Universal approximation of continuous maps between topological vector spaces

Abstract

We study the problem of universal approximation of continuous maps between topological vector spaces by neural networks. We provide a universal approximation theorem for maps between locally convex topological vector spaces with and without paracompactness assumptions. We extend this result to continuous maps between non-locally convex topological vector spaces on compact sets under the assumption of finite topological dimension.

arXiv comment8 pages. Comments are welcome! v2: various typos have been corrected, and Theorem 4.2 has been improved by removing two unnecessary hypotheses