{"paper_id":"0ffcb506-5536-4ab0-a10a-eefe058f1c97","body_text":"Phase Transition in Binary Compressed Sensing via Annealing with Adaptive Regularization | 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 Phase Transition in Binary Compressed Sensing via Annealing with Adaptive Regularization Xiaoxin Huang, Masayuki Ohzeki This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8736696/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 Compressive sensing (CS) is a signal processing technique used to reconstruct sparse signals from significantly fewer measurements than traditionally required. While CS has been extensively studied for continuous signals, many practical applications in digital communications and sensor networks involve signals that are inherently binary. This specialization, known as binary compressed sensing (BCS), has recently been reformulated as a quadratic unconstrained binary optimization (QUBO) problem to leverage the power of annealing-based optimizers. However, the reconstruction performance of QUBO-based BCS is highly sensitive to the regularization parameter, and a principled selection strategy remains an open challenge. In this work, we demonstrate that using a fixed regularization parameter fails to produce consistent phase transition behavior across different sampling and sparsity regimes. By revealing that the optimal parameter follows a structured, instance-dependent pattern, we propose a learning-based framework to predict near-optimal values directly from problem characteristics. Numerical experiments show that our adaptive regularization stabilizes phase transitions under simulated annealing and transfers effectively to quantum annealing solvers. Binary image reconstruction experiments further confirm its practical advantages over fixed-parameter baselines, providing a scalable pathway toward reliable annealing-based signal reconstruction. 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. 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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-8736696\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":582786550,\"identity\":\"f96c4514-d39e-4bd4-941d-bb5efb964fd3\",\"order_by\":0,\"name\":\"Xiaoxin Huang\",\"email\":\"data:image/png;base64,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\",\"orcid\":\"\",\"institution\":\"Tohoku University\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Xiaoxin\",\"middleName\":\"\",\"lastName\":\"Huang\",\"suffix\":\"\"},{\"id\":582786844,\"identity\":\"0710a386-52dd-4168-b08a-9f62ee8f9eb6\",\"order_by\":1,\"name\":\"Masayuki Ohzeki\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Tohoku University / Institute of Science Tokyo\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Masayuki\",\"middleName\":\"\",\"lastName\":\"Ohzeki\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2026-01-30 03:53:23\",\"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-8736696/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-8736696/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":101752966,\"identity\":\"6feaab66-108b-4966-99fa-e4953614b9c6\",\"added_by\":\"auto\",\"created_at\":\"2026-02-03 10:38:31\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":744667,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"PhaseTransitioninBinaryCompressedSensingviaAnnealingwithAdaptiveRegularization.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-8736696/v1_covered_346d8a8b-3c55-4311-a450-13ca98940667.pdf\"}],\"financialInterests\":\"The authors declare no competing interests.\",\"formattedTitle\":\"\\u003cp\\u003ePhase Transition in Binary Compressed Sensing via Annealing with Adaptive Regularization\\u003c/p\\u003e\",\"fulltext\":[],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":false,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":true,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"Tohoku University\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":true,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":true,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"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-8736696/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-8736696/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eCompressive sensing (CS) is a signal processing technique used to reconstruct sparse signals from significantly fewer measurements than traditionally required. 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