Enhancing Neural Function Approximation: The XNet Outperforming KAN
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929715207471104 |
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| author | Li, Xin Zheng, Xiaotao Xia, Zhihong |
| author_facet | Li, Xin Zheng, Xiaotao Xia, Zhihong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18959 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enhancing Neural Function Approximation: The XNet Outperforming KAN Li, Xin Zheng, Xiaotao Xia, Zhihong Machine Learning Artificial Intelligence 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. |
| title | Enhancing Neural Function Approximation: The XNet Outperforming KAN |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2501.18959 |