KAN网络：用数学理论启发的神经网络新范式。
A Practitioner's Guide to Kolmogorov-Arnold Networks
- 基于柯尔莫戈洛夫叠加定理设计，以可学习基函数替代传统权重。
- 相比MLP在低维数据上更高效，且具更好泛化与收敛性。
- 适合想探索新型神经网络架构的研究者或工程师。
柯尔莫戈洛夫-阿诺德网络（KANs）的设计灵感来自柯尔莫戈洛夫叠加定理（KST），而非严格遵循该定理，已成为多层感知机（MLPs）的结构化替代方案。本文系统综述了快速发展的KAN研究文献，围绕三大核心主题展开：(i) 阐明KAN与KST、MLPs及经典核方法之间的关系；(ii) 分析基函数作为关键设计维度的作用；(iii) 总结近期在精度、效率、正则化与收敛性方面的进展。最后，提供一份实用的“选型指南”，并指出开放问题与未来方向。配套的GitHub仓库为持续的KAN研究提供结构化参考。
原文摘要 · Abstract (English)
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.
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