Convolutional Kolmogorov--Arnold Networks (KANs) replace the fixed weights of a convolutional kernel with learnable univariate functions. The dominant formulation attaches one such function to every kernel entry and lets it act on pixel values, expressive but parameter-heavy and prone to overfitting.
arXiv:2608. 00859v1 Announce Type: new Abstract: Kolmogorov--Arnold Networks (KANs) replace scalar edge weights with learnable univariate functions parameterized by multiple basis coefficients.
By Kazi Ahmed Asif Fuad, Lizhong Chen
The paper studies Kolmogorov‑Arnold Networks (KANs), a neural architecture that treats activation functions as learnable components, offering improved interpretability for scientific applications. It investigates how KANs scale with dataset size on image classification tasks (MNIST, Fashion‑MNIST) and a magnetic‑parameter regression task, revealing a broken neural scaling law that transitions from a faster to a slower decay of test loss as data grows. The authors also analyze how the learned activation functions evolve from simple linear approximations to more complex, interpretable symbolic forms as more data is provided.
By Tilen Cadez, Sanghoon Lee, Kyoung-Min Kim
arXiv:2604. 21174v3 Announce Type: replace-cross Abstract: Kolmogorov-Arnold Networks (KANs) replace fixed activations with learnable univariate edge functions whose behavior depends strongly on the chosen basis.
By Amir Noorizadegan, Sifan Wang, Leevan Ling
arXiv:2512. 09084v3 Announce Type: replace Abstract: The Kolmogorov-Arnold representation theorem offers a theoretical alternative to Multi-Layer Perceptrons (MLPs) by placing learnable univariate functions on edges rather than nodes.
By Oscar Eliasson
arXiv:2607. 15525v1 Announce Type: cross Abstract: Kolmogorov--Arnold Networks (KANs) replace fixed node activations with learned one-dimensional edge functions, offering an explicit interface for interpretation and a possible alternative to transformer feed-forward networks.
By Felippe Alves, Renato Vicente