[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122805-en":3,"doc-seo-122805-105":30,"detail-sidebar-cat-0-en-105":92},{"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},122805,3848291630094,"Emma Wilson","https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Bridging formal methods and machine learning with model checking and global optimisation","Formal methods and machine learning rely on fundamentally different foundations, with formal methods providing mathematically rigorous specification, development, and verification for software and hardware, while machine learning improves parameterised models via training data. With growing demand for robust safety and security, the gap between these fields requires deeper communication. The work reviews robustness verification for neural networks, introduces MLS2 to capture safety and security properties, and uses global-optimisation methods with provable convergence guarantees and bounds toward optimality.","J. Log. Algebraic Methods Program. 137 (2024) 100941  \nContents lists available at ScienceDirect  \nJournal of Logical and Algebraic Methods in Programming  \n[journal homepage: www.elsevier.com/locate/jlamp](journal homepage: www.elsevier.com/locate/jlamp)  \n| Bridging formal methods and machine learning with model checking and global optimisation\u003Cbr>Saddek Bensalem a, Xiaowei Huang b,∗ , Wenjie Ruanb, Qiyi Tang b, Changshun Wu a, Xingyu Zhao b\u003Cbr>a University Grenoble Alpes, VERIMAG, Grenoble, France\u003Cbr>b Department of Computer Science, University of Liverpool, Liverpool, L69 3BX, UK |  |  |  |\n| --- | --- | --- | --- |\n| A R T I C L E I N F O |  | A B S T R A C T |  |\n| Keywords:\u003Cbr>Formal methods Machine learning Model checking Global optimisation |  | Formal methods and machine learning are two research fields with drastically different foundations and philosophies. Formal methods utilise mathematically rigorous techniques for software and hardware systems’ specification, development and verification. Machine learning focuses on pragmatic approaches to gradually improve a parameterised model by observing a training data set. While historically, the two fields lack communication, this trend has changed in the past few years with an outburst of research interest in the robustness verification of neural networks. This paper will briefly review these works, and focus on the urgent need for broader and more in-depth communication between the two fields, with the ultimate goal of developing learning-enabled systems with excellent performance and acceptable safety and security. We present a specification language, MLS2 , and show that it can express a set of known safety and security properties, including generalisation, uncertainty, robustness, data poisoning, backdoor, model stealing, membership inference, model inversion, interpretability, and fairness. To verify MLS2 properties, we promote the global optimisation-based methods, which have provable guarantees on the convergence to the optimal solution. Many of them have theoretical bounds on the gap between current solutions and the optimal solution. |  |\n\n1. Introduction  \nRecent advances in machine learning have enabled the development of complex, intelligent software systems with human-level performance. Notable examples include image classification and natural language processing, among many others. However, even if many machine learning systems (or models) have been successfully applied to industrial applications, they are not rigorously engineered. Instead, their design and implementation are based on developers’ experience and have been frequently referred to as“dark art”. Compounded with the intensively discussed safety and security issues discovered through various adversarial attacks, such as [1–7] and the growing expectation that machine learning models will be applied to safety-critical applications, it is clear that rigorous engineering methods are urgently needed [8].  \nSuccessful experience from industrial software engineering, which produced software currently applied in, e.g., automotive and avionic applications, suggests that, to develop high-quality and low-cost software in a limited production time, a software devel-  \n* Corresponding author.  \n[E-mail address:](E-mail address: xiaowei.huang@liverpool.ac.uk)[ xiaowei.huang@liverpool.ac.uk](E-mail address: xiaowei.huang@liverpool.ac.uk) (X. Huang).  \n[https://doi.org/10.1016/j.jlamp.2023.100941](https://doi.org/10.1016/j.jlamp.2023.100941)  \nReceived 29 January 2023; Received in revised form 12 December 2023; Accepted 20 December 2023  \nAvailable online 28 December 2023  \n2352-2208/© 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license ([http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/)).  \nS. Bensalem, X. Huang, W. Ruan et al. Journal of Logical and Algebraic Methods in Programming 137 (2024) 100941  \nFig. 1. V-Models for Software","cbCaivADUhviakyU","https://ap.wps.com/l/cbCaivADUhviakyU","pdf",1289499,1,17,"English","en",105,"# Abstract\n# Introduction\n## Motivation: dark-art engineering and safety-critical need\n## V-model for software and its limitations for ML\n## Role of formal methods in robustness verification","[{\"question\":\"What is the main gap the paper addresses between formal methods and machine learning?\",\"answer\":\"Formal methods and machine learning historically lack communication due to different foundations. The paper argues for broader, deeper interaction to enable learning-enabled systems with strong performance and acceptable safety and security.\"},{\"question\":\"What is MLS2 and what properties does it aim to express?\",\"answer\":\"MLS2 is a specification language proposed to express multiple safety and security properties. It covers aspects such as generalisation, uncertainty, robustness, data poisoning, backdoor behaviour, model stealing, inference and privacy-related risks, interpretability, and fairness.\"},{\"question\":\"How does the paper verify MLS2 properties?\",\"answer\":\"It promotes global-optimisation-based verification methods. These methods provide provable convergence guarantees to the optimal solution and include theoretical bounds on the gap between current solutions and optimality.\"}]","Bridging formal methods and machine learning with model checking and global optimisation | PDF",1785812989,43,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"bridging-formal-methods-and-machine-learning-with-model-checking-and-global-optimisation","",{"@graph":36,"@context":86},[37,54,69],{"@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/bridging-formal-methods-and-machine-learning-with-model-checking-and-global-optimisation/122805/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-04",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What is the main gap the paper addresses between formal methods and machine learning?","Question",{"text":76,"@type":77},"Formal methods and machine learning historically lack communication due to different foundations. The paper argues for broader, deeper interaction to enable learning-enabled systems with strong performance and acceptable safety and security.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What is MLS2 and what properties does it aim to express?",{"text":81,"@type":77},"MLS2 is a specification language proposed to express multiple safety and security properties. It covers aspects such as generalisation, uncertainty, robustness, data poisoning, backdoor behaviour, model stealing, inference and privacy-related risks, interpretability, and fairness.",{"name":83,"@type":74,"acceptedAnswer":84},"How does the paper verify MLS2 properties?",{"text":85,"@type":77},"It promotes global-optimisation-based verification methods. 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