{"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/xx-t-can-be-faster","title":"$XX^{t}$ Can Be Faster","arxiv_id":"2505.09814","date":"2025-05-14","proceeding":null,"authors":["Dmitry Rybin","Yushun Zhang","Zhi-Quan Luo"],"abstract":"We present RXTX, a new algorithm for computing the product of matrix by its transpose $XX^{t}$ for $X\\in \\mathbb{R}^{n\\times m}$. RXTX uses $5\\%$ fewer multiplications and $5\\%$ fewer operations (additions and multiplications) than State-of-the-Art algorithms. Note that the accelerations not only holds asymptotically for large matrices with $n \\rightarrow \\infty$, but also for small matrices including $n = 4$. The algorithm was discovered by combining Machine Learning-based search methods with Combinatorial Optimization.","url_abs":"https://arxiv.org/abs/2505.09814v2","url_pdf":"https://arxiv.org/pdf/2505.09814v2.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":"xx-t-can-be-faster","repo_url":"https://github.com/benearnthof/rxtx","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"xx-t-can-be-faster","repo_url":"https://github.com/zhaoolee/garss","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"combinatorial-optimization","task_name":"Combinatorial Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}