Optimal Neural Network Repair: A Principled Approach to Achieving the Theoretical Limits of Structural Restoration

Optimal Neural Network Repair: A Principled Approach to Achieving the Theoretical Limits of Structural Restoration | 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 Optimal Neural Network Repair: A Principled Approach to Achieving the Theoretical Limits of Structural Restoration José Ignacio Peinador Sala This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7926139/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 This work frames the post-pruning repair of neural networks as a fundamental graph connectivity problem and empirically validates its theoretical limit: the minimum number of connections required to restore structural integrity is exactly equal to the number of disconnected fragments. Through large-scale experiments (850 neurons, >85,000 connections) under aggressive 85% random pruning, our proposed Component Fusion algorithm achieves this theoretical limit with perfect consistency (100% success rate across 100 replications). In stark contrast, heuristic baseline methods fail to guarantee repair despite a doubled resource budget. By establishing a new benchmark for minimal structural intervention, this work provides a foundational algorithm for parsimonious network restoration and a crucial baseline against which more complex, function-aware repair strategies can be evaluated. Artificial Intelligence and Machine Learning Neural Network Repair Structural Restoration Graph Connectivity Network Pruning Post-Pruning Repair Component Fusion Sparse Neural Networks Model Compression Fault Tolerance Green AI Algorithmic Baselines 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-7926139","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":533564571,"identity":"014c3258-8050-4424-910a-96af18fbb21a","order_by":0,"name":"José Ignacio Peinador Sala","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0008-1822-3452","institution":"Independent Researcher","correspondingAuthor":true,"prefix":"","firstName":"José","middleName":"Ignacio Peinador","lastName":"Sala","suffix":""}],"badges":[],"createdAt":"2025-10-22 18:49:36","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-7926139/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7926139/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94247137,"identity":"9977c828-3be0-4f66-9e12-228377bfea50","added_by":"auto","created_at":"2025-10-24 05:41:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":369557,"visible":true,"origin":"","legend":"","description":"","filename":"ONNRRestoration.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7926139/v1_covered_3b566dcb-a362-487a-9c84-68d38d83fc01.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eOptimal Neural Network Repair: A Principled Approach to Achieving the Theoretical Limits of Structural Restoration\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Independent Researcher","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":"Neural Network Repair, Structural Restoration, Graph Connectivity, Network Pruning, Post-Pruning Repair, Component Fusion, Sparse Neural Networks, Model Compression, Fault Tolerance, Green AI, Algorithmic Baselines","lastPublishedDoi":"10.21203/rs.3.rs-7926139/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7926139/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis work frames the post-pruning repair of neural networks as a fundamental graph connectivity problem and empirically validates its theoretical limit: the minimum number of connections required to restore structural integrity is exactly equal to the number of disconnected fragments. 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