A note on Cybenko's Universal Approximation Theorem
Classical Analysis and ODEs
2025-12-08 v2 Neural and Evolutionary Computing
Abstract
In this short note, we point out a mistake in G.Cybenko's proof of his version of the universal approximation theorem which has been widely cited. This mistake might not be easily fixable along the idea of his proof and it also leads to an interesting question in measure theory.
Keywords
Cite
@article{arxiv.2508.18893,
title = {A note on Cybenko's Universal Approximation Theorem},
author = {Kun Wang},
journal= {arXiv preprint arXiv:2508.18893},
year = {2025}
}
Comments
The error in Cybenko's paper pointed out by this note has already been addressed by Cybenko himself in an erratum published in MCSS