ActTensor: Activation Functions for TensorFlow

license releases

What is it?

ActTensor is a Python package that provides state-of-the-art activation functions which facilitate using them in Deep Learning projects in an easy and fast manner.

Why not using tf.keras.activations?

As you may know, TensorFlow only has a few defined activation functions and most importantly it does not include newly-introduced activation functions. Wrting another one requires time and energy; however, this package has most of the widely-used, and even state-of-the-art activation functions that are ready to use in your models.

Requirements

numpy
tensorflow
setuptools
keras
wheel

Where to get it?

The source code is currently hosted on GitHub at: https://github.com/pouyaardehkhani/ActTensor

Binary installers for the latest released version are available at the Python Package Index (PyPI)

# PyPI
pip install ActTensor-tf

License

MIT

How to use?

import tensorflow as tf
import numpy as np
from ActTensor_tf import ReLU # name of the layer

functional api

inputs = tf.keras.layers.Input(shape=(28,28))
x = tf.keras.layers.Flatten()(inputs)
x = tf.keras.layers.Dense(128)(x)
# wanted class name
x = ReLU()(x)
output = tf.keras.layers.Dense(10,activation='softmax')(x)

model = tf.keras.models.Model(inputs = inputs,outputs=output)

sequential api

model = tf.keras.models.Sequential([tf.keras.layers.Flatten(),
                                    tf.keras.layers.Dense(128),
                                    # wanted class name
                                    ReLU(),
                                    tf.keras.layers.Dense(10, activation = tf.nn.softmax)])

NOTE:

The main function of the activation layers are also availabe but it maybe defined as different name. Check this for more information.

from ActTensor_tf import relu

Activations

Classes and Functions are available in ActTensor_tf

Activation Name	Class Name	Function Name
SoftShrink	SoftShrink	softSHRINK
HardShrink	HardShrink	hard_shrink
GLU	GLU	-
Bilinear	Bilinear	-
ReGLU	ReGLU	-
GeGLU	GeGLU	-
SwiGLU	SwiGLU	-
SeGLU	SeGLU	-
ReLU	ReLU	relu
Identity	Identity	identity
Step	Step	step
Sigmoid	Sigmoid	sigmoid
HardSigmoid	HardSigmoid	hard_sigmoid
LogSigmoid	LogSigmoid	log_sigmoid
SiLU	SiLU	silu
PLinear	ParametricLinear	parametric_linear
Piecewise-Linear	PiecewiseLinear	piecewise_linear
Complementary Log-Log	CLL	cll
Bipolar	Bipolar	bipolar
Bipolar-Sigmoid	BipolarSigmoid	bipolar_sigmoid
Tanh	Tanh	tanh
TanhShrink	TanhShrink	tanhshrink
LeCun's Tanh	LeCunTanh	leCun_tanh
HardTanh	HardTanh	hard_tanh
TanhExp	TanhExp	tanh_exp
Absolute	ABS	Abs
Squared-ReLU	SquaredReLU	squared_relu
P-ReLU	ParametricReLU	Parametric_ReLU
R-ReLU	RandomizedReLU	Randomized_ReLU
LeakyReLU	LeakyReLU	leaky_ReLU
ReLU6	ReLU6	relu6
Mod-ReLU	ModReLU	Mod_ReLU
Cosine-ReLU	CosReLU	Cos_ReLU
Sin-ReLU	SinReLU	Sin_ReLU
Probit	Probit	probit
Cos	Cos	Cosine
Gaussian	Gaussian	gaussian
Multiquadratic	Multiquadratic	Multi_quadratic
Inverse-Multiquadratic	InvMultiquadratic	Inv_Multi_quadratic
SoftPlus	SoftPlus	softPlus
Mish	Mish	mish
SMish	Smish	smish
P-SMish	ParametricSmish	Parametric_Smish
Swish	Swish	swish
ESwish	ESwish	eswish
HardSwish	HardSwish	hardSwish
GCU	GCU	gcu
CoLU	CoLU	colu
PELU	PELU	pelu
SELU	SELU	selu
CELU	CELU	celu
ArcTan	ArcTan	arcTan
Shifted-SoftPlus	ShiftedSoftPlus	Shifted_SoftPlus
Softmax	Softmax	softmax
Logit	Logit	logit
GELU	GELU	gelu
Softsign	Softsign	softsign
ELiSH	ELiSH	elish
HardELiSH	HardELiSH	hardELiSH
Serf	Serf	serf
ELU	ELU	elu
Phish	Phish	phish
QReLU	QReLU	qrelu
MQReLU	MQReLU	mqrelu
FReLU	FReLU	frelu

Which activation functions it supports?

