---
res:
  bibo_abstract:
  - "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@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Bernd
      foaf_name: Prach, Bernd
      foaf_surname: Prach
      foaf_workInfoHomepage: http://www.librecat.org/personId=2D561D42-C427-11E9-89B4-9C1AE6697425
  bibo_doi: 10.15479/10.15479/at-ista-19759
  dct_date: 2025^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2663-337X
  dct_language: eng
  dct_publisher: Institute of Science and Technology Austria@
  dct_title: Robust image classification with 1-Lipschitz networks@
...