KAN versus MLP on Irregular or Noisy Functions

TL;DR

This study compares Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptrons (MLP) on various irregular and noisy functions, revealing that MLP can outperform KAN depending on function type and training data size.

Contribution

It provides a systematic comparison of KAN and MLP on diverse irregular and noisy functions, highlighting their relative strengths and limitations.

Findings

MLP outperforms or matches KAN on some function types

Increasing training data size can improve network performance

Noise obscures irregular features, challenging both networks

Abstract

In this paper, we compare the performance of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptron (MLP) networks on irregular or noisy functions. We control the number of parameters and the size of the training samples to ensure a fair comparison. For clarity, we categorize the functions into six types: regular functions, continuous functions with local non-differentiable points, functions with jump discontinuities, functions with singularities, functions with coherent oscillations, and noisy functions. Our experimental results indicate that KAN does not always perform best. For some types of functions, MLP outperforms or performs comparably to KAN. Furthermore, increasing the size of training samples can improve performance to some extent. When noise is added to functions, the irregular features are often obscured by the noise, making it challenging for both MLP and KAN to extract these features effectively. We hope these experiments provide valuable insights for future neural network research and encourage further investigations to overcome these challenges.