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Lipschitz constrained networks have gathered considerable attention in the deep learning community, with usages ranging from Wasserstein distance estimation to the training of certifiably robust classifiers.
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Shape priors for level set representations
Mikael Rousson and Nikos Paragios · 2002
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Distance-based classification with lipschitz functions
Ulrike von Luxburg and Olivier Bousquet · 2004
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Pattern recognition and machine learning
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Fast orthogonal neural networks
Bartłomiej Stasiak and Mykhaylo Yatsymirskyy · 2006
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Weight normalization: A simple reparameterization to accelerate training of deep neural networks
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Unitary evolution recurrent neural networks
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Deep residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
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Robust large margin deep neural networks
J. Sokolic, R. Giryes, G. Sapiro, and M. R. D. Rodrigues · 2017
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Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Parseval networks: Improving robustness to adversarial examples
Moustapha Cisse, Piotr Bojanowski, Edouard Grave, Yann Dauphin, and Nicolas Usunier · 2017
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Towards interpretable deep neural networks by leveraging adversarial examples
Yinpeng Dong, Hang Su, Jun Zhu, and Fan Bao · 2017
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Improved training of wasserstein gans
Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville · 2017
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Spectral norm regularization for improving the generalizability of deep learning
Yuichi Yoshida and Takeru Miyato · 2017
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Efficient orthogonal parametrisation of recurrent neural networks using householder reflections
Zakaria Mhammedi, Andrew Hellicar, Ashfaqur Rahman, and James Bailey · 2017
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Variational inference with orthogonal normalizing flows
Leonard Hasenclever, Jakub M Tomczak, Rianne van den Berg, and Max Welling · 2017
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Learning unitary operators with help from u (n)
Stephanie L Hyland and Gunnar Rätsch · 2017
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Spectrally-normalized margin bounds for neural networks
Peter L Bartlett, Dylan J Foster, and Matus Telgarsky · 2017
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Limitations of the lipschitz constant as a defense against adversarial examples
Todd Huster, Cho-Yu Jason Chiang, and Ritu Chadha · 2018
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Spectral normalization for generative adversarial networks
Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida · 2018
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Lipschitz-margin training: Scalable certification of perturbation invariance for deep neural networks
Yusuke Tsuzuku, Issei Sato, and Masashi Sugiyama · 2018
Rethinking softmax cross-entropy loss for adversarial robustness
Tianyu Pang, Kun Xu, Yinpeng Dong, Chao Du, Ning Chen, and Jun Zhu · 2019
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A closer look at accuracy vs. robustness
Yao-Yuan Yang, Cyrus Rashtchian, Hongyang Zhang, Russ R Salakhutdinov, and Kamalika Chaudhuri · 2020
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Convolutional neural network weights regularization via orthogonalization
Alexander V Gayer and Alexander V Sheshkus · 2020
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Orthogonal convolutional neural networks
Jiayun Wang, Yubei Chen, Rudrasis Chakraborty, and Stella X Yu · 2020
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Stochastic flows and geometric optimization on the orthogonal group
Krzysztof Choromanski, David Cheikhi, Jared Davis, Valerii Likhosherstov, Achille Nazaret, Achraf Bahamou, Xingyou Song, Mrugank Akarte, Jack Parker-Holder, Jacob Bergquist, et al · 2020
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Achieving robustness in classification using optimal transport with hinge regularization
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Towards fast computation of certified robustness for relu networks
Lily Weng, Huan Zhang, Hongge Chen, Zhao Song, Cho-Jui Hsieh, Luca Daniel, Duane Boning, and Inderjit Dhillon · 2018
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Evaluating the robustness of neural networks: An extreme value theory approach
Tsui-Wei Weng, Huan Zhang, Pin-Yu Chen, Jinfeng Yi, Dong Su, Yupeng Gao, Cho-Jui Hsieh, and Luca Daniel · 2018
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Towards deep learning models resistant to adversarial attacks
Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu · 2018
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Lipschitz regularity of deep neural networks: analysis and efficient estimation
Kevin Scaman and Aladin Virmaux · 2018
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Why the failure? how adversarial examples can provide insights for interpretable machine learning
Richard Tomsett, Amy Widdicombe, Tianwei Xing, Supriyo Chakraborty, Simon Julier, Prudhvi Gurram, Raghuveer Rao, and Mani Srivastava · 2018
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Improving the adversarial robustness and interpretability of deep neural networks by regularizing their input gradients
Andrew Ross and Finale Doshi-Velez · 2018
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Mathieu Serrurier, Franck Mamalet, Alberto González-Sanz, Thibaut Boissin, Jean-Michel Loubes, and Eustasio del Barrio · 2021
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Regularisation of neural networks by enforcing lipschitz continuity
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The lipschitz constant of self-attention
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Lipschitz recurrent neural networks
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Training certifiably robust neural networks with efficient local lipschitz bounds
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Convolutional normalization: Improving deep convolutional network robustness and training
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Existence, stability and scalability of orthogonal convolutional neural networks
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Skew orthogonal convolutions
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Constructing orthogonal convolutions in an explicit manner
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Parallel orthogonal deep neural network
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Spectral normalization for deep reinforcement learning: an optimisation perspective
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Lipschitz normalization for self-attention layers with application to graph neural networks
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Classical and quantum algorithms for orthogonal neural networks
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Bridging the gap between adversarial robustness and optimization bias
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Understanding deep learning (still) requires rethinking generalization
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Controlling the complexity and lipschitz constant improves polynomial nets
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Scaling-up diverse orthogonal convolutional networks by a paraunitary framework
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Fast and accurate optimization on the orthogonal manifold without retraction
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