Spatio-Temporal Dimension Reconstruction for Multivariate Time-Series Forecasting

Spatio-Temporal Dimension Reconstruction for Multivariate Time-Series Forecasting | 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 Research Article Spatio-Temporal Dimension Reconstruction for Multivariate Time-Series Forecasting Zhou Shen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9638496/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 Multivariate time-series forecasting requires a model to represent both long-range temporal dynamics and evolving dependencies among variables. Many Transformer forecasters tokenize observations by time step, mixing all variables into a single token and leaving cross-variable structure to be recovered implicitly. This design is often brittle when the graph of variable interactions changes with the temporal context. We present STARFormer, a Transformer architecture that first inverts the time and variable axes, then models temporal and dimensional dependencies in separate attention stages. STARFormer further introduces a dynamic graph module whose adjacency matrices are generated from a small set of learnable orthogonal bases, allowing the spatial structure to adapt while remaining norm-bounded. Experiments on five standard real-world benchmarks, including ETTm1, Weather, ECL, Exchange, and Traffic, show that STARFormer improves over recurrent, graph neural, and Transformer baselines on most forecasting horizons. Ablations indicate that dimension inversion, two-stage attention, and dynamic spatial reconstruction provide complementary gains. Full Text Additional Declarations The authors declare no competing interests. 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-9638496","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":635967403,"identity":"b3c0a929-419a-450d-9199-0f4277d6cfa4","order_by":0,"name":"Zhou Shen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFUlEQVRIiWNgGAWjYDACCSBmbEASMGAH8QwsSNHCcwBESpCiRSIBJo4dyM9uPib5c4dNHoP04cMfPtTckzeXfH51w48CCQb+9u4EbFoY5xxLk+Y9k1bMwJeWJjnjWLHhztk5ZTd7gA6TOHN2AzYtzBI5ZtKMbYcTG3h4zJh52BISDG7npN3gAWoxkMjFqoUNqEXyZ9t/oBb+z5///ANquXkm7eYfPFp4gFokeNsOgGxhAFoH1HKD/dhtfLZISKQlW/O2JSe28bCZSfb2JRhuOJPDdlvGQIIHl1/kZyQfvPmzzS6xn4f58Ycf3xLkDY4ff3bzzR8bOf72XqxaEJ5CcqwBmMSrHA2wPyBF9SgYBaNgFAx/AACORF5UeUjw1AAAAABJRU5ErkJggg==","orcid":"","institution":"Individual","correspondingAuthor":true,"prefix":"","firstName":"Zhou","middleName":"","lastName":"Shen","suffix":""}],"badges":[],"createdAt":"2026-05-07 07:09:50","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9638496/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9638496/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109019178,"identity":"3b9eab9c-0603-4847-9755-b98ae67e38da","added_by":"auto","created_at":"2026-05-11 18:28:22","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":169941,"visible":true,"origin":"","legend":"","description":"","filename":"starformerneurips.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9638496/v1_covered_5bdcf9d7-ac1a-4034-ac6a-c02c8152c0c4.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eSpatio-Temporal Dimension Reconstruction for Multivariate Time-Series Forecasting\u003c/p\u003e","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":"","lastPublishedDoi":"10.21203/rs.3.rs-9638496/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9638496/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMultivariate time-series forecasting requires a model to represent both long-range temporal dynamics and evolving dependencies among variables. 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