title: KAN: Kolmogorov-Arnold Networks
summary: 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.
paper_authors._id: 6631c7748d7c840b14f53b43
paper_authors.name: Ziming Liu
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2024-05-02T08:04:26.453Z
paper_authors._id: 64d59cfa8767727dffa382de
paper_authors.avatarUrl: /avatars/21611131f5f9281ff9eb954939449124.svg
paper_authors.fullname: Ziming Liu
paper_authors.type: user
paper_authors.user: zmliu
paper_authors._id: 6631c7748d7c840b14f53b44
paper_authors.name: Yixuan Wang
paper_authors._id: 6631c7748d7c840b14f53b45
paper_authors.name: Sachin Vaidya
paper_authors._id: 6631c7748d7c840b14f53b46
paper_authors.name: Fabian Ruehle
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2024-05-02T08:04:52.586Z
paper_authors._id: 648f53ddd469965a66c873e3
paper_authors.avatarUrl: /avatars/2383dbd4dc806ea9f601fbb98d7fd8fc.svg
paper_authors.fullname: Fabian Ruehle
paper_authors.type: user
paper_authors.user: Fanianrue
paper_authors._id: 6631c7748d7c840b14f53b47
paper_authors.name: James Halverson
paper_authors._id: 6631c7748d7c840b14f53b48
paper_authors.name: Marin Soljačić
paper_authors._id: 6631c7748d7c840b14f53b49
paper_authors.name: Thomas Y. Hou
paper_authors._id: 6631c7748d7c840b14f53b4a
paper_authors.name: Max Tegmark
paper_title: KAN: Kolmogorov-Arnold Networks
paper_summary: 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.
paper_ai_summary: Kolmogorov-Arnold Networks (KANs) outperform Multi-Layer Perceptrons (MLPs) in accuracy and interpretability by using learnable activation functions and spline-based weights.
paper_ai_keywords: Kolmogorov-Arnold Networks KANs Multi-Layer Perceptrons MLPs learnable activation functions spline-based weights neural scaling laws interpretability data fitting PDE solving mathematical laws physical laws