Don't Fear Peculiar Activation Functions: EUAF and Beyond

TL;DR

This paper introduces PEUAF, a new super-expressive activation function, demonstrating its effectiveness across datasets and broadening the class of such functions with theoretical and empirical support.

Contribution

We propose PEUAF, a novel super-expressive activation function, and generalize the family of super-expressive functions, addressing previous limitations and skepticism.

Findings

PEUAF outperforms traditional activation functions on multiple datasets.

Any continuous function can be approximated by networks with super-expressive activations.

The proposed functions are practical and scalable for real-world applications.

Abstract

In this paper, we propose a new super-expressive activation function called the Parametric Elementary Universal Activation Function (PEUAF). We demonstrate the effectiveness of PEUAF through systematic and comprehensive experiments on various industrial and image datasets, including CIFAR10, Tiny-ImageNet, and ImageNet. Moreover, we significantly generalize the family of super-expressive activation functions, whose existence has been demonstrated in several recent works by showing that any continuous function can be approximated to any desired accuracy by a fixed-size network with a specific super-expressive activation function. Specifically, our work addresses two major bottlenecks in impeding the development of super-expressive activation functions: the limited identification of super-expressive functions, which raises doubts about their broad applicability, and their often peculiar forms, which lead to skepticism regarding their scalability and practicality in real-world applications.