kolmogorov-arnold-networks-kans--24e6ad49·3 events·first seen Aliases: Kolmogorov-Arnold Networks (KANs), Kolmogorov-Arnold Networks
Researchers introduce KANEx, a framework that leverages the symbolic transparency of Kolmogorov-Arnold Networks (KANs) to produce more faithful textual and visual explanations for chest X-ray classifiers. The system includes KAN-Map, a novel heatmap method derived directly from KAN model structure rather than gradient approximations, which feeds grounded context into downstream Vision-Language Models. Benchmarked on MIMIC-CXR, KAN-based architectures with ResNet/ViT backbones show a 10% improvement in visual localization and downstream reasoning quality over baseline approaches. The work positions mathematically interpretable architectural units as a path toward clinician-trustworthy medical AI.
Researchers propose PG-KINN, a physics-informed neural network that combines Kolmogorov-Arnold Networks (KANs) as the trial space with an independent piecewise-polynomial test space under a Petrov-Galerkin weak formulation. The approach uses integration by parts and Gauss-Legendre quadrature to reduce differentiation order and improve conditioning, enabling application to non-self-adjoint, nonlinear, and inverse problems where energy-form methods fail. On benchmarks including crack singularities, hyperelasticity, and inverse parameter identification, PG-KINN outperforms both MLP-based physics-informed networks and KAN-based strong/energy-form alternatives (PIKAN).
This arxiv survey reviews four decades of universal approximation theory for feedforward neural networks, covering classical density results for single-hidden-layer networks and quantitative bounds relating approximation error to network size and target function smoothness. It gives particular emphasis to depth-width trade-offs and the parameter efficiency advantages of deeper architectures for structured function classes. The survey also covers recent theoretical developments on Kolmogorov-Arnold Networks (KANs) as an alternative architectural paradigm with emerging approximation-theoretic analysis.