证明了拓扑空间输入的浅层神经网络可逼近任意连续函数。

On shallow feedforward neural networks with inputs from a topological space

• 将输入扩展到拓扑空间，构建新型浅层神经网络
• 证明其能逼近任意连续函数，实现通用近似
• 为紧致度量空间的柯尔莫哥洛夫叠加定理提供近似形式

我们研究输入来自拓扑空间的前馈神经网络（TFNNs）。证明了浅层TFNNs的通用逼近定理，表明其能够逼近定义在该拓扑空间上的任意连续函数。作为应用，我们得到了紧致度量空间上柯尔莫哥洛夫叠加定理的近似版本。

原文摘要 · Abstract (English)

We study feedforward neural networks with inputs from a topological space (TFNNs). We prove a universal approximation theorem for shallow TFNNs, which demonstrates their capacity to approximate any continuous function defined on this topological space. As an application, we obtain an approximative version of Kolmogorov's superposition theorem for compact metric spaces.

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