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Training convolutional neural networks with a Lipschitz constraint under the $l_{2}$ norm is useful for provable adversarial robustness, interpretable gradients, stable training, etc.
The geometry of algorithms with orthogonality constraints
Edelman, A., Arias, T. A., and Smith, S · 1998
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Optimal transport, old and new, 2008
Villani, C · 2008
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Intriguing properties of neural networks
Szegedy, C., Zaremba, W., Sutskever, I., Bruna, J., Erhan, D., Goodfellow, I., and Fergus, R · 2014
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Wasserstein generative adversarial networks
Arjovsky, M., Chintala, S., and Bottou, L · 2017
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Spectrally-normalized margin bounds for neural networks
Bartlett, P. L., Foster, D. J., and Telgarsky, M · 2017
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Mitigating evasion attacks to deep neural networks via region-based classification
Cao, X. and Gong, N. Z · 2017
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Parseval networks: Improving robustness to adversarial examples
Cissé, M., Bojanowski, P., Grave, E., Dauphin, Y. N., and Usunier, N · 2017
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Improved training of wasserstein gans
Gulrajani, I., Ahmed, F., Arjovsky, M., Dumoulin, V., and Courville, A. C · 2017
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Sorting out lipschitz function approximation
Anil, C., Lucas, J., and Grosse, R. B · 2018
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i-revnet: Deep invertible networks
Jacobsen, J.-H., Smeulders, A. W., and Oyallon, E · 2018
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Certified robustness to adversarial examples with differential privacy
Lécuyer, M., Atlidakis, V., Geambasu, R., Hsu, D., and Jana, S. K. K · 2018
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Towards robust neural networks via random self-ensemble
Liu, X., Cheng, M., Zhang, H., and Hsieh, C · 2018
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Towards deep learning models resistant to adversarial attacks
Madry, A., Makelov, A., Schmidt, L., Tsipras, D., and Vladu, A · 2018
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Spectral normalization for generative adversarial networks
Miyato, T., Kataoka, T., Koyama, M., and Yoshida, Y · 2018
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Computational optimal transport, 2018
Peyré, G. and Cuturi, M · 2018
Cited alongside, same era.
Semidefinite relaxations for certifying robustness to adversarial examples
Raghunathan, A., Steinhardt, J., and Liang, P · 2018
Cited alongside, same era.
Fast and effective robustness certification
Singh, G., Gehr, T., Mirman, M., Püschel, M., and Vechev, M. T · 2018
Cited alongside, same era.
Wasserstein auto-encoders
Tolstikhin, I., Bousquet, O., Gelly, S., and Schoelkopf, B · 2018
Cited alongside, same era.
Robustness may be at odds with accuracy
Tsipras, D., Santurkar, S., Engstrom, L., Turner, A., and Madry, A · 2018
Cited alongside, same era.
Lipschitz-margin training: Scalable certification of perturbation invariance for deep neural networks
Tsuzuku, Y., Sato, I., and Sugiyama, M · 2018
Cited alongside, same era.
Certified adversarial robustness with additive noise
Li, B., Chen, C., Wang, W., and Carin, L · 2019
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L2-nonexpansive neural networks
Qian, H. and Wegman, M. N · 2019
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Plug-and-play methods provably converge with properly trained denoisers
Ryu, E., Liu, J., Wang, S., Chen, X., Wang, Z., and Yin, W · 2019
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Provably robust deep learning via adversarially trained smoothed classifiers
Salman, H., Li, J., Razenshteyn, I., Zhang, P., Zhang, H., Bubeck, S., and Yang, G · 2019
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The singular values of convolutional layers
Sedghi, H., Gupta, V., and Long, P. M · 2019
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Towards fast computation of certified robustness for relu networks
Weng, T.-W., Zhang, H., Chen, H., Song, Z., Hsieh, C.-J., Boning, D., and Daniel, I. S. D. A · 2018
Cited alongside, same era.
Provable defenses against adversarial examples via the convex outer adversarial polytope
Wong, E. and Kolter, Z · 2018
Cited alongside, same era.
Scaling provable adversarial defenses
Wong, E., Schmidt, F. R., Metzen, J. H., and Kolter, J. Z · 2018
Cited alongside, same era.
Dynamical isometry and a mean field theory of CNNs: How to train 10,000-layer vanilla convolutional neural networks
Xiao, L., Bahri, Y., Sohl-Dickstein, J., Schoenholz, S., and Pennington, J · 2018
Cited alongside, same era.
Efficient neural network robustness certification with general activation functions
Zhang, H., Weng, T.-W., Chen, P.-Y., Hsieh, C.-J., and Daniel, L · 2018
Cited alongside, same era.
Certified adversarial robustness via randomized smoothing
Cohen, J. M., Rosenfeld, E., and Kolter, J. Z · 2019
Cited alongside, same era.
Zhang, H., Zhang, P., and Hsieh, C.-J · 2019
Later among the works it cites.
Regularisation of neural networks by enforcing lipschitz continuity, 2020
Gouk, H., Frank, E., Pfahringer, B., and Cree, M. J · 2020
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The convolution exponential and generalized sylvester flows
Hoogeboom, E., Satorras, V. G., Tomczak, J., and Welling, M · 2020
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Curse of dimensionality on randomized smoothing for certifiable robustness
Kumar, A., Levine, A., Goldstein, T., and Feizi, S · 2020
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Generalization bounds for deep convolutional neural networks
Long, P. M. and Sedghi, H · 2020
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Second-order provable defenses against adversarial attacks
Singla, S. and Feizi, S · 2020
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Fast is better than free: Revisiting adversarial training
Wong, E., Rice, L., and Kolter, J. Z · 2020
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Fantastic four: Differentiable and efficient bounds on singular values of convolution layers
Singla, S. and Feizi, S · 2021
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