arXiv:2504.02321 · v3

On shallow feedforward neural networks with inputs from a topological space

首次提交 2025-04-03 14:48

版本更新 2026-10-26 22:08

雷达观测 2026-10-29 00:35

摘要

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.

作者备注：Published version with two minor corrections. Namely, in Theorem 2.1, C(K) was replaced with C(X), and in the proof of Proposition 2.1, the formula for τ(t) was corrected. The results remain unchanged

期刊信息：V.E. Ismailov, Ann. Math. Artif. Intell. (2026)