Deep belief networks are exact
cs.AI, cs.LG, math.PR
Submitted: 2026-09-04
Updated: 2026-09-04
Comments: 6 pages
License: http://creativecommons.org/licenses/by/4.0/
The gist: We prove that every strictly positive probability distribution on-1,1 n is represented exactly by a sigmoid belief network with finite parameters.
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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