computations are representated as a graph of tensors with each tensor holding a reference to a function which can compute the local gradient of that tensor. The calculation of the partial derivative for each tensor is completed when the entire graph is traversed.

The fundamental idea behind autodiff is that it calculates the local derivative for each variable rather than its partial derivative. This way traversing through the computational graph is simple and modular, i.e we could calculate the partial derivative of any variable with respect to the output with just one traversal, with a complexity of O(n).

The difference between partial and local derivative is the way each variable is treated in each equation. When calculating the partial derivative of a function, the expression is broken down into variables, for example c= a* b and d=a+b+c, instead of using c, we say a*b in the d= a+b+(a*b). On the other hand, when calculating the local derivative of a function, each element in the expression is considered a variable. I understand this might not be clear, so refer to the following explanation.

2. Loss functions

2.1 Mean squared error. Example

from matterix.functions import MSE

y_train = ... # Actual/true value
y_pred = ... # model prediction

loss = MSE(y_train, y_pred)

2.2 Root Mean squared error

from matterix.functions import RMSE

y_train = ... # Actual/true value
y_pred = ... # model prediction

loss = RMSE(y_train, y_pred)

3. Optimizers

3.1 Stochastic gradient descent

from matterix.optimizer import SGD

optimizer = SGD(model, model.parameters(), lr=0.001) # model, parameters to optimize, learning rate

# To set the gradient of the parameters to zero
optimizer.zero_grad()

# To update the parameters
optimizer.step()

4. Activation functions

Functions: sigmoid, tanh, relu.

All the activation functions are available from matterix.functions. Example,

from matterix.functions import sigmoid

5. Module

Module provides the necessary functions to design your own neural network. It has methods to set all the gradients of the parameters to zero, get all the parameters of the network.

1. Create a class which inherits from nn.Module to define for network
2. Initiate your parameters
3. Write a forward function

See the example below.

from matterix import Tensor
import matterix.nn as nn

# To define a neural network, just inherit `Module` from `nn`
class SampleModel(nn.Module):

    def __init__(self) -> None:
        # Initilalize your parameters
        self.w1 = Tensor.randn(5, requires_grad=True)
        self.w2 = Tensor.randn(14, requires_grad=True)
        ...

    def forward(self, x) -> Tensor:

        out_1 = x @ self.w1
        ...

        return output

model = SampleModel()

model.zero_grad() # Sets the gradient of all the parameters to zero
model.parameters() # Gets all the parameters

Example

The following is a simple example

# MNIST classifier

import numpy as np
from matterix import Tensor, datasets
import matterix.nn as nn
import matterix.functions as F
from matterix.optim import SGD

from tqdm import trange

# Get the MNIST dataset
x_train, y_train, x_test, y_test = datasets.getMNIST()


class MnistModel(nn.Module):
    def __init__(self) -> None:

        self.l1 = nn.Linear(28 * 28, 128, bias=False)
        self.l2 = nn.Linear(128, 10, bias=False)

    def forward(self, x) -> Tensor:

        o1 = self.l1(x)
        o2 = self.l2(o1)
        out = F.softmax(o2)

        return out


model = MnistModel()
EPOCHS = 1000
batch_size = 1000
lr = 0.01

optimizer = SGD(parameters=model.parameters(), lr=lr, momentum=0.9)

t_bar = trange(EPOCHS)

losses = []

for epoch in t_bar:

    optimizer.zero_grad()

    # Batching
    ids = np.random.choice(60000, batch_size)
    x = Tensor(x_train[ids])
    y = Tensor(y_train[ids])

    y_pred = model(x)
    diff = y - y_pred
    loss = (diff ** 2).sum() * (1.0 / diff.shape[0])

    loss.backward()

    optimizer.step()
    losses.append(loss.data)

    t_bar.set_description("Epoch: %.0f Loss: %.8f" % (epoch, loss.data))

y_pred = model(Tensor(x_test))

acc = np.array(np.argmax(y_pred.data, axis=1) == np.argmax(y_test, axis=1)).sum()
print("Accuracy: ", acc / len(x_test))

Development setup

Install the necessary dependecies in a seperate virtual environment

# Create a virtual environment during development to avoid dependency issues
pip install -r requirements.txt

# Before submitting a PR, run the unittests locally
pytest -v

Release history

• 1.1.1

  • ADD: Linear layer: Provides an abstraction to a linear model
  • ADD: Log, exp and softmax functions
  • ADD: Momentum to SGD
  • ADD: Uniform weight initialization to linear layer
  • FIX: Softmax underflow issue, Tanh bug,

• 1.0.1

  • Used 1.0.0 for testing
  • ADD: Tanh function, RMSE loss, randn and randint

• 0.1.1

  • ADD: Optimizer: SGD
  • ADD: Functions: Relu
  • ADD: Loss functions: RMSE, MSETensor
  • ADD: Module: For defining neural networks
  • FIX: Floating point precision issue when calculating gradient

• 0.1.0

  • First stable release
  • ADD: Tensor, tensor operations, sigmoid functions
  • FIX: Inaccuracies with gradient computation

Contributing

1. Fork it

2. Create your feature branch

   git checkout -b feature/new_feature

3. Commit your changes

   git commit -m 'add new feature'
   

4. Push to the branch

   git push origin feature/new_feature
   

5. Create a new pull request (PR)

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Siddesh Sambasivam Suseela - @ssiddesh45 - [email protected]

Distributed under the MIT license. See LICENSE for more information.