Deep belief networks are exact

arXiv:2609.05572v1 Announce Type: cross 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.

Source: arXiv cs.LG | 2026-09-09