{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/geometry-of-the-restricted-boltzmann-machine","title":"Geometry of the restricted Boltzmann machine","arxiv_id":"0908.4425","date":"2009-08-30","proceeding":null,"authors":["Maria Angelica Cueto","Jason Morton","Bernd Sturmfels"],"abstract":"The restricted Boltzmann machine is a graphical model for binary random\nvariables. Based on a complete bipartite graph separating hidden and observed\nvariables, it is the binary analog to the factor analysis model. We study this\ngraphical model from the perspectives of algebraic statistics and tropical\ngeometry, starting with the observation that its Zariski closure is a Hadamard\npower of the first secant variety of the Segre variety of projective lines. We\nderive a dimension formula for the tropicalized model, and we use it to show\nthat the restricted Boltzmann machine is identifiable in many cases. Our\nmethods include coding theory and geometry of linear threshold functions.","url_abs":"http://arxiv.org/abs/0908.4425v1","url_pdf":"http://arxiv.org/pdf/0908.4425v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"geometry-of-the-restricted-boltzmann-machine","repo_url":"https://github.com/Kevin-Sean-Chen/Restriced_Boltzmann_Machine","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"geometry-of-the-restricted-boltzmann-machine","repo_url":"https://github.com/echen/restricted-boltzmann-machines","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"restricted-boltzmann-machine","method_name":"Restricted Boltzmann Machine"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}