A Matrix Multiplication Permutation Law More Suitable for Computers

A Matrix Multiplication Permutation Law More Suitable for Computers | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Physical Sciences - Article A Matrix Multiplication Permutation Law More Suitable for Computers xuzhao peng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6545188/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Matrix multiplication, as the core fundamental operation of AI, has always been a bottleneck in its development due to its high computational complexity. In the 50 years since the Strassen algorithm was proposed, the academic community has been using the laser method under the Coppersmith Winograd tensor decomposition theory framework. The laser method has approached its theoretical limit, and in order to further improve, it is necessary to improve on the original method of the laser method. This study proposes a breakthrough solution, which involves replacing the positions of the elements in the second half of the A and B matrices in advance, recombining the matrices, and then multiplying them together. It has discovered a faster matrix multiplication algorithm, marking the first time we have found a new method outside of the laser method. This will become a new direction for studying fast matrix multiplication. Scientific community and society/Scientific community Physical sciences/Mathematics and computing Matrix multiplication Strassen algorithm laser method permutation method Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6545188","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":449038840,"identity":"28d2798a-0652-43d0-af8d-9b4f105fdd12","order_by":0,"name":"xuzhao peng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxElEQVRIiWNgGAWjYBCDBAYG5gMka2FLIFkLjwFxSs3Zew+/5m2ry+Nv7/l44w2DnZxuAwEtlj3n0ixntrEVS5w5u9lyDkOysdkBAloMbuSYGXxs40lsuJG7TZqH4UDiNoJa7r8xM0hsk0icfyPnGZFabvAYP/jYZpC44UYOG3FaLHtyzBhnnEtI3HjmmLHlHAMi/GLOfsb4M09ZXeK8480Pb7ypsJMj7H1gFErAOBJERQ1QDfMHhBYidIyCUTAKRsHIAwD/FkN6xkxzGQAAAABJRU5ErkJggg==","orcid":"","institution":"Zhengzhou University","correspondingAuthor":true,"prefix":"","firstName":"xuzhao","middleName":"","lastName":"peng","suffix":""}],"badges":[],"createdAt":"2025-04-28 07:45:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6545188/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6545188/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81696468,"identity":"70053aac-1c9b-4b82-ab9a-a4be219017fb","added_by":"auto","created_at":"2025-04-30 12:19:13","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":778094,"visible":true,"origin":"","legend":"","description":"","filename":"Matrixmultiplicationpermutationlaw.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6545188/v1_covered_72359526-fc52-4414-9ac5-defaf1135d69.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"A Matrix Multiplication Permutation Law More Suitable for Computers","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Matrix multiplication, Strassen algorithm, laser method, permutation method","lastPublishedDoi":"10.21203/rs.3.rs-6545188/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6545188/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Matrix multiplication, as the core fundamental operation of AI, has always been a bottleneck in its development due to its high computational complexity. 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