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Lipschitz continuity is a crucial functional property of any predictive model, that naturally governs its robustness, generalisation, as well as adversarial vulnerability.
Neural networks and the bias/variance dilemma
Stuart Geman, Elie Bienenstock, and René Doursat · 1992
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Geometric Measure Theory , chapter 3.1.1, pp. 209
Herbert Federer · 1996
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Learning Multiple Layers of Features from Tiny Images
Alex Krizhevsky · 2009
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Lipschitz Bounded Equilibrium Networks
Max Revay, Ruigang Wang, and Ian R. Manchester · 2010
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Sam Greydanus · 2011
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Intriguing properties of neural networks
Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian J. Goodfellow, and Rob Fergus · 2014
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Explaining and Harnessing Adversarial Examples
Ian J. Goodfellow, Jonathon Shlens, and Christian Szegedy · 2015
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Deep Learning , chapter 9.1, pp. 329
Ian Goodfellow, Yoshua Bengio, and Aaron Courville · 2016
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Deep residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
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Martín Arjovsky, Soumith Chintala, and Léon Bottou · 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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Parseval Networks: Improving Robustness to Adversarial Examples
Moustapha Cissé, Piotr Bojanowski, Edouard Grave, Yann N. Dauphin, and Nicolas Usunier · 2017
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Effective Lipschitz constraint enforcement for Wasserstein GAN training
Shaobo Cui and Yong Jiang · 2017
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Adversarial Machine Learning at Scale
Alexey Kurakin, Ian J. Goodfellow, and Samy Bengio · 2017
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On the regularization of Wasserstein GANs
Henning Petzka, Asja Fischer, and Denis Lukovnikov · 2017
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The Marginal Value of Adaptive Gradient Methods in Machine Learning
Ashia C. Wilson, Rebecca Roelofs, Mitchell Stern, Nathan Srebro, and Benjamin Recht · 2017
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Sorting out Lipschitz function approximation
Cem Anil, James Lucas, and Roger Baker Grosse · 2018
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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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Neural tangent kernel: Convergence and generalization in neural networks
Arthur Jacot, Franck Gabriel, and Clément Hongler · 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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A Modern Take on the Bias-Variance Tradeoff in Neural Networks
Brady Neal, Sarthak Mittal, Aristide Baratin, Vinayak Tantia, Matthew Scicluna, Simon Lacoste-Julien, and Ioannis Mitliagkas · 2018
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Lightweight Lipschitz Margin Training for Certified Defense against Adversarial Examples
Hajime Ono, Tsubasa Takahashi, and Kazuya Kakizaki · 2018
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How Does Lipschitz Regularization Influence GAN Training?
Yipeng Qin, Niloy Jyoti Mitra, and Peter Wonka · 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
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Lipschitz regularity of deep neural networks: analysis and efficient estimation
Aladin Virmaux and Kevin Scaman · 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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Understanding the effectiveness of lipschitz constraint in training of gans via gradient analysis
Zhiming Zhou, Yuxuan Song, Lantao Yu, and Yong Yu · 2018
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On exact computation with an infinitely wide neural net
Sanjeev Arora, Simon S Du, Wei Hu, Zhiyuan Li, Russ R Salakhutdinov, and Ruosong Wang · 2019
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Reconciling modern machine-learning practice and the classical bias-variance trade-off
Mikhail Belkin, Daniel J. Hsu, Siyuan Ma, and Soumik Mandal · 2019
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Lipschitz Recurrent Neural Networks
N. Benjamin Erichson, Omri Azencot, Alejandro F. Queiruga, Liam Hodgkinson, and Michael W. Mahoney · 2021
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Regularisation of neural networks by enforcing Lipschitz continuity
Henry Gouk, Eibe Frank, Bernhard Pfahringer, and Michael J. Cree · 2021
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Globally-Robust Neural Networks
Klas Leino, Zifan Wang, and Matt Fredrikson · 2021
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Optimal Regularization can Mitigate Double Descent
Preetum Nakkiran, Prayaag Venkat, Sham M. Kakade, and Tengyu Ma · 2021
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Training Robust Neural Networks Using Lipschitz Bounds
Patricia Pauli, Anne Koch, Julian Berberich, Paul Kohler, and Frank Allgöwer · 2021
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Skew Orthogonal Convolutions
Sahil Singla and Soheil Feizi · 2021
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On lazy training in differentiable programming
Lenaic Chizat, Edouard Oyallon, and Francis Bach · 2019
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Gradient Descent Provably Optimizes Over-parameterized Neural Networks
Simon S. Du, Xiyu Zhai, Barnabás Póczos, and Aarti Singh · 2019
Cited alongside, same era.
Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks
Mahyar Fazlyab, Alexander Robey, Hamed Hassani, Manfred Morari, and George J. Pappas · 2019
Cited alongside, same era.
Preventing Gradient Attenuation in Lipschitz Constrained Convolutional Networks
Qiyang Li, Saminul Haque, Cem Anil, James Lucas, Roger B Grosse, and Jörn-Henrik Jacobsen · 2019
Cited alongside, same era.
Adversarial Lipschitz Regularization
Dávid Terjék · 2019
Cited alongside, same era.
Lipschitz Generative Adversarial Nets
Zhiming Zhou, Jiadong Liang, Yuxuan Song, Lantao Yu, Hongwei Wang, Weinan Zhang, Yong Yu, and Zhihua Zhang · 2019
Cited alongside, same era.
The Neural Tangent Kernel in High Dimensions: Triple Descent and a Multi-Scale Theory of Generalization, 2020
Ben Adlam and Jeffrey Pennington · 2020
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Adapting Stepsizes by Momentumized Gradients Improves Optimization and Generalization
Yizhou Wang, Yue Kang, Can Qin, Yi Xu, Huan Wang, Yulun Zhang, and Yun Fu · 2021
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Constructing Orthogonal Convolutions in an explicit manner
Tan Yu, Jun Li, Yunfeng Cai, and Ping Li · 2021
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Understanding deep learning (still) requires rethinking generalization
Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2021
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Pay attention to your loss: understanding misconceptions about 1-Lipschitz neural networks
Louis Béthune, Thibaut Boissin, Mathieu Serrurier, Franck Mamalet, Corentin Friedrich, and Alberto Gonzalez Sanz · 2022
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Why neural networks find simple solutions: The many regularizers of geometric complexity
Benoit Dherin, Michael Munn, Mihaela Rosca, and David Barrett · 2022
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The generalization error of random features regression: Precise asymptotics and the double descent curve
Song Mei and Andrea Montanari · 2022
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A dynamical system perspective for Lipschitz neural networks
Laurent Meunier, Blaise J Delattre, Alexandre Araujo, and Alexandre Allauzen · 2022
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The interpolation phase transition in neural networks: Memorization and generalization under lazy training
Andrea Montanari and Yiqiao Zhong · 2022
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Almost-Orthogonal Layers for Efficient General-Purpose Lipschitz Networks
Bernd Prach and Christoph H Lampert · 2022
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Feature learning and random features in standard finite-width convolutional neural networks: An empirical study
Maxim Samarin, Volker Roth, and David Belius · 2022
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Phenomenology of Double Descent in Finite-Width Neural Networks
Sidak Pal Singh, Aurélien Lucchi, Thomas Hofmann, and Bernhard Schölkopf · 2022
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A Quantitative Geometric Approach to Neural-Network Smoothness
Zi Wang, Gautam Prakriya, and Somesh Jha · 2022
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A Unified Algebraic Perspective on Lipschitz Neural Networks
Alexandre Araujo, Aaron J. Havens, Blaise Delattre, Alexandre Allauzen, and Bin Hu · 2023
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On the Lipschitz Constant of Deep Networks and Double Descent
Matteo Gamba, Hossein Azizpour, and Mårten Björkman · 2023
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Proper ResNet implementation for CIFAR10/CIFAR100 in PyTorch
Yerlan Idelbayev · 2023
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A margin-based multiclass generalization bound via geometric complexity, 2023
Michael Munn, Benoit Dherin, and Javier Gonzalvo · 2023
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Direct Parameterization of Lipschitz-bounded Deep Networks
Ruigang Wang and Ian Manchester · 2023
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