KAN: Kolmogorov-Arnold Networks

2024/04/30 by Ziming Liu, Liu, Ziming, Yixuan Wang +13 · 16 voices · 171 citations
Computer Science · #Cognitive Computing and Networks #Computability, Logic, AI Algorithms #cond-mat.dis-nn #cs.AI #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.2404.19756

openalex publication_date 2024/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs.

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Discussions

• Kan: Kolmogorov-Arnold Networks [hn, 28 points, 4 comments]
• Kan: Kolmogorov-Arnold Networks [hn, 4 points, 0 comments]
• Kan: Kolmogorov–Arnold Networks [hn, 3 points, 0 comments]
• Kan: Kolmogorov-Arnold Networks [hn, 3 points, 0 comments]
• Kan: Kolmogorov-Arnold Networks [hn, 3 points, 1 comments]
• Kolmogorov–Arnold Networks: Alternative to Multilayer Perceptrons. [hn, 2 points, 3 comments]
• Intested in KAN: Kolmogorov-Arnold Networks? arxiv.org/abs/2404.19756 Fair, I guess everyone is 🙃 Good that @ZimingLiu11 will join us on Mon May 13th 11am EDT, to discuss it in our Zoom reading grou [bsky, 2 points, 0 comments]
• Kolmogorov-Arnold Networks, an alternative to Multi-Layer Perceptrons [hn, 2 points, 0 comments]
• Lots of KAN KAN: arxiv.org/abs/2404.19756 #KAN #Kolmogorov #Arnold #MLP #NeuralNetworks [bsky, 2 points, 0 comments]
• arxiv.org/abs/2404.19756 Saw this make a small splash in certain circles back on Twitter a year ago [bsky, 1 points, 0 comments]
• Has anyone tried KANs yet? I'm always about the promise of fewer, more interpretable parameters, but the last (few) time(s) an arXiv model came my way hyped, it was a bust: arxiv.org/abs/2404.19756 [bsky, 1 points, 0 comments]
• Here's why I cannot take you guys seriously. In part as an effort to make LLM technology more efficient, an entirely new neural architecture is being developed and considered. It's a MAJOR innovation, [bsky, 1 points, 3 comments]
• I'm a huuuuge Kolmogorov fan. Very interested in this new paper... arxiv.org/abs/2404.19756 [bsky, 0 points, 0 comments]
• I feel as though the features of this which allows for this many different functions to be used within a neural net, and which prevent catastrophic forgetting, could be essential to LLMs having a deep [bsky, 0 points, 0 comments]
• Inspired by the Kolmogorov-Arnold representation theorem, they propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs) arxiv.org/abs/2404.19756 #machinele [bsky, 0 points, 0 comments]
• Kolmogorov-Arnold networks, KAN arxiv.org/pdf/2404.19756 [bsky, 0 points, 0 comments]

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