Kolmogorov Arnold Networks and Multi-Layer Perceptrons: A Paradigm Shift in Neural Modelling

TL;DR

This paper compares Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptrons (MLP), demonstrating KAN's superior accuracy and efficiency in various computational tasks, suggesting a paradigm shift in neural modeling.

Contribution

It introduces KAN as a transformative neural network architecture rooted in Kolmogorov's theorem, outperforming MLPs in accuracy and computational efficiency across multiple benchmarks.

Findings

KAN outperforms MLP in accuracy across datasets

KAN achieves lower computational costs than MLP

KAN maintains high performance in resource-limited environments

Abstract

The research undertakes a comprehensive comparative analysis of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptrons (MLP), highlighting their effectiveness in solving essential computational challenges like nonlinear function approximation, time-series prediction, and multivariate classification. Rooted in Kolmogorov's representation theorem, KANs utilize adaptive spline-based activation functions and grid-based structures, providing a transformative approach compared to traditional neural network frameworks. Utilizing a variety of datasets spanning mathematical function estimation (quadratic and cubic) to practical uses like predicting daily temperatures and categorizing wines, the proposed research thoroughly assesses model performance via accuracy measures like Mean Squared Error (MSE) and computational expense assessed through Floating Point Operations (FLOPs). The results indicate that KANs reliably exceed MLPs in every benchmark, attaining higher predictive accuracy with significantly reduced computational costs. Such an outcome highlights their ability to maintain a balance between computational efficiency and accuracy, rendering them especially beneficial in resource-limited and real-time operational environments. By elucidating the architectural and functional distinctions between KANs and MLPs, the paper provides a systematic framework for selecting the most suitable neural architectures for specific tasks. Furthermore, the proposed study highlights the transformative capabilities of KANs in progressing intelligent systems, influencing their use in situations that require both interpretability and computational efficiency.