English

A three layer neural network can represent any multivariate function

Machine Learning 2022-01-19 v2 Functional Analysis Machine Learning

Abstract

In 1987, Hecht-Nielsen showed that any continuous multivariate function can be implemented by a certain type three-layer neural network. This result was very much discussed in neural network literature. In this paper we prove that not only continuous functions but also all discontinuous functions can be implemented by such neural networks.

Cite

@article{arxiv.2012.03016,
  title  = {A three layer neural network can represent any multivariate function},
  author = {Vugar Ismailov},
  journal= {arXiv preprint arXiv:2012.03016},
  year   = {2022}
}

Comments

9 pages; a few references added

R2 v1 2026-06-23T20:45:04.094Z