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.

翻译：科尔莫戈罗夫-阿诺德网络（KANs）的设计灵感源于——而非受制于——科尔莫戈罗夫叠加定理，已作为MLPs的结构化替代方案崭露头角。本综述对快速扩展的KAN文献进行了系统而全面的梳理，围绕三大核心主题展开：(i)阐明KANs与科尔莫戈罗夫叠加理论（KST）、MLPs及经典核方法之间的关系；(ii)将基函数分析作为核心设计轴线；(iii)总结近期在精度、效率、正则化与收敛性方面的进展。最后，我们提供了实用的"Choose-Your-KAN"指南，并概述了开放的研究挑战与未来方向。随附的GitHub仓库为持续进行的KAN研究提供了结构化参考。