Padé Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks

Unofficial PyTorch reimplementation of the paper Padé Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks by Molina et al., published at ICLR 2020.

This repository includes an easy-to-use pure PyTorch implementation of the Padé Activation Unit (PAU).

Please note that the official implementation provides a probably faster CUDA implementation!

Installation

The PAU can be installed by using pip.

pip install git+https://github.com/ChristophReich1996/Pade-Activation-Unit

Example Usage

The PAU can be simply used as a standard nn.Module:

import torch
import torch.nn as nn
from pau import PAU

network: nn.Module = nn.Sequential(
    nn.Linear(2, 2),
    PAU(),
    nn.Linear(2, 2)
)

output: torch.Tensor = network(torch.rand(16, 2))

The PAU is implemented in an efficient way (checkpointing and sequential computation of Vandermonde matrix), if you want to use the faster but more memory intensive version please use PAU(efficient=False)

If a nominator degree of 5 and a denominator degree of 4 is used the following initializations are available: ReLU (initial_shape=relu), Leaky ReLU negative slope=0.01 (initial_shape=leaky_relu_0_01), Leaky ReLU negative slope=0.2 (initial_shape=leaky_relu_0_2), Leaky ReLU negative slope=0.25 (initial_shape=leaky_relu_0_25), Leaky ReLU negative slope=0.3 (initial_shape=leaky_relu_0_3), Leaky ReLU negative slope=-0.5 (initial_shape=leaky_relu_m0_5), Tanh (initial_shape=tanh), Swish (initial_shape=swish), Sigmoid (initial_shape=sigmoid).

If a different nominator and denominator degree or initial_shape=None is utilized the PAU is initialized with random weights.

If you would like to fix the weights of multiple PAUs in a nn.Module just call module = pau.freeze_pau(module).

For a more detailed examples on hwo to use this implementation please refer to the example file (requires Matplotlib to be installed).

The PAU takes the following parameters.

Parameter	Description	Type
m	Size of nominator polynomial. Default 5.	int
n	Size of denominator polynomial. Default 4.	int
initial_shape	Initial shape of PAU, if None random shape is used, also if m and n are not the default value (5 and 4) a random shape is utilized. Default "leaky_relu_0_2".	Optional[str]
efficient	If true efficient variant with checkpointing is used. Default True.	bool
eps	Constant for numerical stability. Default 1e-08.	float
**kwargs	Unused additional key word arguments	Any

Reference

@inproceedings{Molina2020,
    title={{Padé Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks}},
    author={Alejandro Molina and Patrick Schramowski and Kristian Kersting},
    booktitle={International Conference on Learning Representations},
    year={2020}
}