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Kan 2.0: Kolmogorov-Arnold Networks Meet Science (arxiv.org)
8 points by johnsutor on Aug 29, 2024 | hide | past | pdf | discuss on HN

In plain words: Each connection holds a small learnable curve instead of a fixed weight, so the network can be rewritten as a readable formula rather than a black box. The toolkit converts such networks into symbolic laws and back, recovering conserved quantities, symmetries and Lagrangians from data.

Abstract · KAN 2.0: Kolmogorov-Arnold Networks Meet Science

A major challenge of AI + Science lies in their inherent incompatibility: today's AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold Networks (KANs) and science. The framework highlights KANs' usage for three aspects of scientific discovery: identifying relevant features, revealing modular structures, and discovering symbolic formulas. The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs). We highlight major new functionalities in the pykan package: (1) MultKAN: KANs with multiplication nodes. (2) kanpiler: a KAN compiler that compiles symbolic formulas into KANs. (3) tree converter: convert KANs (or any neural networks) to tree graphs. Based on these tools, we demonstrate KANs' capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws.

Ziming Liu, Pingchuan Ma, Yixuan Wang, Wojciech Matusik, Max Tegmark
arXiv:2408.10205 · cs.LG, cs.AI, physics.comp-ph, physics.data-an · submitted Aug 19, 2024
abstract · pdf · html · 27 pages, 14 figures

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