{"publication_identifier":{"issn":["2663-337X"]},"oa_version":"Published Version","oa":1,"citation":{"ama":"Prach B. Robust image classification with 1-Lipschitz networks. 2025. doi:<a href=\"https://doi.org/10.15479/10.15479/at-ista-19759\">10.15479/10.15479/at-ista-19759</a>","ista":"Prach B. 2025. Robust image classification with 1-Lipschitz networks. Institute of Science and Technology Austria.","short":"B. Prach, Robust Image Classification with 1-Lipschitz Networks, Institute of Science and Technology Austria, 2025.","chicago":"Prach, Bernd. “Robust Image Classification with 1-Lipschitz Networks.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/10.15479/at-ista-19759\">https://doi.org/10.15479/10.15479/at-ista-19759</a>.","apa":"Prach, B. (2025). <i>Robust image classification with 1-Lipschitz networks</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/10.15479/at-ista-19759\">https://doi.org/10.15479/10.15479/at-ista-19759</a>","mla":"Prach, Bernd. <i>Robust Image Classification with 1-Lipschitz Networks</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/10.15479/at-ista-19759\">10.15479/10.15479/at-ista-19759</a>.","ieee":"B. Prach, “Robust image classification with 1-Lipschitz networks,” Institute of Science and Technology Austria, 2025."},"date_updated":"2026-04-07T11:49:52Z","abstract":[{"lang":"eng","text":"Despite generating remarkable results in various computer vision tasks, deep learning comes\r\nwith some surprising shortcomings. For example, tiny perturbations, often imperceptible to\r\nthe human eye, can completely change the predictions of image classifiers. Despite a decade\r\nof research, the field has made limited progress in developing image classifiers that are both\r\naccurate and robust. This thesis aims to address this gap.\r\nAs our first contribution, we aim to simplify the process of training certifiably robust image\r\nclassifiers. We do this by designing a convolutional layer that does not require executing an\r\niterative procedure in every forward pass, but relies on an explicit bound instead. We also\r\npropose a loss function that allows optimizing for a particular margin more precisely.\r\nNext, we provide an overview and comparison of various methods that create robust image\r\nclassifiers by constraining the Lipschitz constant. This is important since generally longer\r\ntraining times and more parameters improve the performance of robust classifiers, making it\r\nchallenging to determine the most practical and effective methods from existing literature.\r\nIn 1-Lipschitz classification, the performance of current methods is still much worse than what\r\nwe expect on the simple tasks we consider. Therefore, we next investigate potential causes of\r\nthis shortcoming. We first consider the role of the activation function. We prove a theoretical\r\nshortcoming of the commonly used activation function, and provide an alternative without it.\r\nHowever this theoretical improvement does barely translate to the empirical performance of\r\nrobust classifiers, suggesting a different bottleneck.\r\nTherefore, in the final chapter, we study how the performance depends on the amount of\r\ntraining data. We prove that in the worst case, we might require far more data to train a\r\nrobust classifier compared to a normal one. We furthermore find that the amount of training\r\ndata is a key determinant of the performance current methods achieve on popular datasets.\r\nAdditionally, we show that linear subspaces exist with tiny data variance, and yet we can\r\nstill train very accurate classifiers after projecting into those subspaces. This shows that on\r\nthe datasets considered, enforcing robustness in classification makes the task strictly more\r\nchallenging.\r\n\r\n-----------------“In reference to IEEE copyrighted material which is used with permission in this thesis, the IEEE does not endorse any of [name of university or educational entity]’s products or services. Internal or personal use of this material is permitted. If interested in reprinting/republishing IEEE copyrighted material for advertising or promotional purposes or for creating new collective works for resale or redistribution, please go to http://www.ieee.org/publications_standards/publications/rights/rights_link.html to learn how to obtain a License from RightsLink. If applicable, University Microfilms and/or ProQuest Library, or the Archives of Canada may supply single copies of the dissertation.”\r\n"}],"date_created":"2025-05-28T16:20:48Z","type":"dissertation","article_processing_charge":"No","day":"30","has_accepted_license":"1","alternative_title":["ISTA Thesis"],"date_published":"2025-05-30T00:00:00Z","degree_awarded":"PhD","ddc":["000"],"language":[{"iso":"eng"}],"department":[{"_id":"GradSch"},{"_id":"ChLa"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","publisher":"Institute of Science and Technology Austria","doi":"10.15479/10.15479/at-ista-19759","corr_author":"1","title":"Robust image classification with 1-Lipschitz networks","year":"2025","page":"84","file":[{"file_size":3578077,"date_created":"2025-06-10T18:11:05Z","file_name":"ThesisFinal.pdf","file_id":"19829","date_updated":"2025-06-10T18:11:05Z","relation":"main_file","content_type":"application/pdf","checksum":"e5108e759014e2a9020c973c778fafc9","creator":"bprach","access_level":"open_access"},{"file_size":74894357,"file_id":"19830","date_updated":"2025-06-10T18:14:03Z","date_created":"2025-06-10T18:14:03Z","file_name":"ThesisFinal.zip","content_type":"application/x-zip-compressed","relation":"source_file","access_level":"closed","checksum":"51bf6c11fb6d8a9f8010b458c600a83f","creator":"bprach"}],"_id":"19759","file_date_updated":"2025-06-10T18:14:03Z","publication_status":"published","author":[{"first_name":"Bernd","id":"2D561D42-C427-11E9-89B4-9C1AE6697425","full_name":"Prach, Bernd","last_name":"Prach"}],"supervisor":[{"orcid":"0000-0001-8622-7887","last_name":"Lampert","first_name":"Christoph","full_name":"Lampert, Christoph","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"id":"15039","status":"public","relation":"part_of_dissertation"},{"id":"18874","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"17426"},{"relation":"part_of_dissertation","status":"public","id":"11839"}]},"month":"05","status":"public","OA_place":"publisher"}