On the universal approximation of real functions with varying domain

TL;DR

This paper provides conditions under which shallow neural networks can approximate any continuous real function on varying domains, using the Gromov-Hausdorff distance to measure domain differences.

Contribution

It extends universal approximation results to functions with varying domains by incorporating the Gromov-Hausdorff distance into the analysis.

Findings

Sufficient conditions for neural network density on varying domains

Application of Gromov-Hausdorff distance in approximation theory

Extension of classical universal approximation theorems

Abstract

We establish sufficient conditions for the density of shallow neural networks \cite{C89} on the family of continuous real functions defined on a compact metric space, taking into account variations in the function domains. For this we use the Gromov-Hausdorff distance defined in \cite{5G}.