Sparse Counterfactual Path Optimization for Efficient Model Robustness Evaluation

Sparse Counterfactual Path Optimization for Efficient Model Robustness Evaluation | 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 Sparse Counterfactual Path Optimization for Efficient Model Robustness Evaluation Jiahui Wang, Meilin Xu, Zeyu Liu, Yuchen Gao, Zhou Shen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7994349/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 introduce Sparse Counterfactual Path Optimization (SCPO), a novel approach aimed at efficiently evaluating the robustness of machine learning models. As machine learning systems are increasingly deployed in critical applications, understanding their vulnerabilities to adversarial attacks is paramount. Existing adversarial example generation techniques often rely on discrete perturbations that fail to capture the complexities of real-world scenarios. In contrast, SCPO formulates a continuous trajectory in the input space, termed a counterfactual path, which induces minimal perturbations to trigger output changes in the model. By leveraging variational calculus and sparse optimization, our framework optimizes for the sparsest path, offering a realistic portrayal of how perturbations may unfold. This paper details the mathematical foundations of the problem, experiments across various domains, and demonstrates the superior interpretability and efficacy of SCPO compared to traditional adversarial methods. Our empirical evaluations show that SCPO not only minimizes the extent of perturbations required for output flipping but also enhances the understanding of model vulnerabilities, establishing a new benchmark for robustness assessment in machine learning. counterfactual optimization model robustness sparse trajectories variational calculus adversarial machine learning deep learning 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-7994349","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":537814879,"identity":"b9d6c8e7-bf99-4fce-bcba-edbe6e452466","order_by":0,"name":"Jiahui Wang","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Jiahui","middleName":"","lastName":"Wang","suffix":""},{"id":537814880,"identity":"8600be3d-1da6-4167-890e-b21b691ce3af","order_by":1,"name":"Meilin Xu","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Meilin","middleName":"","lastName":"Xu","suffix":""},{"id":537814881,"identity":"c0f94d24-1208-4f41-a82f-7fa5c0963dc8","order_by":2,"name":"Zeyu Liu","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Zeyu","middleName":"","lastName":"Liu","suffix":""},{"id":537814882,"identity":"37df53d7-ddfc-480c-b42e-584720e772b8","order_by":3,"name":"Yuchen Gao","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Yuchen","middleName":"","lastName":"Gao","suffix":""},{"id":537814883,"identity":"81a1ba7c-de78-436c-9696-8926e44fc78c","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":"2025-10-31 04:35:18","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-7994349/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7994349/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":95223462,"identity":"d78386af-6a14-4951-b3d0-d3d141971ee0","added_by":"auto","created_at":"2025-11-05 16:22:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":230921,"visible":true,"origin":"","legend":"","description":"","filename":"paper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7994349/v1_covered_fd2f6a47-aa99-4236-aab5-52619930ea5d.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eSparse Counterfactual Path Optimization for Efficient Model Robustness Evaluation\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":"counterfactual optimization, model robustness, sparse trajectories, variational calculus, adversarial machine learning, deep learning","lastPublishedDoi":"10.21203/rs.3.rs-7994349/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7994349/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we introduce Sparse Counterfactual Path Optimization (SCPO), a novel approach aimed at efficiently evaluating the robustness of machine learning models. 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