Unification of popular artificial neural network activation functions

TL;DR

This paper introduces a unified, flexible activation function framework based on Mittag-Leffler functions, capable of interpolating between popular functions and adapting during training to improve neural network performance.

Contribution

It proposes a novel, unified activation function representation that can be learned and adapted, addressing issues like vanishing gradients and enhancing training flexibility.

Findings

Unified activation functions improve training stability.

Adaptive activation functions outperform fixed ones in experiments.

The approach is computationally feasible for various datasets.

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.