arXiv:2510.06372stat.MLcs.LG2025-10
给出浅层神经网络逼近连续函数所需神经元的通用上界
A General Constructive Upper Bound on Shallow Neural Nets Complexity
- 基于石-维尔斯特定理思路，构造性推导出上界
- 适用于任意紧集上的任意连续函数
- 比已有结果更通用，适合理论研究者
我们给出了浅层神经网络在紧集上以指定精度逼近连续函数所需的神经元数量的上界。该方法受石-维尔斯特定理某证明的启发，具有构造性，且比以往同类上界更通用，可适用于任意连续函数和任意紧集。
原文摘要 · Abstract (English)
We provide an upper bound on the number of neurons required in a shallow neural network to approximate a continuous function on a compact set with a given accuracy. This method, inspired by a specific proof of the Stone-Weierstrass theorem, is constructive and more general than previous bounds of this character, as it applies to any continuous function on any compact set.
神经网络逼近理论上界
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