On the expressiveness and spectral bias of KANs

Understand

Kolmogorov-Arnold Networks (KAN) \cite{liu2024kan} were very recently proposed as a potential alternative to the prevalent architectural backbone of many deep learning models, the multi-layer perceptron (MLP).

• KANs have seen success in various tasks of AI for science, with their empirical efficiency and accuracy demostrated in function regression, PDE solving, and many more scientific problems.
• In this article, we revisit the comparison of KANs and MLPs, with emphasis on a theoretical perspective.
• On the one hand, we compare the representation and approximation capabilities of KANs and MLPs.