KAN: Kolmogorov-Arnold Networks – Ziming Liu

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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.

Speakers: Ziming Liu

Twitter Hannes: https://twitter.com/HannesStaerk
Twitter Dominique: https://twitter.com/dom_beaini

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Chapters
00:00 – Intro + Background
05:06 – From KART to KAN
07:56 – MLP vs KAN
16:05 – Accuracy: Scaling of KANs
26:35 – Interpretability: KAN for Science
38:04 – Q+A Break
57:15 – Strengths and Weaknesses
59:28 – Philosophy
1:08:45 – Anecdotes Behind the Scenes
1:11:49 – Final Thoughts
1:14:58 – Q+A

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