On shallow feedforward neural networks with inputs from a topological space
Machine Learning
2026-01-23 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.2504.02321,
title = {On shallow feedforward neural networks with inputs from a topological space},
author = {Vugar Ismailov},
journal= {arXiv preprint arXiv:2504.02321},
year = {2026}
}
Comments
Major revision (14 pages): improved exposition, expanded references, and additional subsections