Soft Shrink:
$f(x) =\begin{cases}x-\lambda & x > \lambda\\ x+\lambda & x < -\lambda\\ 0 & otherwise \end{cases}$

Hard Shrink:
$f(x) = \begin{cases}x & x > \lambda\\ x & x < -\lambda\\ 0 & otherwise \end{cases}$

GLU:
$GLU\left ( a,b \right )= a \oplus \sigma \left ( b \right )$

Source Paper : Language Modeling with Gated Convolutional Networks

Bilinear:

Source Paper : Parameter Efficient Deep Neural Networks with Bilinear Projections

ReGLU:

ReGLU is an activation function which is a variant of GLU.
$ReGLU\left ( x, W, V, b, c \right )= max(0, xW + b) \oplus (xV + b)$

Source Paper : GLU Variants Improve Transformer

GeGLU:

GeGLU is an activation function which is a variant of GLU.
$GeGLU\left ( x, W, V, b, c \right )= GELU(xW + b) \oplus (xV + b)$

Source Paper : GLU Variants Improve Transformer

SwiGLU:

SwiGLU is an activation function which is a variant of GLU.
$SwiGLU\left ( x, W, V, b, c \right )= Swish_b(xW + b) \oplus (xV + b)$

Source Paper : GLU Variants Improve Transformer

SeGLU:

SeGLU is an activation function which is a variant of GLU.
ReLU:
$f(x) =\begin{cases}x & x \geq 0\\0 & x < 0 \end{cases}$

Source Paper : Nair, Vinod, and Geoffrey E. Hinton. "Rectified linear units improve restricted boltzmann machines." In Icml. 2010.

Identity:

$f(x) = x$

Step:
$f(x) =\begin{cases}1 & x < 0\\0 & x \geq 0\end{cases}$

Sigmoid:
$f(x) = \frac{1}{1+e^{-x}}$

Source Paper : Han, Jun, and Claudio Moraga. "The influence of the sigmoid function parameters on the speed of backpropagation learning." In International workshop on artificial neural networks, pp. 195-201. Springer, Berlin, Heidelberg, 1995.

Hard Sigmoid:
$f(x) = max(0, min(1,\frac{x+1}{2}))$

Source Paper : Courbariaux, Matthieu, Yoshua Bengio, and Jean-Pierre David. "Binaryconnect: Training deep neural networks with binary weights during propagations." Advances in neural information processing systems 28 (2015).

Log Sigmoid:
$LogSigmoid(x)=\log\left(\dfrac{1}{1+\exp(-x_i)}\right)$

SiLU:
$f(x) = x(\frac{1}{1+e^{-x}})$

Source Paper : Elfwing, Stefan, Eiji Uchibe, and Kenji Doya. "Sigmoid-weighted linear units for neural network function approximation in reinforcement learning." Neural Networks 107 (2018): 3-11.

ParametricLinear:

$f(x) = a*x$
PiecewiseLinear:

Choose some xmin and xmax, which is our "range". Everything less than than this range will be 0, and everything greater than this range will be 1. Anything else is linearly-interpolated between.
$f(x) = \begin{cases}0 & x < x_{min}\\ mx + b & x_{min} < x < x_{max}\\ 1 & x > x_{xmax} \end{cases}$

$m = \frac{1}{x_{max} - x_{min}}$ $b = -mx_{min} = 1 - mx_{max}$

Complementary Log-Log (CLL):
$f(x) = 1-e^{-e^x}$

Source Paper : Gomes, Gecynalda S. da S., and Teresa B. Ludermir. "Complementary log-log and probit: activation functions implemented in artificial neural networks." In 2008 Eighth International Conference on Hybrid Intelligent Systems, pp. 939-942. IEEE, 2008.

