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Sigmoid belief networks proven to exactly represent probability distributions

By PulseAugur Editorial · [1 sources] ·

A new paper published on arXiv demonstrates that sigmoid belief networks can precisely represent any strictly positive probability distribution on a binary set. This finding resolves a long-standing question posed by researchers Sutskever and Hinton. The proof utilizes Brouwer's fixed-point theorem to enhance a previous approximation method into an exact representation. AI

IMPACT This research provides a theoretical foundation for understanding the representational capacity of certain neural network architectures.

RANK_REASON Academic paper published on arXiv detailing a mathematical proof. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.AI →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Sigmoid belief networks proven to exactly represent probability distributions

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Academic paper published on arXiv detailing a mathematical proof. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.AI TIER_1 Nederlands(NL) · Gleb Smirnov ·

    Deep belief networks are exact

    arXiv:2609.05572v1 Announce Type: new 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 pr…

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