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Robustness against image perturbations bounded by a $\ell_p$ ball have been well-studied in recent literature.
A unified approach to the change of resolution: Space and gray-level
Shmuel Peleg, Michael Werman, and Hillel Rom · 1989
Earlier work this paper cites.
The earth mover’s distance as a metric for image retrieval
Yossi Rubner, Carlo Tomasi, and Leonidas Guibas · 2000
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Intriguing properties of neural networks
Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus · 2013
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Explaining and harnessing adversarial examples
Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy · 2015
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Imagenet large scale visual recognition challenge
Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, Alexander C. Berg, and Fei-Fei Li · 2015
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Towards evaluating the robustness of neural networks
Nicholas Carlini and David Wagner · 2017
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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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Certified defenses against adversarial examples
Aditi Raghunathan, Jacob Steinhardt, and Percy Liang · 2018
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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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Provable defenses against adversarial examples via the convex outer adversarial polytope
Eric Wong and Zico Kolter · 2018
Cited alongside, same era.
Certified adversarial robustness via randomized smoothing
Jeremy Cohen, Elan Rosenfeld, and Zico Kolter · 2019
Cited alongside, same era.
Adversarial robustness as a prior for learned representations
Functional adversarial attacks
Cassidy Laidlaw and Soheil Feizi · 2019
Later among the works it cites.
Wasserstein smoothing: Certified robustness against wasserstein adversarial attacks
Alexander Levine and Soheil Feizi · 2019
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Towards verifying robustness of neural networks against semantic perturbations
Jeet Mohapatra, Tsui-Wei Weng, Pin-Yu Chen, Sijia Liu, and Luca Daniel · 2019
Later among the works it cites.
Wasserstein adversarial examples via projected Sinkhorn iterations
Eric Wong, Frank Schmidt, and Zico Kolter · 2019
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Fast is better than free: Revisiting adversarial training
Eric Wong, Leslie Rice, and Zico Kolter · 2020
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Logan Engstrom, Andrew Ilyas, Shibani Santurkar, Dimitris Tsipras, Brandon Tran, and Aleksander Madry · 2019
Cited alongside, same era.
Provably robust deep learning via adversarially trained smoothed classifiers
Hadi Salman, Jerry Li, Ilya Razenshteyn, Pengchuan Zhang, Huan Zhang, Sebastien Bubeck, and Greg Yang
Cited in the paper.
A convex relaxation barrier to tight robustness verification of neural networks
Hadi Salman, Greg Yang, Huan Zhang, Cho-Jui Hsieh, and Pengchuan Zhang
Cited in the paper.