A practitioner’s guide to Kolmogorov–Arnold networks

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 (https://github.com/AmirNoori68/kan-review) serves as a structured reference for ongoing KAN research.