{"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/irls-and-slime-mold-equivalence-and","title":"IRLS and Slime Mold: Equivalence and Convergence","arxiv_id":"1601.02712","date":"2016-01-12","proceeding":null,"authors":["Damian Straszak","Nisheeth K. Vishnoi"],"abstract":"In this paper we present a connection between two dynamical systems arising\nin entirely different contexts: one in signal processing and the other in\nbiology. The first is the famous Iteratively Reweighted Least Squares (IRLS)\nalgorithm used in compressed sensing and sparse recovery while the second is\nthe dynamics of a slime mold (Physarum polycephalum). Both of these dynamics\nare geared towards finding a minimum l1-norm solution in an affine subspace.\nDespite its simplicity the convergence of the IRLS method has been shown only\nfor a certain regularization of it and remains an important open problem. Our\nfirst result shows that the two dynamics are projections of the same dynamical\nsystem in higher dimensions. As a consequence, and building on the recent work\non Physarum dynamics, we are able to prove convergence and obtain complexity\nbounds for a damped version of the IRLS algorithm.","url_abs":"http://arxiv.org/abs/1601.02712v1","url_pdf":"http://arxiv.org/pdf/1601.02712v1.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":"irls-and-slime-mold-equivalence-and","repo_url":"https://github.com/DamianStraszak/IRLS-and-Physarum-Dynamics","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"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}