[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119128-en":3,"doc-seo-119128-105":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},119128,8796095462418,"Noah","https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780",8,"Research & Report","Provably Robust Machine Learning through Structure-Aware Computation - Doctoral Dissertation","Standard machine learning algorithms can fail catastrophically under input uncertainties, including adversarial attacks, making guaranteed robustness essential for safety-critical deployment in domains such as autonomous driving, healthcare, and power systems. This dissertation develops theoretical and computational tools for provably robust machine learning, introducing efficient optimization for certifying existing models and constructing new models equipped with mathematical robustness guarantees. By exploiting structure in the certification problems, the proposed approaches improve robustness and efficiency.","UC Berkeley  \nUC Berkeley Electronic Theses and Dissertations  \nTitle  \nProvably Robust Machine Learning through Structure-Aware Computation  \nPermalink  \n[https://escholarship.org/uc/item/7bs706pb](https://escholarship.org/uc/item/7bs706pb)  \nAuthor  \nAnderson, Brendon G  \nPublication Date  \n2024  \nPeer reviewed|Thesis/dissertation  \n[eScholarship.org](eScholarship.org) Powered by the California Digital Library  \nUniversity of California  \nProvably Robust Machine Learning through Structure-Aware Computation  \nby  \nBrendon G. Anderson  \nA dissertation submitted in partial satisfaction of the requirements for the degree of  \nDoctor of Philosophy  \nin  \nEngineering—Mechanical Engineering in the  \nGraduate Division  \nof the  \nUniversity of California, Berkeley  \nCommittee in charge:  \nAssociate Professor Somayeh Sojoudi, Chair Associate Professor Javad Lavaei  \nProfessor Kameshwar Poolla  \nSpring 2024  \nProvably Robust Machine Learning through Structure-Aware Computation  \nCopyright 2024  \nby  \nBrendon G. Anderson  \n1  \nAbstract  \nProvably Robust Machine Learning through Structure-Aware Computation  \nby  \nBrendon G. Anderson  \nDoctor of Philosophy in Engineering—Mechanical Engineering University of California, Berkeley  \nAssociate Professor Somayeh Sojoudi, Chair  \nStandard machine learning (ML) algorithms exhibit catastrophic failures when subject to uncertainties in their input data, such as attacks generated by an adversary. Robustness against such uncertainties must be guaranteed in order to reliably deploy ML in safetycritical settings, such as autonomous driving, healthcare, and the operation of power systems. This dissertation presents theoretical and computational advancements in provably robust machine learning. We both introduce efficient optimization methods to certify the robustness of prior ML models, as well as design novel ML models endowed with mathematical proof of robustness. By exploiting key structures in the underlying certification problems, the proposed methods achieve state-of-the-art robustness and efficiency.  \nIn the first part of this dissertation, we consider certifying the robustness of given, pretrained machine learning models. This robustness certification problem amounts to solving a difficult nonconvex optimization problem, and therefore a more tractable approach for generating safety guarantees is to lower-bound the optimization. We begin by considering a branchand-bound approach to computing such lower bounds. In doing so, we leverage the piecewise linear structure of ReLU neural networks to develop branching schemes that minimize the looseness of the desired lower bounds in a worst-case sense. Next, we show that ReLU neural networks may be rewritten in a min-max affine form. We prove that this min-max affine structure allows us to efficiently solve the nonconvex robustness certification problem to global optimality by solving an equivalent convex reformulation. We also consider certifying the robustness of models in the case where the inputs are subject to random noise. A datadriven, convex optimization-based method is developed that simultaneously localizes neural network outputs and verifies their safety, all with high-probability guarantees. We show that our data-driven method’s sample complexity can be dramatically reduced by leveraging the compositional structure of neural networks.  \nIn the second part of this dissertation, we consider the design of robust machine learning models that are capable of withstanding uncertainties and attacks in their inputs, and are  \n2  \namenable to robustness certification. First, we propose feature-convex neural networks, which consist of the composition of a Lipschitz continuous feature map followed by a convex neural network. We utilize this composite convex structure of our model to derive deterministic, closed-form robustness certificates that match or outperform those of prior provably robust ML methods. Finally, we introduce locally biased randomize","cbCailhgWJl9fiyw","https://ap.wps.com/l/cbCailhgWJl9fiyw","pdf",5295293,1,209,"English","en",105,"# 1 Introduction\n# 2 Towards Optimal Branching for ReLU Neural Networks\n## 2.1 Introduction\n## 2.2 Problem Statement\n## 2.3 Partitioned LP Relaxation\n## 2.4 Partitioned SDP Relaxation\n## 2.5 Implementing the Branching Schemes\n## 2.6 Numerical Simulations\n## 2.7 Conclusions\n# 3 Globally Optimal Certification of Min-Max Affine Models\n## 3.1 Introduction\n## 3.2 Min-Max Affine Functions\n## 3.3 Theoretical Robustness Certificates\n## 3.4 Numerical Simulations\n## 3.5 Conclusions\n# 4 Data-Driven Certification for Probabilistic Robustness\n## 4.1 Introduction\n## 4.2 Problem Statement\n## 4.3 Formulating the Certificate\n## 4.4 Data-Driven Reformulation\n## 4.5 Exploiting Network Structure\n## 4.6 Numerical Simulations\n## 4.7 Conclusions","[{\"question\":\"Why is robustness certification needed in machine learning?\",\"answer\":\"Because standard ML can fail catastrophically when inputs are uncertain, including under adversarial attacks. Guaranteed robustness is required for reliable use in safety-critical settings such as autonomous driving, healthcare, and power systems.\"},{\"question\":\"How does the dissertation certify robustness of pretrained ReLU models?\",\"answer\":\"It reframes certification as a difficult nonconvex optimization problem and uses methods to obtain tractable lower bounds. It also leverages the piecewise linear structure of ReLU networks to design branching schemes and employs a min-max affine reformulation to enable globally optimal certification via an equivalent convex reformulation.\"},{\"question\":\"What new model structures does the dissertation introduce for provable robustness?\",\"answer\":\"It proposes feature-convex neural networks, combining a Lipschitz continuous feature map with a convex neural network to derive deterministic closed-form robustness certificates. It also introduces locally biased randomized smoothing to robustify a general pretrained classifier and provides certified robustness guarantees with improved empirical resistance to adversarial attacks.\"}]","Provably Robust Machine Learning through Structure-Aware Computation - Doctoral Dissertation | PDF",1785722548,527,{"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},"provably-robust-machine-learning-through-structure-aware-computation-doctoral-dissertation","",{"@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/provably-robust-machine-learning-through-structure-aware-computation-doctoral-dissertation/119128/",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","2026-08-06","2026-08-03",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},"Why is robustness certification needed in machine learning?","Question",{"text":76,"@type":77},"Because standard ML can fail catastrophically when inputs are uncertain, including under adversarial attacks. Guaranteed robustness is required for reliable use in safety-critical settings such as autonomous driving, healthcare, and power systems.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the dissertation certify robustness of pretrained ReLU models?",{"text":81,"@type":77},"It reframes certification as a difficult nonconvex optimization problem and uses methods to obtain tractable lower bounds. It also leverages the piecewise linear structure of ReLU networks to design branching schemes and employs a min-max affine reformulation to enable globally optimal certification via an equivalent convex reformulation.",{"name":83,"@type":74,"acceptedAnswer":84},"What new model structures does the dissertation introduce for provable robustness?",{"text":85,"@type":77},"It proposes feature-convex neural networks, combining a Lipschitz continuous feature map with a convex neural network to derive deterministic closed-form robustness certificates. It also introduces locally biased randomized smoothing to robustify a general pretrained classifier and provides certified robustness guarantees with improved empirical resistance to adversarial attacks.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]