Bipolar:
$f(x) =\begin{cases}-1 & x \leq 0\\1 & x > 0\end{cases}$

Bipolar Sigmoid:
$f(x) = \frac{1-e^{-x}}{1+e^{-x}}$

Source Paper : Mansor, Mohd Asyraf, and Saratha Sathasivam. "Activation function comparison in neural-symbolic integration." In AIP Conference Proceedings, vol. 1750, no. 1, p. 020013. AIP Publishing LLC, 2016.

Tanh:
$f(x) = \frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}$

Source Paper : Harrington, Peter de B. "Sigmoid transfer functions in backpropagation neural networks." Analytical Chemistry 65, no. 15 (1993): 2167-2168.

Tanh Shrink:
$f(x) = x-tanh(x)$

LeCunTanh:
$f(x) = 1.7159\ tanh(\frac{2}{3}x)$

Source Paper : LeCun, Yann A., Léon Bottou, Genevieve B. Orr, and Klaus-Robert Müller. "Efficient backprop." In Neural networks: Tricks of the trade, pp. 9-48. Springer, Berlin, Heidelberg, 2012.

Hard Tanh:
$f(x) =\begin{cases}-1 & x < -1\\x & -1 \leq x \leq 1\\1 & x > 1 \end{cases}$

TanhExp:
$f(x) = x\ tanh(e^x)$

Source Paper : Liu, Xinyu, and Xiaoguang Di. "TanhExp: A smooth activation function with high convergence speed for lightweight neural networks." IET Computer Vision 15, no. 2 (2021): 136-150.

ABS:
$f(x) = |x|$

SquaredReLU:
$f(x) =\begin{cases}x^2 & x \geq 0\\0 & x < 0 \end{cases}$

Source Paper : So, David, Wojciech Mańke, Hanxiao Liu, Zihang Dai, Noam Shazeer, and Quoc V. Le. "Searching for Efficient Transformers for Language Modeling." Advances in Neural Information Processing Systems 34 (2021): 6010-6022.

ParametricReLU (PReLU):
$f(x) =\begin{cases}x & x \geq 0\\ \alpha x & x < 0 \end{cases}$

Source Paper : He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. "Delving deep into rectifiers: Surpassing human-level performance on imagenet classification." In Proceedings of the IEEE international conference on computer vision, pp. 1026-1034. 2015.

RandomizedReLU (RReLU):
$f(x) =\begin{cases}x & x \geq 0\\ \alpha x & x < 0 \end{cases}$ $a \sim U(l,u)$

Source Paper : Xu, Bing, Naiyan Wang, Tianqi Chen, and Mu Li. "Empirical evaluation of rectified activations in convolutional network." arXiv preprint arXiv:1505.00853 (2015).

LeakyReLU:
$f(x) =\begin{cases}x & x \geq 0\\ 0.01 x & x < 0 \end{cases}$

ReLU6:
$f(x) = min(6, max(0,x))$

Source Paper : Howard, Andrew G., Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam. "Mobilenets: Efficient convolutional neural networks for mobile vision applications." arXiv preprint arXiv:1704.04861 (2017).

ModReLU:
$f(x) =\begin{cases}(|x|+b)\frac{x}{|x|} & |x|+b \geq 0 \\0 & |x|+b \leq 0\end{cases}$

Source Paper : Arjovsky, Martin, Amar Shah, and Yoshua Bengio. "Unitary evolution recurrent neural networks." In International conference on machine learning, pp. 1120-1128. PMLR, 2016.

CosReLU:
$f(x) = max(0,x) + cos(x)$

SinReLU:
$f(x) = max(0,x) + sin(x)$

Probit:
$f(x) = \sqrt{2}\ \ erfinv(2x - 1)$

Cosine:
$f(x) = Cos(x)$

Gaussian:
$f(x) = e^{-\frac{1}{2}x^2}$

Multiquadratic:

Choose some point (x,y).
$\rho(z) = \sqrt{(z - x)^{2} + y^{2}}$

InvMultiquadratic:
$\rho(z) = \frac{1}{\sqrt{(z - x)^{2} + y^{2}} }$

SoftPlus:
$f(x) = ln(1+e^x)$

Source Paper : Dugas, Charles, Yoshua Bengio, François Bélisle, Claude Nadeau, and René Garcia. "Incorporating second-order functional knowledge for better option pricing." Advances in neural information processing systems 13 (2000).

