Rational Activations - Learnable Rational Activation Functions

First introduce as PAU in Padé Activation Units: End-to-end Learning of Activation Functions in Deep Neural Network.

1. About Rational Activation Functions

Rational Activations are a novel learnable activation functions. Rationals encode activation functions as rational functions, trainable in an end-to-end fashion using backpropagation and can be seemingless integrated into any neural network in the same way as common activation functions (e.g. ReLU).

Rationals: Beyond known Activation Functions

Rational can approximate any known activation function arbitrarily well (cf. Padé Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks): (*the dashed lines represent the rational approximation of every function)

Rational are made to be optimized by the gradient descent, and can discover good properties of activation functions after learning (cf Recurrent Rational Networks):

Rationals evaluation on different tasks

• They were first applied (as Padé Activation Units) to Supervised Learning (image classification) in Padé Activation Units:....

  

  See rational_sl github repo

Rational matches or outperforms common activations in terms of predictive performance and training time. And, therefore relieves the network designer of having to commit to a potentially underperforming choice.

• Recurrent Rational Functions have then been introduced in Recurrent Rational Networks, and both Rational and Recurrent Rational Networks are evaluated on RL Tasks. See rational_rl github repo

2. Dependencies

We support MxNet, Keras, and PyTorch. Instructions for MxNet can be found here. Instructions for Keras here. The following README instructions assume that you want to use rational activations in PyTorch.

PyTorch>=1.4.0
CUDA>=10.2

3. Installation

To install the rational_activations module, you can use pip, but:

‼️ rational_activations is currently compatible with torch==1.9.0 by default ‼️

For non TensorFlow and MXNet users, or if the command bellow don't work the package listed bellow don't work on your machine:

TensorFlow or MXNet (and torch==1.9.0)

 pip3 install -U pip wheel
 pip3 install torch rational_activations

Other CUDA/Pytorch

For any other torch version, please install from source: Modify requirements.txt to your corresponding torch version

 pip3 install airspeed  # to compile the CUDA templates
 git clone https://github.com/ml-research/rational_activations.git
 cd rational_activations
 pip3 install -r requirements.txt --user
 python3 setup.py install --user

If you encounter any trouble installing rational, please contact this person.

4. Using Rational in Neural Networks

Rational can be integrated in the same way as any other common activation function.

import torch
from rational.torch import Rational

model = torch.nn.Sequential(
    torch.nn.Linear(D_in, H),
    Rational(), # e.g. instead of torch.nn.ReLU()
    torch.nn.Linear(H, D_out),
)

Please also check the documentation 📔

5. Cite Us in your paper

@inproceedings{molina2019pade,
  title={Pad{\'e} Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks},
  author={Molina, Alejandro and Schramowski, Patrick and Kersting, Kristian},
  booktitle={International Conference on Learning Representations},
  year={2019}
}

@article{delfosse2021recurrent,
  title={Recurrent Rational Networks},
  author={Delfosse, Quentin and Schramowski, Patrick and Molina, Alejandro and Kersting, Kristian},
  journal={arXiv preprint arXiv:2102.09407},
  year={2021}
}

@misc{delfosse2020rationals,
  author = {Delfosse, Quentin and Schramowski, Patrick and Molina, Alejandro and Beck, Nils and Hsu, Ting-Yu and Kashef, Yasien and Rüling-Cachay, Salva and Zimmermann, Julius},
  title = {Rational Activation functions},
  year = {2020},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished={\url{https://github.com/ml-research/rational_activations}}
}