Unification of popular artificial neural network activation functions

TL;DR

By training an array of neural network architectures of different complexities on various benchmark datasets, it is demonstrated that adopting a unified gated representation of activation functions offers a promising and affordable alternative to individual built-in implementations of activation functions in conventional machine learning frameworks.

Abstract

We present a unified representation of the most popular neural network activation functions. Adopting Mittag-Leffler functions of fractional calculus, we propose a flexible and compact functional form that is able to interpolate between various activation functions and mitigate common problems in training neural networks such as vanishing and exploding gradients. The presented gated representation extends the scope of fixed-shape activation functions to their adaptive counterparts whose shape can be learnt from the training data. The derivatives of the proposed functional form can also be expressed in terms of Mittag-Leffler functions making it a suitable candidate for gradient-based backpropagation algorithms. By training multiple neural networks of different complexities on various datasets with different sizes, we demonstrate that adopting a unified gated representation of activation functions offers a promising and affordable alternative to individual built-in implementations of activation functions in conventional machine learning frameworks.

Figures (5)

• Figure 1: Plots of built-in and gated representation of various activation functions
• Figure 2: The interpolation of $x { \Phi\biggl[x\biggl|1\genfrac..{0pt}{}{2~ 2\ x^2}{2\ \beta\ x^2}\biggr] }$ between linear and hyperbolic tangent functions
• Figure 3: LeNet-5 neural network architecture
• Figure 4: The final (target) convolution layer in the ShuffleNet-v2 architecture
• Figure 5: The bottleneck design with an identity shortcut in the ResNet-101 architecture