Rational Activations – Learnable Rational Activation Functions
First introduce as PAU in Padé Activation Units: Endtoend 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 endtoend 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: Endtoend 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.
CUDA>=10.2
“>
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:
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/mlresearch/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
5. Cite Us in your paper
@inproceedings{molina2019pade,
title={Pad{\'e} Activation Units: Endtoend 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, TingYu and Kashef, Yasien and RülingCachay, Salva and Zimmermann, Julius},
title = {Rational Activation functions},
year = {2020},
publisher = {GitHub},
journal = {GitHub repository},
howpublished={\url{https://github.com/mlresearch/rational_activations}}
}