---
OA_place: publisher
_id: '19759'
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"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Bernd
full_name: Prach, Bernd
id: 2D561D42-C427-11E9-89B4-9C1AE6697425
last_name: Prach
citation:
ama: Prach B. Robust image classification with 1-Lipschitz networks. 2025. doi:10.15479/10.15479/at-ista-19759
apa: Prach, B. (2025). Robust image classification with 1-Lipschitz networks.
Institute of Science and Technology Austria. https://doi.org/10.15479/10.15479/at-ista-19759
chicago: Prach, Bernd. “Robust Image Classification with 1-Lipschitz Networks.”
Institute of Science and Technology Austria, 2025. https://doi.org/10.15479/10.15479/at-ista-19759.
ieee: B. Prach, “Robust image classification with 1-Lipschitz networks,” Institute
of Science and Technology Austria, 2025.
ista: Prach B. 2025. Robust image classification with 1-Lipschitz networks. Institute
of Science and Technology Austria.
mla: Prach, Bernd. Robust Image Classification with 1-Lipschitz Networks.
Institute of Science and Technology Austria, 2025, doi:10.15479/10.15479/at-ista-19759.
short: B. Prach, Robust Image Classification with 1-Lipschitz Networks, Institute
of Science and Technology Austria, 2025.
corr_author: '1'
date_created: 2025-05-28T16:20:48Z
date_published: 2025-05-30T00:00:00Z
date_updated: 2026-04-07T11:49:52Z
day: '30'
ddc:
- '000'
degree_awarded: PhD
department:
- _id: GradSch
- _id: ChLa
doi: 10.15479/10.15479/at-ista-19759
file:
- access_level: open_access
checksum: e5108e759014e2a9020c973c778fafc9
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creator: bprach
date_created: 2025-06-10T18:11:05Z
date_updated: 2025-06-10T18:11:05Z
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file_name: ThesisFinal.pdf
file_size: 3578077
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has_accepted_license: '1'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: '84'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '15039'
relation: part_of_dissertation
status: public
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relation: part_of_dissertation
status: public
- id: '17426'
relation: part_of_dissertation
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status: public
supervisor:
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
title: Robust image classification with 1-Lipschitz networks
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2025'
...