# Deep belief networks are exact

arXiv: https://arxiv.org/abs/2609.05572 · HTML: https://mlsanity.com/paper/2609.05572/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 8 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Builds on (most cited first, 1 of 1)

- [Stochastic Feedforward Neural Networks: Universal Approximation](https://mlsanity.com/paper/1910.09763/) (2019)

## Abstract (arXiv)

We prove that every strictly positive probability distribution on (-1,1n) is represented exactly by a sigmoid belief network with finite parameters. This answers a question of Sutskever and Hinton. The proof upgrades their probability-sharing approximation to exact representation using Brouwer's fixed-point theorem.