Deep belief networks are exact

Gleb Smirnov

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arXiv · 2609.05572

Deep belief networks are exact

Gleb Smirnov

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Abstract

We prove that every strictly positive probability distribution on \(\{-1,1\}^n\) 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.

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Gleb Smirnov. 2026-09-04. Deep belief networks are exact. https://arxiv.org/abs/2609.05572

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