On shallow feedforward neural networks with inputs from a topological space

TL;DR

A universal approximation theorem is proved for shallow TFNNs, which demonstrates their capacity to approximate any continuous function defined on this topological space and obtain an approximative version of Kolmogorov's superposition theorem for compact metric spaces.

Abstract

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.