Enhancing Neural Function Approximation: The XNet Outperforming KAN
Abstract
XNet is a single-layer neural network architecture that leverages Cauchy integral-based activation functions for high-order function approximation. Through theoretical analysis, we show that the Cauchy activation functions used in XNet can achieve arbitrary-order polynomial convergence, fundamentally outperforming traditional MLPs and Kolmogorov-Arnold Networks (KANs) that rely on increased depth or B-spline activations. Our extensive experiments on function approximation, PDE solving, and reinforcement learning demonstrate XNet's superior performance - reducing approximation error by up to 50000 times and accelerating training by up to 10 times compared to existing approaches. These results establish XNet as a highly efficient architecture for both scientific computing and AI applications.
Cite
@article{arxiv.2501.18959,
title = {Enhancing Neural Function Approximation: The XNet Outperforming KAN},
author = {Xin Li and Xiaotao Zheng and Zhihong Xia},
journal= {arXiv preprint arXiv:2501.18959},
year = {2025}
}
Comments
arXiv admin note: text overlap with arXiv:2410.02033