Meta-Regularization Selection: An Optimization Framework for Dynamic Regularization in Deep Neural Networks

Meta-Regularization Selection: An Optimization Framework for Dynamic Regularization in Deep Neural Networks | 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 Meta-Regularization Selection: An Optimization Framework for Dynamic Regularization in Deep Neural Networks Weihao Liu, Xinyue Tang, Zhirong Meng, Lianhua Gao, Zhou Shen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8208845/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 In this paper, we propose a novel optimization framework for dynamic regularization in deep neural networks, termed meta-regularization selection. Traditional regularization techniques often impose fixed constraints that can hinder model adaptability and generalization. Our approach addresses this limitation by formulating meta-regularization selection as a nested bi-level optimization problem, allowing both the type and strength of regularization strategies to be continuously optimized throughout training. We rigorously establish the mathematical foundations of this framework, ensuring its existence and convergence under specific conditions. Our extensive experimental validation demonstrates that the proposed method significantly enhances generalization performance across various benchmarks compared to static and hand-tuned regularization approaches. By enabling real-time adaptive adjustments to regularization techniques, our framework not only improves model robustness but also unlocks new potentials for efficient learning in complex environments. This research represents a significant step forward in deep learning, offering insights into the dynamic interplay between model parameters and regularization strategies that can lead to better-performing neural networks. meta-regularization bi-level optimization dynamic regularization deep learning generalization hyperparameter optimization 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-8208845","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":550922689,"identity":"698be8ec-c858-431a-a255-c6320a4e4ce9","order_by":0,"name":"Weihao Liu","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Weihao","middleName":"","lastName":"Liu","suffix":""},{"id":550922690,"identity":"cff6ceb8-a267-4f1c-8e0f-914d7dc8ad85","order_by":1,"name":"Xinyue Tang","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Xinyue","middleName":"","lastName":"Tang","suffix":""},{"id":550922691,"identity":"38904049-75c3-4e4c-8f55-4512bb30c1b4","order_by":2,"name":"Zhirong Meng","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Zhirong","middleName":"","lastName":"Meng","suffix":""},{"id":550922692,"identity":"311a7318-2de7-4f0e-a9b4-2ad79eaabf2b","order_by":3,"name":"Lianhua Gao","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Lianhua","middleName":"","lastName":"Gao","suffix":""},{"id":550922693,"identity":"eea29b1c-08da-40f9-bf9f-e7a12382210e","order_by":4,"name":"Zhou Shen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFElEQVRIiWNgGAWjYDACCSBmbEASMGAH8QwsSNHCcwBESpCiRSIBJo4dyM9uPvbw5w6bxAbpw4c/fKi5J28u+fzqhh8FEgz87d0J2LQY3DmWbiB5Ji2xgS8tTXLGsWLDnbNzym72AB0mcebsBqxaJHLMJAzbDic28PCYMfOwJSQY3M5Ju8ED1GIgkYtVi/yM/G8SiWAt/J8///kH1HLzTNrNP3i0MNzIYZM4CLGFQZqxDajlBvux2/hsMbiRZibZ2JZm3MbDZibZ25dguOFMDtttGQMJHlx+kZ+R/EzyZ5uNbD8P8+MPP74lyBscP/7s5ps/NnL87b3YHQYDbAgmjwGYxKscDbA/IEX1KBgFo2AUDH8AAA8DYpsNUdNBAAAAAElFTkSuQmCC","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Zhou","middleName":"","lastName":"Shen","suffix":""}],"badges":[],"createdAt":"2025-11-26 05:25:58","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-8208845/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8208845/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96886547,"identity":"281fbe22-4b5e-4bd5-a9bf-971a688afb6b","added_by":"auto","created_at":"2025-11-27 08:24:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":229585,"visible":true,"origin":"","legend":"","description":"","filename":"paper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8208845/v1_covered_09b23e3f-6d4e-427a-98f2-3b8664439f18.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eMeta-Regularization Selection: An Optimization Framework for Dynamic Regularization in Deep Neural Networks\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":"meta-regularization, bi-level optimization, dynamic regularization, deep learning, generalization, hyperparameter optimization","lastPublishedDoi":"10.21203/rs.3.rs-8208845/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8208845/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we propose a novel optimization framework for dynamic regularization in deep neural networks, termed meta-regularization selection. 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