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：Kolmogorov-Arnold网络（KANs）的设计灵感源于Kolmogorov叠加定理而非由其严格限定，现已发展为多层感知机（MLPs）的一种结构化替代方案。本文对快速增长的KAN文献进行了系统而全面的梳理。综述围绕三个核心主题展开：（i）厘清KANs与Kolmogorov叠加理论（KST）、MLPs及经典核方法之间的关系；（ii）分析作为核心设计维度的基函数；（iii）总结在精度、效率、正则化与收敛性方面的最新进展。最后，我们提供了实用的“选择你的KAN”指南，并展望了开放的研究挑战与未来方向。附带的GitHub仓库为持续发展的KAN研究提供了结构化参考。