Dysformer: A Spatial-Spectral Dual-Stream Dynamic Hyperbolic Hypergraph Transformer

Dysformer: A Spatial-Spectral Dual-Stream Dynamic Hyperbolic Hypergraph Transformer | 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 Article Dysformer: A Spatial-Spectral Dual-Stream Dynamic Hyperbolic Hypergraph Transformer Hao Wu, Zhangyu Mei, Shuang Wu, Xiangren Yi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8513633/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Graph representation learning has become a fundamental paradigm for modeling and analyzing complex structured data. In principle, the geometry of the embedding space should be well-aligned with the intrinsic structure of the underlying data to minimize representational distortion. However, most existing methods rely on Euclidean geometry and static graph topologies, which severely limit their ability to capture the hierarchical organization and higher-order dependencies that are prevalent in real-world networks. In addition, deep graph neural networks often suffer from the oversmoothing problem, where node representations become increasingly indistinguishable as network depth grows. To overcome these limitations, we propose Dysformer, a novel spatial–spectral dual-stream fusion framework for graph representation learning. Dysformer integrates a dynamic node–hyperedge–node message-passing mechanism with a Hyperbolic Graph Wavelet Transform, enabling the joint modeling of high-order relational structures and multi-scale spectral information. An adaptive geometric gating mechanism is further introduced to fuse global hierarchical topology with fine-grained local geometric features. Moreover, we design a Dynamic Trainable Curvature Regulation module that allows layer-wise geometric adaptation, enabling the curvature of the hyperbolic manifold to dynamically align with the semantic granularity of features across network depths. Extensive experiments on benchmark datasets demonstrate that Dysformer consistently and substantially outperforms both hyperbolic and Euclidean state-of-the-art baselines. Furthermore, when applied to real-world clinical data, Dysformer effectively disentangles key determinants of anxiety and depression, offering robust data-driven insights to support targeted socio-medical interventions. Physical sciences/Mathematics and computing/Computer science Physical sciences/Mathematics and computing/Computational science Hyperbolic geometry Dynamic hypergraph Graph representation learning Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Under Review 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-8513633","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":583482617,"identity":"9e1b9fc0-03d1-4ff1-9c97-73a7a76a213f","order_by":0,"name":"Hao Wu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAr0lEQVRIiWNgGAWjYBACAzBZwcDYAKQkSNByhmQtjG2kaDFnP3xMmndeneyGA8wHb/Mw2OUR1GLZk5YmzbvtsPGGA2zJ1jwMycWEHXYgx+w277YDiRsO8JhJ8zAcSGwgqOX8G6CWOXVALfzfiNRyA2RLAzPIFjZitTxL/znn2GHjmYfZjC3nGCQT47DkwwZvaupk+443P7zxpsKOsBYEYAabQLz6UTAKRsEoGAV4AABwOjzgYvUN6wAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-2340-9258","institution":"Shandong University","correspondingAuthor":true,"prefix":"","firstName":"Hao","middleName":"","lastName":"Wu","suffix":""},{"id":583482618,"identity":"40c9c88c-4046-44b5-8ff0-16d72d5bba1f","order_by":1,"name":"Zhangyu Mei","email":"","orcid":"https://orcid.org/0009-0000-0172-7832","institution":"Shandong University","correspondingAuthor":false,"prefix":"","firstName":"Zhangyu","middleName":"","lastName":"Mei","suffix":""},{"id":583482619,"identity":"7d312ca3-3684-4f1a-a83c-195dd38f6f18","order_by":2,"name":"Shuang Wu","email":"","orcid":"","institution":"Jining University","correspondingAuthor":false,"prefix":"","firstName":"Shuang","middleName":"","lastName":"Wu","suffix":""},{"id":583482620,"identity":"f09afe47-f9f0-4344-8ff9-0eeb2f9fc7ed","order_by":3,"name":"Xiangren Yi","email":"","orcid":"","institution":"Department of Sport and Health, School of Physical Education, Shandong University, Jinan, China","correspondingAuthor":false,"prefix":"","firstName":"Xiangren","middleName":"","lastName":"Yi","suffix":""}],"badges":[],"createdAt":"2026-01-04 14:15:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8513633/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8513633/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102298107,"identity":"d6f1e6d1-a219-4d37-9138-29e165b5bba6","added_by":"auto","created_at":"2026-02-10 10:30:40","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8336939,"visible":true,"origin":"","legend":"Article File","description":"","filename":"main.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8513633/v1_covered_61bb12fc-94b0-46c3-942c-25d5414695a5.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Dysformer: A Spatial-Spectral Dual-Stream Dynamic Hyperbolic Hypergraph Transformer","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"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":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Hyperbolic geometry, Dynamic hypergraph, Graph representation learning","lastPublishedDoi":"10.21203/rs.3.rs-8513633/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8513633/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Graph representation learning has become a fundamental paradigm for modeling and analyzing complex structured data. 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