Enhancing Neural Function Approximation: The XNet Outperforming KAN

Xin Li; Xiaotao Zheng; Zhihong Xia

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arXiv · 2501.18959

Enhancing Neural Function Approximation: The XNet Outperforming KAN

Xin Li·Xiaotao Zheng·Zhihong Xia

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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.

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Xin Li, Xiaotao Zheng, Zhihong Xia. 2025-01-31. Enhancing Neural Function Approximation: The XNet Outperforming KAN. https://arxiv.org/abs/2501.18959

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