Improving Adversarial Robustness of DNNs via Margin-Based Label Encoding

Improving Adversarial Robustness of DNNs via Margin-Based Label Encoding | 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 Improving Adversarial Robustness of DNNs via Margin-Based Label Encoding Keji Han, Yun Li, Deqiang Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8362986/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Deep learning systems are known to be vulnerable to adversarial attacks. The attacker fools deep learning models with adversarial examples crafted by adding perturbations to the original ones. Although many defense methods have been proposed to increase the robustness of deep learning systems, the defensive effectiveness is not satisfactory yet. For example, the trade-off between robustness and accuracy still exists. Current research validates that label encoding is a promising approach for tackling this challenge. Nevertheless, existing label-encoding techniques have not been specifically developed to enhance adversarial robustness and offer limited inspiration for solving adversarial issue. This paper explores a new perspective on influencing the robustness of deep learning systems and further proposes a margin-based label-encoding strategy. Specifically, we define two margin-based label-encoding classification systems: margin-based binary-label classification and margin-based interval-label classification. In these systems, margins are designed between different labels to increase the cost of adversarial attacks. Furthermore, when a sample is correctly classified, the loss in margin-based label-encoding classification systems becomes zero—this mechanism helps mitigate the overfitting issue. Both theoretical analysis and experimental results demonstrate that our margin-based label-encoding methods are notably robust by comparing with the vanilla one-hot methods with retaining the classification system accuracy on legitimate examples\footnote{The previous version has been accepted by ICML 2021 Workshop on Adversarial Machine Learning (oral, please see \url{ https://openreview.net/forum?id=uK2CQwaV77}} . Deep Learning Margin Learning Adversarial Example Label Encoding Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 05 May, 2026 Reviewers agreed at journal 02 May, 2026 Reviewers agreed at journal 13 Apr, 2026 Reviewers invited by journal 26 Dec, 2025 Editor assigned by journal 26 Dec, 2025 Submission checks completed at journal 17 Dec, 2025 First submitted to journal 15 Dec, 2025 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-8362986","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":566453602,"identity":"b52a8a57-3cd9-43b8-9b4d-9bcc98a1f4ba","order_by":0,"name":"Keji Han","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6ElEQVRIiWNgGAWjYBACefmH7Z9/8NgwMDaA+cyEtRg2JB9jZpBJA2kB6SJCC8OBtDRmBpvDICaRWhgbzpg9Lsg5n8c8I/f4A4YK68QG9rMH8GphZ+wxN55x5nYx44y8xAaGM+mJDTx5CfhtaeYxkODtuZ3YOCPHsIGx7XBigwSPAX6XHQNp+XcOquUfMVrOsKVJ8/AcgGppIEKL4Qzmw4YzeJITG3veJc5IOJZu3MaTg1+LvARj44MPPHaJG9tzD3z4UGMt289+hoDD4NY18DAwJAAZbMSpB1nHwEO02lEwCkbBKBhhAADASkkF4NDXLwAAAABJRU5ErkJggg==","orcid":"","institution":"Nanjing University of Posts and Telecommunications","correspondingAuthor":true,"prefix":"","firstName":"Keji","middleName":"","lastName":"Han","suffix":""},{"id":566453603,"identity":"b150e8eb-3fad-44b5-958d-b6ec0e700635","order_by":1,"name":"Yun Li","email":"","orcid":"","institution":"Nanjing University of Posts and Telecommunications","correspondingAuthor":false,"prefix":"","firstName":"Yun","middleName":"","lastName":"Li","suffix":""},{"id":566453606,"identity":"27f4395d-2273-4375-935a-5a275c905e0e","order_by":2,"name":"Deqiang Li","email":"","orcid":"","institution":"Nanjing University of Posts and Telecommunications","correspondingAuthor":false,"prefix":"","firstName":"Deqiang","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2025-12-15 07:24:03","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8362986/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8362986/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99135095,"identity":"8019e83f-d95c-4707-b884-03e5f5e2fa2d","added_by":"auto","created_at":"2025-12-29 06:24:42","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1020569,"visible":true,"origin":"","legend":"","description":"","filename":"snarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8362986/v1/f14ca4f7a471c1a92a47b3d0.pdf"},{"id":99315585,"identity":"7bffdc75-6e25-48a9-a3c2-bccda0dc49f2","added_by":"auto","created_at":"2025-12-31 16:27:05","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5294,"visible":true,"origin":"","legend":"","description":"","filename":"717c313699b3463ab5fc2c0a91a7ce18.json","url":"https://assets-eu.researchsquare.com/files/rs-8362986/v1/2b66c4f0409e09d11a956b74.json"},{"id":99323426,"identity":"e83a4ed1-b7f4-4604-bf79-97e295d67274","added_by":"auto","created_at":"2025-12-31 16:45:22","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2361487,"visible":true,"origin":"","legend":"","description":"","filename":"snarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8362986/v1_covered_bb894aed-80ab-4259-95ce-0fec89ed06a9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Improving Adversarial Robustness of DNNs via Margin-Based Label Encoding","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"cluster-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Cluster Computing](https://www.springer.com/journal/10586)","snPcode":"10586","submissionUrl":"https://submission.nature.com/new-submission/10586/3","title":"Cluster Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Deep Learning, Margin Learning, Adversarial Example, Label Encoding","lastPublishedDoi":"10.21203/rs.3.rs-8362986/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8362986/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Deep learning systems are known to be vulnerable to adversarial attacks. 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