{"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/equivalence-of-restricted-boltzmann-machines","title":"Equivalence of restricted Boltzmann machines and tensor network states","arxiv_id":"1701.04831","date":"2017-01-17","proceeding":null,"authors":["Jing Chen","Song Cheng","Haidong Xie","Lei Wang","Tao Xiang"],"abstract":"The restricted Boltzmann machine (RBM) is one of the fundamental building\nblocks of deep learning. RBM finds wide applications in dimensional reduction,\nfeature extraction, and recommender systems via modeling the probability\ndistributions of a variety of input data including natural images, speech\nsignals, and customer ratings, etc. We build a bridge between RBM and tensor\nnetwork states (TNS) widely used in quantum many-body physics research. We\ndevise efficient algorithms to translate an RBM into the commonly used TNS.\nConversely, we give sufficient and necessary conditions to determine whether a\nTNS can be transformed into an RBM of given architectures. Revealing these\ngeneral and constructive connections can cross-fertilize both deep learning and\nquantum many-body physics. Notably, by exploiting the entanglement entropy\nbound of TNS, we can rigorously quantify the expressive power of RBM on complex\ndata sets. Insights into TNS and its entanglement capacity can guide the design\nof more powerful deep learning architectures. On the other hand, RBM can\nrepresent quantum many-body states with fewer parameters compared to TNS, which\nmay allow more efficient classical simulations.","url_abs":"http://arxiv.org/abs/1701.04831v2","url_pdf":"http://arxiv.org/pdf/1701.04831v2.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":"equivalence-of-restricted-boltzmann-machines","repo_url":"https://github.com/yzcj105/rbm2mps","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"},{"task_slug":"recommendation-systems","task_name":"Recommendation Systems"}],"methods":[{"method_slug":"restricted-boltzmann-machine","method_name":"Restricted Boltzmann Machine"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1701.04831","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}