{"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/flip-graphs-with-symmetry-and-new-matrix","title":"Flip Graphs with Symmetry and New Matrix Multiplication Schemes","arxiv_id":"2502.04514","date":"2025-02-06","proceeding":null,"authors":["Jakob Moosbauer","Michael Poole"],"abstract":"The flip graph algorithm is a method for discovering new matrix multiplication schemes by following random walks on a graph. We introduce a version of the flip graph algorithm for matrix multiplication schemes that admit certain symmetries. This significantly reduces the size of the search space, allowing for more efficient exploration of the flip graph. The symmetry in the resulting schemes also facilitates the process of lifting solutions from $F_2$ to $\\mathbb{Z}$. Our results are new schemes for multiplying $5\\times 5$ matrices using $93$ multiplications and $6\\times 6$ matrices using $153$ multiplications over arbitrary ground fields.","url_abs":"https://arxiv.org/abs/2502.04514v1","url_pdf":"https://arxiv.org/pdf/2502.04514v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"flip-graphs-with-symmetry-and-new-matrix","repo_url":"https://github.com/jakobmoosbauer/symmetric-flips","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"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}