[2601.18672] A Dynamic Framework for Grid Adaptation in Kolmogorov-Arnold Networks

Computer Science > Machine Learning arXiv:2601.18672 (cs) [Submitted on 26 Jan 2026 (v1), last revised 30 Mar 2026 (this version, v2)] Title:A Dynamic Framework for Grid Adaptation in Kolmogorov-Arnold Networks Authors:Spyros Rigas, Thanasis Papaioannou, Panagiotis Trakadas, Georgios Alexandridis View a PDF of the paper titled A Dynamic Framework for Grid Adaptation in Kolmogorov-Arnold Networks, by Spyros Rigas and 3 other authors View PDF HTML (experimental) Abstract:Kolmogorov-Arnold Networks (KANs) have recently demonstrated promising potential in scientific machine learning, partly due to their capacity for grid adaptation during training. However, existing adaptation strategies rely solely on input data density, failing to account for the geometric complexity of the target function or metrics calculated during network training. In this work, we propose a generalized framework that treats knot allocation as a density estimation task governed by Importance Density Functions (IDFs), allowing training dynamics to determine grid resolution. We introduce a curvature-based adaptation strategy and evaluate it across synthetic function fitting, regression on a subset of the Feynman dataset and different instances of the Helmholtz PDE, demonstrating that it significantly outperforms the standard input-based baseline. Specifically, our method yields average relative error reductions of 25.3% on synthetic functions, 9.4% on the Feynman dataset, and 23.3% on the PDE benchmark. St...