# Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach

arXiv: https://arxiv.org/abs/1907.11457 · HTML: https://mlsanity.com/paper/1907.11457/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2019.

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

- [A Theoretical Study of Neural Network Expressive Power via Manifold Topology](https://mlsanity.com/paper/2410.16542/) (2024)

## Abstract (arXiv)

It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network which approximates the function. Such result proves the existence, but it does not provide a method for finding it. In this paper, a constructive approach to the proof of this property is given for the case of two-hidden-layer feedforward networks. This approach is based on an approximation of continuous functions by simplicial maps. Once a triangulation of the space is given, a concrete architecture and set of weights can be obtained. The quality of the approximation depends on the refinement of the covering of the space by simplicial complexes.