{"slug": "deep-belief-networks-are-exact", "title": "Deep belief networks are exact", "summary": "A paper submitted to arXiv on 4 Sep 2026 proves that every strictly positive probability distribution on {-1,1}^n is represented exactly by a sigmoid belief network with finite parameters, answering a question posed by Ilya Sutskever and Geoffrey Hinton. The proof upgrades the pair's earlier probability-sharing approximation to an exact representation using Brouwer's fixed-point theorem.", "body_md": "# Computer Science > Artificial Intelligence\n\n  [Submitted on 4 Sep 2026]\n\n# Title:Deep belief networks are exact\n\n[View PDF](/pdf/2609.05572)\n\n[HTML (experimental)](https://arxiv.org/html/2609.05572v1)\n\nAbstract: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.\n    \n\n### Current browse context:\n\ncs.AI\n\n### References & Citations\n\nLoading...\n\n# Bibliographic and Citation Tools\n\nBibliographic Explorer \n\n*(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer))\nConnected Papers \n\n*(*[What is Connected Papers?](https://www.connectedpapers.com/about))\nLitmaps \n\n*(*[What is Litmaps?](https://www.litmaps.co/))\nscite Smart Citations \n\n*(*[What are Smart Citations?](https://www.scite.ai/))\n# Code, Data and Media Associated with this Article\n\nalphaXiv \n\n*(*[What is alphaXiv?](https://alphaxiv.org/))\nCatalyzeX Code Finder for Papers \n\n*(*[What is CatalyzeX?](https://www.catalyzex.com))\nDagsHub \n\n*(*[What is DagsHub?](https://dagshub.com/))\nGotit.pub \n\n*(*[What is GotitPub?](http://gotit.pub/faq))\nHugging Face \n\n*(*[What is Huggingface?](https://huggingface.co/huggingface))\nScienceCast \n\n*(*[What is ScienceCast?](https://sciencecast.org/welcome))\n# Demos\n\n# Recommenders and Search Tools\n\nInfluence Flower \n\n*(*[What are Influence Flowers?](https://influencemap.cmlab.dev/))\nCORE Recommender \n\n*(*[What is CORE?](https://core.ac.uk/services/recommender))\n# arXivLabs: experimental projects with community collaborators\n\narXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.\n\nBoth individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.\n\nHave an idea for a project that will add value for arXiv's community? [**Learn more about arXivLabs**](https://info.arxiv.org/labs/index.html).", "url": "https://wpnews.pro/news/deep-belief-networks-are-exact", "canonical_source": "https://arxiv.org/abs/2609.05572", "published_at": "2026-09-10 04:00:00+00:00", "updated_at": "2026-09-10 04:21:25.459632+00:00", "lang": "en", "topics": ["artificial-intelligence", "machine-learning", "neural-networks", "ai-research"], "entities": ["arXiv", "Ilya Sutskever", "Geoffrey Hinton", "sigmoid belief network", "Brouwer's fixed-point theorem"], "alternates": {"html": "https://wpnews.pro/news/deep-belief-networks-are-exact", "markdown": "https://wpnews.pro/news/deep-belief-networks-are-exact.md", "text": "https://wpnews.pro/news/deep-belief-networks-are-exact.txt", "jsonld": "https://wpnews.pro/news/deep-belief-networks-are-exact.jsonld"}}