Combinations of Fast Activation and Trigonometric Functions in Kolmogorov-Arnold Networks

TL;DR

This paper explores combining fast activation functions like ReLU and trigonometric functions within Kolmogorov-Arnold Networks to improve computational efficiency and maintain competitive performance.

Contribution

It introduces the novel integration of fast computational functions into KANs, enhancing efficiency while preserving effectiveness.

Findings

Maintains competitive performance with new function combinations

Potential improvements in training time and generalization

Supports GPU-friendly implementations

Abstract

For years, many neural networks have been developed based on the Kolmogorov-Arnold Representation Theorem (KART), which was created to address Hilbert's 13th problem. Recently, relying on KART, Kolmogorov-Arnold Networks (KANs) have attracted attention from the research community, stimulating the use of polynomial functions such as B-splines and RBFs. However, these functions are not fully supported by GPU devices and are still considered less popular. In this paper, we propose the use of fast computational functions, such as ReLU and trigonometric functions (e.g., ReLU, sin, cos, arctan), as basis components in Kolmogorov-Arnold Networks (KANs). By integrating these function combinations into the network structure, we aim to enhance computational efficiency. Experimental results show that these combinations maintain competitive performance while offering potential improvements in training time and generalization.