On shallow feedforward neural networks with inputs from a topological space

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.

Major revision (14 pages): improved exposition, expanded references, and additional subsections

References in corpus (3)

• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• On the approximation by single hidden layer feedforward neural networks with fixed weights
• Approximation capability of two hidden layer feedforward neural networks with fixed weights