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Training convolutional neural networks (CNNs) with a strict Lipschitz constraint under the $l_{2}$ norm is useful for provable adversarial robustness, interpretable gradients and stable training.
Optimal transport, old and new, 2008
Cedric Villani · 2008
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Spectrally-normalized margin bounds for neural networks
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Spectral normalization for generative adversarial networks
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Semidefinite relaxations for certifying robustness to adversarial examples
Aditi Raghunathan, Jacob Steinhardt, and Percy Liang · 2018
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Fast and effective robustness certification
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Robustness may be at odds with accuracy
Dimitris Tsipras, Shibani Santurkar, Logan Engstrom, Alexander Turner, and Aleksander Madry · 2018
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Lipschitz-margin training: Scalable certification of perturbation invariance for deep neural networks
Yusuke Tsuzuku, I. Sato, and Masashi Sugiyama · 2018
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Towards fast computation of certified robustness for ReLU networks
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Provable defenses against adversarial examples via the convex outer adversarial polytope
Eric Wong and Zico Kolter · 2018
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Scaling provable adversarial defenses
Eric Wong, Frank R. Schmidt, Jan Hendrik Metzen, and J. Zico Kolter · 2018
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Dynamical isometry and a mean field theory of CNNs: How to train 10,000-layer vanilla convolutional neural networks
The singular values of convolutional layers
Hanie Sedghi, Vineet Gupta, and Philip M. Long · 2019
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Huan Zhang, Pengchuan Zhang, and Cho-Jui Hsieh · 2019
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Regularisation of neural networks by enforcing lipschitz continuity, 2020
Henry Gouk, Eibe Frank, Bernhard Pfahringer, and Michael J. Cree · 2020
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Certifying confidence via randomized smoothing
Aounon Kumar, Alexander Levine, Soheil Feizi, and Tom Goldstein · 2020
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Generalization bounds for deep convolutional neural networks
Philip M. Long and Hanie Sedghi · 2020
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Second-order provable defenses against adversarial attacks
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