---
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:
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degree_awarded: PhD
department:
- _id: GradSch
- _id: ChLa
doi: 10.15479/10.15479/at-ista-19759
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creator: bprach
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date_updated: 2025-06-10T18:11:05Z
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file_name: ThesisFinal.pdf
file_size: 3578077
relation: main_file
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checksum: 51bf6c11fb6d8a9f8010b458c600a83f
content_type: application/x-zip-compressed
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date_updated: 2025-06-10T18:14:03Z
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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:
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status: public
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status: public
- id: '11839'
relation: part_of_dissertation
status: public
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'
...
---
OA_place: repository
OA_type: green
_id: '20455'
abstract:
- lang: eng
text: Despite extensive research since the community learned about adversarial examples
10 years ago, we still do not know how to train high-accuracy classifiers that
are guaranteed to be robust to small perturbations of their inputs. Previous works
often argued that this might be because no classifier exists that is robust and
accurate at the same time. However, in computer vision this assumption does not
match reality where humans are usually accurate and robust on most tasks of interest.
We offer an alternative explanation and show that in certain settings robust generalization
is only possible with unrealistically large amounts of data. Specifically, we
find a setting where a robust classifier exists, it is easy to learn an accurate
classifier, yet it requires an exponential amount of data to learn a robust classifier.
Based on this theoretical result, we evaluate the influence of the amount of training
data on datasets such as CIFAR10. Our findings indicate that the the amount of
training data is the main factor determining the robust performance. Furthermore
we show that that there are low magnitude directions in the data which are useful
for non-robust generalization but are not available for robust classifiers. This
implies that robust classification is a strictly harder tasks than normal classification,
thereby providing an explanation why robust classification requires more data.
article_processing_charge: No
arxiv: 1
author:
- first_name: Bernd
full_name: Prach, Bernd
id: 2D561D42-C427-11E9-89B4-9C1AE6697425
last_name: Prach
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
citation:
ama: 'Prach B, Lampert C. Intriguing properties of robust classification. In: 2025
IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops.
IEEE; 2025:660-669. doi:10.1109/CVPRW67362.2025.00071'
apa: 'Prach, B., & Lampert, C. (2025). Intriguing properties of robust classification.
In 2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops
(pp. 660–669). Nashville, TN, United States: IEEE. https://doi.org/10.1109/CVPRW67362.2025.00071'
chicago: Prach, Bernd, and Christoph Lampert. “Intriguing Properties of Robust Classification.”
In 2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops,
660–69. IEEE, 2025. https://doi.org/10.1109/CVPRW67362.2025.00071.
ieee: B. Prach and C. Lampert, “Intriguing properties of robust classification,”
in 2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops,
Nashville, TN, United States, 2025, pp. 660–669.
ista: 'Prach B, Lampert C. 2025. Intriguing properties of robust classification.
2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops.
CVPR: Conference on Computer Vision and Pattern Recognition, 660–669.'
mla: Prach, Bernd, and Christoph Lampert. “Intriguing Properties of Robust Classification.”
2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops,
IEEE, 2025, pp. 660–69, doi:10.1109/CVPRW67362.2025.00071.
short: B. Prach, C. Lampert, in:, 2025 IEEE/CVF Conference on Computer Vision and
Pattern Recognition Workshops, IEEE, 2025, pp. 660–669.
conference:
end_date: 2025-06-12
location: Nashville, TN, United States
name: 'CVPR: Conference on Computer Vision and Pattern Recognition'
start_date: 2025-06-11
corr_author: '1'
date_created: 2025-10-12T22:01:26Z
date_published: 2025-06-15T00:00:00Z
date_updated: 2025-10-13T07:18:26Z
day: '15'
department:
- _id: ChLa
doi: 10.1109/CVPRW67362.2025.00071
external_id:
arxiv:
- '2412.04245'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2412.04245
month: '06'
oa: 1
oa_version: Preprint
page: 660-669
publication: 2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops
publication_identifier:
eissn:
- 2160-7516
isbn:
- '9798331599942'
issn:
- 2160-7508
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
record:
- id: '18874'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Intriguing properties of robust classification
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: repository
_id: '18874'
abstract:
- lang: eng
text: "Despite extensive research since the community learned about adversarial\r\nexamples
10 years ago, we still do not know how to train high-accuracy\r\nclassifiers that
are guaranteed to be robust to small perturbations of their\r\ninputs. Previous
works often argued that this might be because no classifier\r\nexists that is
robust and accurate at the same time. However, in computer\r\nvision this assumption
does not match reality where humans are usually accurate\r\nand robust on most
tasks of interest. We offer an alternative explanation and\r\nshow that in certain
settings robust generalization is only possible with\r\nunrealistically large
amounts of data. More precisely we find a setting where a\r\nrobust classifier
exists, it is easy to learn an accurate classifier, yet it\r\nrequires an exponential
amount of data to learn a robust classifier. Based on\r\nthis theoretical result,
we explore how well robust classifiers generalize on\r\ndatasets such as CIFAR-10.
