{"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/a-new-linear-time-bi-level-ell-1-infty","title":"A new Linear Time Bi-level $\\ell_{1,\\infty}$ projection ; Application to the sparsification of auto-encoders neural networks","arxiv_id":"2407.16293","date":"2024-07-23","proceeding":null,"authors":["Michel Barlaud","Guillaume Perez","Jean-Paul Marmorat"],"abstract":"The $\\ell_{1,\\infty}$ norm is an efficient-structured projection, but the complexity of the best algorithm is, unfortunately, $\\mathcal{O}\\big(n m \\log(n m)\\big)$ for a matrix $n\\times m$.\\\\ In this paper, we propose a new bi-level projection method, for which we show that the time complexity for the $\\ell_{1,\\infty}$ norm is only $\\mathcal{O}\\big(n m \\big)$ for a matrix $n\\times m$. Moreover, we provide a new $\\ell_{1,\\infty}$ identity with mathematical proof and experimental validation. Experiments show that our bi-level $\\ell_{1,\\infty}$ projection is $2.5$ times faster than the actual fastest algorithm and provides the best sparsity while keeping the same accuracy in classification applications.","url_abs":"https://arxiv.org/abs/2407.16293v1","url_pdf":"https://arxiv.org/pdf/2407.16293v1.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":"a-new-linear-time-bi-level-ell-1-infty","repo_url":"https://github.com/MichelBarlaud/SAE-Supervised-Autoencoder-Omics","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}