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
Kolmogorov-Arnold Networks (KANs) replace fixed activations in deep architectures with learnable univariate edge functions, making the choice of edge parametrisation central. Existing variants rely on...
arXiv:2608. 00737v1 Announce Type: new Abstract: Hard-constrained recurrent physics-informed networks (HRPINNs) embed known dynamics inside a recurrent numerical integrator and restrict a neural branch to learning only the residual dynamics that the first-principles model does not capture.
By Enzo Nicolas Spotorno, Josafat Leal Filho
arXiv:2608. 25807v1 Announce Type: new Abstract: Kolmogorov-Arnold Networks (KANs) replace fixed activations in deep architectures with learnable univariate edge functions, making the choice of edge parametrisation central.
By K S Sesh Kumar
The paper introduces Mixture of Activations (MoA), a token‑adaptive feedforward network design that mixes multiple activation functions using lightweight gates while sharing linear projections. It also presents learnable activations (LA) as an input‑independent variant. The authors theoretically prove that MoA strictly surpasses both fixed‑activation FFNs and LA in expressive power, and empirically demonstrate that MoA achieves lower loss and better scaling on dense and MoE language models from 0.12 B to 2 B parameters with minimal overhead.
By Mingze Wang, Jinbo Wang, Yikuan Xia, Kai Shen, Shu Zhong
arXiv:2609.32503v2 Announce Type: replace
Abstract: Kolmogorov-Arnold Networks (KANs) are motivated in part by interpretability: their learned edge functions can be inspected, pruned, and reduced to...
By Ami Tavory, Meir Feder
arXiv:2609.26067v1 Announce Type: new
Abstract: Kolmogorov--Arnold Networks (KANs) replace scalar edge weights with learnable univariate functions, increasing flexibility but also parameter memory be...
By Kazi Ahmed Asif Fuad, Lizhong Chen