We come to the conclusion that on this datasets, the\r\nlimitation of current
robust models also lies in the generalization, and that\r\nthey require a lot
of data to do well on the test set. We also show that the\r\nproblem is not in
the expressiveness or generalization capabilities of current\r\narchitectures,
and that there are low magnitude features in the data which are\r\nuseful for
non-robust generalization but are not available for robust\r\nclassifiers."
article_number: '2412.04245'
article_processing_charge: No
arxiv: 1
author:
- first_name: Bernd
full_name: Prach, Bernd
id: 2D561D42-C427-11E9-89B4-9C1AE6697425
last_name: Prach
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
citation:
ama: Prach B, Lampert C. Intriguing properties of robust classification. arXiv.
doi:10.48550/arXiv.2412.04245
apa: Prach, B., & Lampert, C. (n.d.). Intriguing properties of robust classification.
arXiv. https://doi.org/10.48550/arXiv.2412.04245
chicago: Prach, Bernd, and Christoph Lampert. “Intriguing Properties of Robust Classification.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2412.04245.
ieee: B. Prach and C. Lampert, “Intriguing properties of robust classification,”
arXiv. .
ista: Prach B, Lampert C. Intriguing properties of robust classification. arXiv,
2412.04245.
mla: Prach, Bernd, and Christoph Lampert. “Intriguing Properties of Robust Classification.”
ArXiv, 2412.04245, doi:10.48550/arXiv.2412.04245.
short: B. Prach, C. Lampert, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-01-24T16:57:29Z
date_published: 2024-12-05T00:00:00Z
date_updated: 2026-04-07T11:49:51Z
day: '05'
department:
- _id: GradSch
- _id: ChLa
doi: 10.48550/arXiv.2412.04245
external_id:
arxiv:
- '2412.04245'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2412.04245
month: '12'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
record:
- id: '20455'
relation: later_version
status: public
- id: '19759'
relation: dissertation_contains
status: public
status: public
title: Intriguing properties of robust classification
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '17426'
abstract:
- lang: eng
text: "The robustness of neural networks against input perturbations with bounded\r\nmagnitude
represents a serious concern in the deployment of deep learning\r\nmodels in safety-critical
systems. Recently, the scientific community has\r\nfocused on enhancing certifiable
robustness guarantees by crafting 1-Lipschitz\r\nneural networks that leverage
Lipschitz bounded dense and convolutional layers.\r\nAlthough different methods
have been proposed in the literature to achieve this\r\ngoal, understanding the
performance of such methods is not straightforward,\r\nsince different metrics
can be relevant (e.g., training time, memory usage,\r\naccuracy, certifiable robustness)
for different applications. For this reason,\r\nthis work provides a thorough
theoretical and empirical comparison between\r\nmethods by evaluating them in
terms of memory usage, speed, and certifiable\r\nrobust accuracy. The paper also
provides some guidelines and recommendations to\r\nsupport the user in selecting
the methods that work best depending on the\r\navailable resources. We provide
code at\r\nhttps://github.com/berndprach/1LipschitzLayersCompared."
acknowledgement: "This work was partially supported by project SERICS (PE00000014)
under the MUR National Recovery and Resilience Plan funded by the European Union
- NextGenerationEU.\r\n"
article_processing_charge: No
arxiv: 1
author:
- first_name: Bernd
full_name: Prach, Bernd
id: 2D561D42-C427-11E9-89B4-9C1AE6697425
last_name: Prach
- first_name: Fabio
full_name: Brau, Fabio
last_name: Brau
- first_name: Giorgio
full_name: Buttazzo, Giorgio
last_name: Buttazzo
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
citation:
ama: 'Prach B, Brau F, Buttazzo G, Lampert C. 1-Lipschitz layers compared: Memory,
speed, and certifiable robustness. In: Proceedings of the IEEE/CVF Conference
on Computer Vision and Pattern Recognition. Computer Vision Foundation; 2024:24574-24583.
doi:10.1109/CVPR52733.2024.02320'
apa: 'Prach, B., Brau, F., Buttazzo, G., & Lampert, C. (2024). 1-Lipschitz layers
compared: Memory, speed, and certifiable robustness. In Proceedings of the
IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 24574–24583).
