{"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/statistical-mechanics-of-low-rank-tensor","title":"Statistical mechanics of low-rank tensor decomposition","arxiv_id":"1810.10065","date":"2018-10-23","proceeding":"NeurIPS 2018 12","authors":["Jonathan Kadmon","Surya Ganguli"],"abstract":"Often, large, high dimensional datasets collected across multiple modalities\ncan be organized as a higher order tensor. Low-rank tensor decomposition then\narises as a powerful and widely used tool to discover simple low dimensional\nstructures underlying such data. However, we currently lack a theoretical\nunderstanding of the algorithmic behavior of low-rank tensor decompositions. We\nderive Bayesian approximate message passing (AMP) algorithms for recovering\narbitrarily shaped low-rank tensors buried within noise, and we employ dynamic\nmean field theory to precisely characterize their performance. Our theory\nreveals the existence of phase transitions between easy, hard and impossible\ninference regimes, and displays an excellent match with simulations. Moreover,\nit reveals several qualitative surprises compared to the behavior of symmetric,\ncubic tensor decomposition. Finally, we compare our AMP algorithm to the most\ncommonly used algorithm, alternating least squares (ALS), and demonstrate that\nAMP significantly outperforms ALS in the presence of noise.","url_abs":"http://arxiv.org/abs/1810.10065v1","url_pdf":"http://arxiv.org/pdf/1810.10065v1.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":"statistical-mechanics-of-low-rank-tensor","repo_url":"https://github.com/ganguli-lab/tensorAMP","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}