Score: 1

A Practitioner's Guide to Kolmogorov-Arnold Networks

Published: October 28, 2025 | arXiv ID: 2510.25781v2

By: Amir Noorizadegan, Sifan Wang, Leevan Ling

Potential Business Impact:

Makes AI smarter and learn faster.

Business Areas:
Machine Learning Artificial Intelligence, Data and Analytics, Software

The so-called Kolmogorov-Arnold Networks (KANs), whose design is merely inspired, rather than dictated, by the Kolmogorov superposition theorem, have emerged as a promising alternative to traditional Multilayer Perceptrons (MLPs). This review provides a systematic and comprehensive overview of the rapidly expanding KAN landscape. By collecting and categorizing a large set of open-source implementations, we map the vibrant ecosystem supporting modern KAN development. We organize the review around four core themes: (i) presenting a precise history of Kolmogorov's superposition theory toward neural-network formulations; (ii) establishing the formal equivalence between KANs and MLPs; (iii) analyzing the critical role of basis functions; and (iv) organizing recent advancements in accuracy, efficiency, regularization, and convergence. Finally, we provide a practical Choose-Your-KAN guide to assist practitioners in selecting appropriate architectures, and we close by identifying current research gaps and future directions. The associated GitHub repository (https://github.com/AmirNoori68/kan-review) complements this paper and serves as a structured reference for ongoing KAN research.