PreprintCC BY 4.0arXiv
Deep belief networks are exact
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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BibTeX
@misc{smirnov2026deep,
title = {{Deep belief networks are exact}},
author = {Gleb Smirnov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05572},
eprint = {2609.05572},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05572},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Deep belief networks are exact
AU - Gleb Smirnov
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05572
UR - https://arxiv.org/abs/2609.05572
AB - 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.
ER -