Mish:
$f(x) = x\ tanh(SoftPlus(x))$

Source Paper : Misra, Diganta. "Mish: A self regularized non-monotonic neural activation function." arXiv preprint arXiv:1908.08681 4, no. 2 (2019): 10-48550.

Smish:
$f(x) = x\ tanh(log(1+Sigmoid(x)))$

ParametricSmish (PSmish):
$f(x) = a\ tanh(log(1+Sigmoid(b)))$ $a= \alpha x$ $b= \beta x$

Swish:
$f(x) = \frac{x}{1-e^{-\beta x}}$

Source Paper : Ramachandran, Prajit, Barret Zoph, and Quoc V. Le. "Searching for activation functions." arXiv preprint arXiv:1710.05941 (2017).

ESwish:
$f(x) = \beta\ \frac{x}{1-e^{-\beta x}}$

Source Paper : Alcaide, Eric. "E-swish: Adjusting activations to different network depths." arXiv preprint arXiv:1801.07145 (2018).

Hard Swish:
$f(x) = x\ \frac{ReLU6(x+3)}{6}$

Source Paper : Howard, Andrew, Mark Sandler, Grace Chu, Liang-Chieh Chen, Bo Chen, Mingxing Tan, Weijun Wang et al. "Searching for mobilenetv3." In Proceedings of the IEEE/CVF international conference on computer vision, pp. 1314-1324. 2019.

GCU:
$f(x) = x\ cos(x)$

Source Paper : Noel, Mathew Mithra, Advait Trivedi, and Praneet Dutta. "Growing cosine unit: A novel oscillatory activation function that can speedup training and reduce parameters in convolutional neural networks." arXiv preprint arXiv:2108.12943 (2021).

CoLU:
$f(x) = \frac{x}{1-x e^{-(x+e^x)}}$

Source Paper : Vagerwal, Advait. "Deeper Learning with CoLU Activation." arXiv preprint arXiv:2112.12078 (2021).

PELU:
$f(x) =\begin{cases}cx & x > 0\\ \alpha e^{\frac{x}{b}}-1 & x \leq 0 \end{cases}$

Source Paper : Trottier, Ludovic, Philippe Giguere, and Brahim Chaib-Draa. "Parametric exponential linear unit for deep convolutional neural networks." In 2017 16th IEEE International Conference on Machine Learning and Applications (ICMLA), pp. 207-214. IEEE, 2017.

SELU:
$f\left(x\right) = \lambda{x} \text{ if } x \geq{0}$$ $$f\left(x\right) = \lambda{\alpha\left(\exp\left(x\right) -1 \right)} \text{ if } x < 0$
where $\alpha \approx 1.6733$ & $\lambda \approx 1.0507$

Source Paper : Klambauer, Günter, Thomas Unterthiner, Andreas Mayr, and Sepp Hochreiter. "Self-normalizing neural networks." Advances in neural information processing systems 30 (2017).

CELU:
$CELU\left ( x \right )= max(0, x) + min(0 , \alpha (e^{\frac{x}{\alpha }} -1))$

Source Paper : Barron, Jonathan T. "Continuously differentiable exponential linear units." arXiv preprint arXiv:1704.07483 (2017).

ArcTan:
$f(x) = ArcTang(x)$

ShiftedSoftPlus:
$f(x) = log(0.5+0.5e^x)$

Source Paper : Schütt, Kristof, Pieter-Jan Kindermans, Huziel Enoc Sauceda Felix, Stefan Chmiela, Alexandre Tkatchenko, and Klaus-Robert Müller. "Schnet: A continuous-filter convolutional neural network for modeling quantum interactions." Advances in neural information processing systems 30 (2017).

