KAN: Kolmogorov-Arnold Networks
Authors: name: Ziming Liu; name: Yixuan Wang; name: Sachin Vaidya; name: Fabian Ruehle; name: James Halverson; name: Marin Soljačić; name: Thomas Y. Hou; name: Max Tegmark
Published: 2024-04-30 17:58:29

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.