deepsplines 1.0.0

A framework to train the activation functions of a neural network

DeepSplines is a framework to train the activation functions of a neural network.

The aim of this repository is to:

• Facilitate the reproduction of the results reported in the research papers:

  • Learning Activation Functions in Deep (Spline) Neural Networks;

  • Deep Neural Networks with Trainable Activations and Controlled Lipschitz Constant.

• Enable a seamless integration of deep spline activation functions in a custom neural network.

The proposed scheme is based on the theoretical work of M.Unser.

Table of Contents

• Requirements

• Installation

  • Quick Install

  • Developper Install

• Usage

  • Reproducing results

• Developers

• References

• License

• Acknowledgements

Requirements

• python >= 3.7

• numpy >= 1.10

• pytorch >= 1.5.1

• torchvision >= 0.2.2

• matplotlib >= 3.3.1

• (optional) CUDA

The code was developed and tested on a x86_64 Linux system.

Installation

To install the package, we first create an environment with python 3.7 (or greater):

>> conda create -y -n deepsplines python=3.7
>> source activate deepsplines

Quick Install

DeepSplines is available on Pypi. Therefore, you can install the package via the command:

>> pip install deepsplines

For NVIDIA GPU compatibility, you need to additionally install cudatoolkit (via conda install -c anaconda cudatoolkit)

Developper Install

It is also possible to install DeepSplines from the source for developpers:

>> git clone https://github.com/joaquimcampos/DeepSplines
>> cd <repository_dir>/
>> pip install -e .

Usage

Here we show an example on how to adapt the PyTorch CIFAR-10 tutorial to use DeepBSpline activations.

from deepsplines.ds_modules import dsnn


class DSNet(dsnn.DSModule):
    def __init__(self):

        super().__init__()

        self.conv_ds = nn.ModuleList()
        self.fc_ds = nn.ModuleList()

        # deepspline parameters
        opt_params = {
            'size': 51,
            'range_': 4,
            'init': 'leaky_relu',
            'save_memory': False
        }

        # convolutional layer with 6 output channels
        self.conv1 = nn.Conv2d(3, 6, 5)
        self.conv_ds.append(dsnn.DeepBSpline('conv', 6, **opt_params))
        self.pool = nn.MaxPool2d(2, 2)
        self.conv2 = nn.Conv2d(6, 16, 5)
        self.conv_ds.append(dsnn.DeepBSpline('conv', 16, **opt_params))

        # fully-connected layer with 120 output units
        self.fc1 = nn.Linear(16 * 5 * 5, 120)
        self.fc_ds.append(dsnn.DeepBSpline('fc', 120, **opt_params))
        self.fc2 = nn.Linear(120, 84)
        self.fc_ds.append(dsnn.DeepBSpline('fc', 84, **opt_params))
        self.fc3 = nn.Linear(84, 10)

    def forward(self, x):

        x = self.pool(self.conv_ds[0](self.conv1(x)))
        x = self.pool(self.conv_ds[1](self.conv2(x)))
        x = torch.flatten(x, 1)  # flatten all dimensions except batch
        x = self.fc_ds[0](self.fc1(x))
        x = self.fc_ds[1](self.fc2(x))
        x = self.fc3(x)

        return x

dsnet = DSNet()
dsnet.to(device)

main_optimizer = optim.SGD(dsnet.parameters_no_deepspline(),
                           lr=0.001,
                           momentum=0.9)
aux_optimizer = optim.Adam(dsnet.parameters_deepspline())

lmbda = 1e-4 # regularization weight
lipschitz = False # lipschitz control

for epoch in range(2):

    for i, data in enumerate(trainloader):
        # get the inputs; data is a list of [inputs, labels]
        inputs, labels = data[0].to(device), data[1].to(device)

        # zero the parameter gradients
        main_optimizer.zero_grad()
        aux_optimizer.zero_grad()

        outputs = dsnet(inputs)
        loss = criterion(outputs, labels)

        # add regularization loss
        if lipschitz is True:
            loss = loss + lmbda * dsnet.BV2()
        else:
            loss = loss + lmbda * dsnet.TV2()

        loss.backward()
        main_optimizer.step()
        aux_optimizer.step()

For full details, please consult scripts/deepsplines_tutorial.py.

Reproducing results

To reproduce the results shown in the research papers [Bohra-Campos2020] and [Aziznejad2020] one can run the following scripts:

>> ./scripts/run_resnet32_cifar.py
>> ./scripts/run_nin_cifar.py
>> ./scripts/run_twoDnet.py

To see the running options, please add --help to the commands above.

Developers

DeepSplines is developed by the Biomedical Imaging Group, École Polytéchnique Fédérale de Lausanne, Switzerland.

For citing this package, please see: http://doi.org/10.5281/zenodo.5156042

Original authors:

• Joaquim Campos ([e-mail])

• Pakshal Bohra ([e-mail])

Contributors:

• Harshit Gupta

References

[Bohra-Campos2020]

16. Bohra, J. Campos, H. Gupta, S. Aziznejad, M. Unser, “Learning Activation Functions in Deep (Spline) Neural Networks,” IEEE Open Journal of Signal Processing, vol. 1, pp.295-309, November 19, 2020.

[Aziznejad2020]

19. Aziznejad, H. Gupta, J. Campos, M. Unser, “Deep Neural Networks with Trainable Activations and Controlled Lipschitz Constant,” IEEE Transactions on Signal Processing, vol. 68, pp. 4688-4699, August 10, 2020.

License

The code is released under the terms of the MIT License

Acknowledgements

This work was supported in part by the Swiss National Science Foundation under Grant 200020_184646 / 1 and in part by the European Research Council (ERC) under Grant 692726-GlobalBioIm.

MIT License

Copyright (c) 2021 Joaquim Campos, Pakshal Bohra

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.