Softmax:
$f(x) = \frac{x_i}{\sum_j x_j}$

Source Paper : Gold, Steven, and Anand Rangarajan. "Softmax to softassign: Neural network algorithms for combinatorial optimization." Journal of Artificial Neural Networks 2, no. 4 (1996): 381-399.

Logit:
$f(x) = \frac{x}{1-x}$

GELU:
$f(X) = x \ \phi \( x )$

Softsign:
$f(x) = \frac{x}{|x|+1}$

ELiSH:
$f(x) =\begin{cases}\frac{x}{1+e^{-x}} & x \geq 0\\ \frac{e^x-1}{1+e^{-x}} & x < 0 \end{cases}$

Source Paper : Basirat, Mina, and Peter M. Roth. "The quest for the golden activation function." arXiv preprint arXiv:1808.00783 (2018).

Hard ELiSH:
$f(x) =\begin{cases}x\ max(0,min(1,\frac{x+1}{2})) & x \geq 0\\ (e^x-1) max(0,min(1,\frac{x+1}{2})) & x < 0 \end{cases}$

Source Paper : Basirat, Mina, and Peter M. Roth. "The quest for the golden activation function." arXiv preprint arXiv:1808.00783 (2018).

Serf:
$f(x) = x\ erf(ln(1+e^x))$

Source Paper : Nag, Sayan, and Mayukh Bhattacharyya. "SERF: Towards better training of deep neural networks using log-Softplus ERror activation Function." arXiv preprint arXiv:2108.09598 (2021).

ELU:
$f(x) =\begin{cases}x & x > 0\\ \alpha (exp(x)-1) & x \leq 0 \end{cases}$

Source Paper : Clevert, Djork-Arné, Thomas Unterthiner, and Sepp Hochreiter. "Fast and accurate deep network learning by exponential linear units (elus)." arXiv preprint arXiv:1511.07289 (2015).

Phish:
$f(x) = x\ tanh(gelu(x))$

Source Paper : Naveen, Philip. "Phish: A novel hyper-optimizable activation function." (2022).

QReLU:
$f(x) =\begin{cases}x & x > 0\\ 0.01\ x(x-2) & x \leq 0 \end{cases}$

Source Paper : Parisi, Luca, Daniel Neagu, Renfei Ma, and Felician Campean. "QReLU and m-QReLU: Two novel quantum activation functions to aid medical diagnostics." arXiv preprint arXiv:2010.08031 (2020).

m-QReLU:
$f(x) =\begin{cases}x & x > 0\\ 0.01\ x -x & x \leq 0 \end{cases}$

Source Paper : Parisi, Luca, Daniel Neagu, Renfei Ma, and Felician Campean. "QReLU and m-QReLU: Two novel quantum activation functions to aid medical diagnostics." arXiv preprint arXiv:2010.08031 (2020).

FReLU:
$f(x) =\begin{cases}x+b & x > 0\\ b & x \leq 0 \end{cases}$

Source Paper : Qiu, Suo, Xiangmin Xu, and Bolun Cai. "FReLU: flexible rectified linear units for improving convolutional neural networks." In 2018 24th international conference on pattern recognition (icpr), pp. 1223-1228. IEEE, 2018.

Cite this repository

@software{Pouya_ActTensor_2022,
author = {Pouya, Ardehkhani and Pegah, Ardehkhani},
license = {MIT},
month = {7},
title = {{ActTensor}},
url = {https://github.com/pouyaardehkhani/ActTensor},
version = {1.0.0},
year = {2022}
}

ActTensor
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Metadata

ActTensor: Activation Functions for TensorFlow

What is it?

Why not using tf.keras.activations?

Requirements

Where to get it?

License

How to use?

Activations

Which activation functions it supports?

Cite this repository

← Metadata

Owner

Metadata

ActTensor ActTensor copied to clipboard

Metadata

ActTensor: Activation Functions for TensorFlow

What is it?

Why not using tf.keras.activations?

Requirements

Where to get it?

License

How to use?

Activations

Which activation functions it supports?

Cite this repository

← Metadata

Owner

Metadata

ActTensor
ActTensor copied to clipboard