Seattle, WA, United States: Computer Vision Foundation. https://doi.org/10.1109/CVPR52733.2024.02320'
chicago: 'Prach, Bernd, Fabio Brau, Giorgio Buttazzo, and Christoph Lampert. “1-Lipschitz
Layers Compared: Memory, Speed, and Certifiable Robustness.” In Proceedings
of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 24574–83.
Computer Vision Foundation, 2024. https://doi.org/10.1109/CVPR52733.2024.02320.'
ieee: 'B. Prach, F. Brau, G. Buttazzo, and C. Lampert, “1-Lipschitz layers compared:
Memory, speed, and certifiable robustness,” in Proceedings of the IEEE/CVF
Conference on Computer Vision and Pattern Recognition, Seattle, WA, United
States, 2024, pp. 24574–24583.'
ista: 'Prach B, Brau F, Buttazzo G, Lampert C. 2024. 1-Lipschitz layers compared:
Memory, speed, and certifiable robustness. Proceedings of the IEEE/CVF Conference
on Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision
and Pattern Recognition, 24574–24583.'
mla: 'Prach, Bernd, et al. “1-Lipschitz Layers Compared: Memory, Speed, and Certifiable
Robustness.” Proceedings of the IEEE/CVF Conference on Computer Vision and
Pattern Recognition, Computer Vision Foundation, 2024, pp. 24574–83, doi:10.1109/CVPR52733.2024.02320.'
short: B. Prach, F. Brau, G. Buttazzo, C. Lampert, in:, Proceedings of the IEEE/CVF
Conference on Computer Vision and Pattern Recognition, Computer Vision Foundation,
2024, pp. 24574–24583.
conference:
end_date: 2024-06-22
location: Seattle, WA, United States
name: 'CVPR: Conference on Computer Vision and Pattern Recognition'
start_date: 2024-06-16
corr_author: '1'
date_created: 2024-08-14T08:42:32Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2026-04-07T11:49:51Z
day: '01'
department:
- _id: GradSch
- _id: ChLa
doi: 10.1109/CVPR52733.2024.02320
external_id:
arxiv:
- '2311.16833'
isi:
- '001344387500055'
has_accepted_license: '1'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2311.16833
month: '06'
oa: 1
oa_version: Preprint
page: 24574-24583
publication: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern
Recognition
publication_status: published
publisher: Computer Vision Foundation
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/berndprach/1LipschitzLayersCompared
record:
- id: '19759'
relation: dissertation_contains
status: public
status: public
title: '1-Lipschitz layers compared: Memory, speed, and certifiable robustness'
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2024'
...
---
OA_place: repository
_id: '15039'
abstract:
- lang: eng
text: 'A crucial property for achieving secure, trustworthy and interpretable deep
learning systems is their robustness: small changes to a system''s inputs should
not result in large changes to its outputs. Mathematically, this means one strives
for networks with a small Lipschitz constant. Several recent works have focused
on how to construct such Lipschitz networks, typically by imposing constraints
on the weight matrices. In this work, we study an orthogonal aspect, namely the
role of the activation function. We show that commonly used activation functions,
such as MaxMin, as well as all piece-wise linear ones with two segments unnecessarily
restrict the class of representable functions, even in the simplest one-dimensional
setting. We furthermore introduce the new N-activation function that is provably
more expressive than currently popular activation functions. We provide code at
this https URL.'
article_number: '2311.06103'
article_processing_charge: No
arxiv: 1
author:
- first_name: Bernd
full_name: Prach, Bernd
id: 2D561D42-C427-11E9-89B4-9C1AE6697425
last_name: Prach
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
citation:
ama: Prach B, Lampert C. 1-Lipschitz neural networks are more expressive with N-activations.
arXiv. doi:10.48550/ARXIV.2311.06103
apa: Prach, B., & Lampert, C. (n.d.). 1-Lipschitz neural networks are more expressive
with N-activations. arXiv. https://doi.org/10.48550/ARXIV.2311.06103
chicago: Prach, Bernd, and Christoph Lampert. “1-Lipschitz Neural Networks Are More
Expressive with N-Activations.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2311.06103.
ieee: B. Prach and C. Lampert, “1-Lipschitz neural networks are more expressive
with N-activations,” arXiv. .
ista: Prach B, Lampert C. 1-Lipschitz neural networks are more expressive with N-activations.
arXiv, 2311.06103.
mla: Prach, Bernd, and Christoph Lampert. “1-Lipschitz Neural Networks Are More
Expressive with N-Activations.” ArXiv, 2311.06103, doi:10.48550/ARXIV.2311.06103.
short: B. Prach, C. Lampert, ArXiv (n.d.).
corr_author: '1'
date_created: 2024-02-28T17:59:32Z
date_published: 2023-11-10T00:00:00Z
date_updated: 2026-04-07T11:49:51Z
day: '10'
department:
- _id: GradSch
- _id: ChLa
doi: 10.48550/ARXIV.2311.06103
external_id:
arxiv:
- '2311.06103'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2311.06103
month: '11'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
record:
- id: '19759'
relation: dissertation_contains
status: public
status: public
title: 1-Lipschitz neural networks are more expressive with N-activations
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2023'
...
