# An elementary proof of a universal approximation theorem

arXiv: https://arxiv.org/abs/2406.10002 · HTML: https://mlsanity.com/paper/2406.10002/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 3 references that are in the map.
- First posted on arXiv 14 Jun 2024.

## Built on by (most cited first, 1 of 1)

- [Geometric separation and constructive universal approximation with two hidden layers](https://mlsanity.com/paper/2602.12482/) (2026)

## Abstract (arXiv)

In this short note, we give an elementary proof of a universal approximation theorem for neural networks with three hidden layers and increasing, continuous, bounded activation function. The result is weaker than the best known results, but the proof is elementary in the sense that no machinery beyond undergraduate analysis is used.