[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120566-en":3,"doc-seo-120566-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120566,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","Trustworthy Machine Learning for High-Assurance Systems - thesis","Deploying neural networks in safety-critical applications requires mathematical guarantees about their behaviour that empirical testing alone cannot provide. Despite strong performance across domains, neural networks face adversarial examples and lack of formal specifications, limiting trust in high-assurance contexts. This thesis proposes a comprehensive formal verification framework using interactive theorem proving in Isabelle/HOL, including formal interval arithmetic, multiple verified network representations, and proofs of key continuity and inclusion properties.","Trustworthy Machine Learning for High-Assurance Systems  \nAmy Stell Department of Computer Science  \nUniversity of Exeter  \nSubmitted by Amy Stell, to the University of Exeter as a thesis for the degree of Doctor of Philosophy in Computer Science, July, 2025 .  \nThis thesis is available for Library use on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement.  \nI certify that all material in this thesis which is not my own work has been identified and that any material that has previously been submitted and approved for the award of a degree by this or any other University has been acknowledged.  \nAcknowledgements  \nI would like to express my deepest gratitude to my supervisor, Prof. Achim D. Brucker, for his unwavering support throughout my doctoral studies. His patience, guidance, and countless hours of discussion have been instrumental in shaping both this research and my development as a researcher. I am also particularly grateful for his mentorship in developing the research proposal that secured EPSRC funding for this project.  \nI extend my thanks to my second supervisor, Dr Diego Marmsoler, whose thoughtful questions during annual reviews challenged me to think more deeply about my work.  \nThis work was made possible by funding from the Engineering and Physical Sciences Research Council (EPSRC) . I am honoured to have received support for my own research proposal - an exciting opportunity that has allowed me to pursue this research into neural network verification.  \nFinally, I would like to acknowledge those who have provided personal support during this journey. Special thanks to my family for their patience, encouragement, and understanding throughout the inevitable highs and lows of doctoral research.  \nii  \nList of Publications  \n2025  \n• Achim D. Brucker, Amy Stell: Verifying Feedforward Neural Networks. Arch. Formal Proofs 2025 (2025) To be submitted  \n• Achim D. Brucker, Amy Stell: Feedforward Neural Networks. Arch. Formal Proofs 2025 (2025)  \n2024  \n• Achim D. Brucker, Amy Stell: (Extended) Interval Analysis. Arch. Formal Proofs 2024 (2024)  \n• Achim D. Brucker, Teddy Cameron-Burke, Amy Stell: Formally Verified Interval Arithmetic and Its Application to Program Verification. FormaliSE@ICSE 2024: 111-121  \n2023  \n• Achim D. Brucker, Amy Stell: Verifying Feedforward Neural Networks for Classification in Isabelle/HOL. FM 2023: 427-444  \niv  \nAbstract  \nDeploying neural networks in safety-critical applications requires mathematical guarantees about their behaviour that cannot be provided through empirical testing alone. While neural networks have demonstrated remarkable performance across diverse domains, their susceptibility to adversarial examples and lack of formal specifications present challenges for high-assurance systems where predictable behaviour is essential. This thesis presents a comprehensive formal neural network verification framework using interactive theorem proving in Isabelle/HOL.  \nFirst, we establish a complete formalisation of interval arithmetic for neural networks. Second, we develop three complementary formal representations of neural networks (directed graph, list-based, and matrix-based sequential models), each optimised for different verification scenarios with proven equivalences that enable conversion between the representations. Third, we prove the inclusion isotonicity, interval extension, and Lipschitz continuity of neural network computations.  \nOur verification methodology provides three approaches. Closed-form verification produces exact mathematical definitions through symbolic execution. Interval analysis provides a scalable approximation with soundness guarantees. Interval refinement combines both approaches through subdivision and refinement, which offers precision that converges to arbitrary accuracy.  \nOur tooling infrastructure enables a complete workflow of formal machine learning verification","cbCaisF7kkurTAvI","https://ap.wps.com/l/cbCaisF7kkurTAvI","pdf",2083046,1,175,"English","en",105,"# Introduction\n## Verification of Neural Networks\n## Challenges in Neural Network Verification\n## Main Contributions\n## Thesis Structure\n## Typographic Conventions\n# Background\n## Neural Networks and Deep Learning","[{\"question\":\"Why is formal verification needed for neural networks in safety-critical systems?\",\"answer\":\"Safety-critical deployment requires mathematical guarantees that cannot be ensured through empirical testing alone. The thesis addresses challenges including adversarial examples and missing formal specifications.\"},{\"question\":\"What formal framework does the thesis use for neural network verification?\",\"answer\":\"The thesis presents a formal neural network verification framework based on interactive theorem proving in Isabelle/HOL, built around formal interval arithmetic and verified network representations.\"},{\"question\":\"What verification approaches are proposed in the methodology?\",\"answer\":\"The thesis provides three approaches: closed-form verification via symbolic execution, interval analysis for scalable sound approximations, and interval refinement combining both by subdivision to increase precision.\"}]","Trustworthy Machine Learning for High-Assurance Systems - thesis | PDF",1785730686,441,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"trustworthy-machine-learning-for-high-assurance-systems-thesis","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/trustworthy-machine-learning-for-high-assurance-systems-thesis/120566/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why is formal verification needed for neural networks in safety-critical systems?","Question",{"text":75,"@type":76},"Safety-critical deployment requires mathematical guarantees that cannot be ensured through empirical testing alone. The thesis addresses challenges including adversarial examples and missing formal specifications.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What formal framework does the thesis use for neural network verification?",{"text":80,"@type":76},"The thesis presents a formal neural network verification framework based on interactive theorem proving in Isabelle/HOL, built around formal interval arithmetic and verified network representations.",{"name":82,"@type":73,"acceptedAnswer":83},"What verification approaches are proposed in the methodology?",{"text":84,"@type":76},"The thesis provides three approaches: closed-form verification via symbolic execution, interval analysis for scalable sound approximations, and interval refinement combining both by subdivision to increase precision.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]