---
_id: '11839'
abstract:
- lang: eng
text: "It is a highly desirable property for deep networks to be robust against\r\nsmall
input changes. One popular way to achieve this property is by designing\r\nnetworks
with a small Lipschitz constant. In this work, we propose a new\r\ntechnique for
constructing such Lipschitz networks that has a number of\r\ndesirable properties:
it can be applied to any linear network layer\r\n(fully-connected or convolutional),
it provides formal guarantees on the\r\nLipschitz constant, it is easy to implement
and efficient to run, and it can be\r\ncombined with any training objective and
optimization method. In fact, our\r\ntechnique is the first one in the literature
that achieves all of these\r\nproperties simultaneously. Our main contribution
is a rescaling-based weight\r\nmatrix parametrization that guarantees each network
layer to have a Lipschitz\r\nconstant of at most 1 and results in the learned
weight matrices to be close to\r\northogonal. Hence we call such layers almost-orthogonal
Lipschitz (AOL).\r\nExperiments and ablation studies in the context of image classification
with\r\ncertified robust accuracy confirm that AOL layers achieve results that
are on\r\npar with most existing methods. Yet, they are simpler to implement and
more\r\nbroadly applicable, because they do not require computationally expensive\r\nmatrix
orthogonalization or inversion steps as part of the network\r\narchitecture. We
provide code at https://github.com/berndprach/AOL."
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Bernd
full_name: Prach, Bernd
id: 2D561D42-C427-11E9-89B4-9C1AE6697425
last_name: Prach
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
citation:
ama: 'Prach B, Lampert C. Almost-orthogonal layers for efficient general-purpose
Lipschitz networks. In: Computer Vision – ECCV 2022. Vol 13681. Springer
Nature; 2022:350-365. doi:10.1007/978-3-031-19803-8_21'
apa: 'Prach, B., & Lampert, C. (2022). Almost-orthogonal layers for efficient
general-purpose Lipschitz networks. In Computer Vision – ECCV 2022 (Vol.
13681, pp. 350–365). Tel Aviv, Israel: Springer Nature. https://doi.org/10.1007/978-3-031-19803-8_21'
chicago: Prach, Bernd, and Christoph Lampert. “Almost-Orthogonal Layers for Efficient
General-Purpose Lipschitz Networks.” In Computer Vision – ECCV 2022, 13681:350–65.
Springer Nature, 2022. https://doi.org/10.1007/978-3-031-19803-8_21.
ieee: B. Prach and C. Lampert, “Almost-orthogonal layers for efficient general-purpose
Lipschitz networks,” in Computer Vision – ECCV 2022, Tel Aviv, Israel,
2022, vol. 13681, pp. 350–365.
ista: 'Prach B, Lampert C. 2022. Almost-orthogonal layers for efficient general-purpose
Lipschitz networks. Computer Vision – ECCV 2022. ECCV: European Conference on
Computer Vision, LNCS, vol. 13681, 350–365.'
mla: Prach, Bernd, and Christoph Lampert. “Almost-Orthogonal Layers for Efficient
General-Purpose Lipschitz Networks.” Computer Vision – ECCV 2022, vol.
13681, Springer Nature, 2022, pp. 350–65, doi:10.1007/978-3-031-19803-8_21.
short: B. Prach, C. Lampert, in:, Computer Vision – ECCV 2022, Springer Nature,
2022, pp. 350–365.
conference:
end_date: 2022-10-27
location: Tel Aviv, Israel
name: 'ECCV: European Conference on Computer Vision'
start_date: 2022-10-23
corr_author: '1'
date_created: 2022-08-12T15:09:47Z
date_published: 2022-10-23T00:00:00Z
date_updated: 2026-04-07T11:49:51Z
day: '23'
department:
- _id: GradSch
- _id: ChLa
doi: 10.1007/978-3-031-19803-8_21
external_id:
arxiv:
- '2208.03160'
isi:
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intvolume: ' 13681'
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language:
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page: 350-365
publication: Computer Vision – ECCV 2022
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publication_status: published
publisher: Springer Nature
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status: public
scopus_import: '1'
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title: Almost-orthogonal layers for efficient general-purpose Lipschitz networks
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 13681
year: '2022'
...