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:2606. 02936v1 Announce Type: new Abstract: In this manuscript, we propose and analyze hierarchical Kolmogorov--Arnold neural network architectures employing radial basis functions as activation functions for approximating deterministic functions and random field models.
By Mingtao Xia, Qijing Shen
arXiv:2606. 22984v2 Announce Type: replace-cross Abstract: Efficient sampling of the Boltzmann distribution in frustrated spin glasses is central to statistical mechanics and combinatorial optimization.
By Lu Zhong, Wenli Duan, Jing Liu, Pan Zhang, Ying Tang
arXiv:2209. 01432v4 Announce Type: replace-cross Abstract: In this paper we study probabilistic and neural network approximations for solutions to Poisson equation subject to Holder data in general bounded domains of $\mathbb{R}^d$.
By Lucian Beznea, Iulian Cimpean, Oana Lupascu-Stamate, Ionel Popescu, Arghir Zarnescu
arXiv:2606. 09434v1 Announce Type: new Abstract: The Fokker-Planck equation (FPE) plays a pivotal role in describing the time evolution of probability density functions (PDFs) for systems governed by stochastic dynamics.
By Li Zeng, Xiaoliang Wan, Yaobin Wang, Fabio Nobile, Tao Zhou
arXiv:2508. 11522v4 Announce Type: replace Abstract: Neural tangent kernels (NTKs) are a powerful tool for analyzing deep, non-linear neural networks.
By Max Guillen, Philipp Misof, Jan E. Gerken