A Practitioner's Guide to Kolmogorov-Arnold Networks

TL;DR

This paper reviews Kolmogorov-Arnold Networks (KANs), highlighting their theoretical foundations, design choices, recent advancements, and providing practical guidance and a GitHub resource for researchers.

Contribution

It offers a comprehensive overview of KANs, clarifies their relationship with existing theories, and presents a practical guide along with open research challenges.

Findings

Improved understanding of KANs and their relation to KST, MLPs, and kernel methods.

Summarized recent advances in accuracy, efficiency, and regularization.

Provided a practical guide and a structured GitHub repository for ongoing research.

Abstract

Kolmogorov-Arnold Networks (KANs), whose design is inspired-rather than dictated-by the Kolmogorov superposition theorem, have emerged as a structured alternative to MLPs. This review provides a systematic and comprehensive overview of the rapidly expanding KAN literature. The review is organized around three core themes: (i) clarifying the relationships between KANs and Kolmogorov superposition theory (KST), MLPs, and classical kernel methods; (ii) analyzing basis functions as a central design axis; and (iii) summarizing recent advances in accuracy, efficiency, regularization, and convergence. Finally, we provide a practical "Choose-Your-KAN" guide and outline open research challenges and future directions. The accompanying GitHub repository serves as a structured reference for ongoing KAN research.