# A three layer neural network can represent any multivariate function

arXiv: https://arxiv.org/abs/2012.03016 · HTML: https://mlsanity.com/paper/2012.03016/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2020.

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## Abstract (arXiv)

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.