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We derive bounds for a notion of adversarial risk, designed to characterize the robustness of linear and neural network classifiers to adversarial perturbations.
Comparison theorems, random geometry and some limit theorems for empirical processes
M. Ledoux and M. Talagrand · 1989
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Probability in Banach Spaces: Isoperimetry and Processes
M. Ledoux and M. Talagrand · 1991
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Algebraic Graph Theory
C. Godsil and G. Royle · 2001
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Convexity, classification, and risk bounds
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Robust Optimization
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Foundations of Machine Learning
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Robust solutions of optimization problems affected by uncertain probabilities
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Intriguing properties of neural networks
C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus · 2013
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Data-driven distributionally robust optimization using the wasserstein metric: Performance guarantees and tractable reformulations
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Explaining and harnessing adversarial examples
I. J. Goodfellow, J. Shlens, and C. Szegedy · 2015
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Rademacher complexity margin bounds for learning with a large number of classes
V. Kuznetsov, M. Mohri, and U. Syed · 2015
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Deep Learning , volume 1
I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio · 2016
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Stochastic gradient methods for distributionally robust optimization with f f -divergences
H. Namkoong and J. C. Duchi · 2016
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The limitations of deep learning in adversarial settings
N. Papernot, P. McDaniel, S. Jha, M. Fredrikson, Z. B. Celik, and A. Swami · 2016
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Spectrally-normalized margin bounds for neural networks
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Analysis of classifiers’ robustness to adversarial perturbations
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Size-independent sample complexity of neural networks
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Black-box adversarial attacks with limited queries and information
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Towards deep learning models resistant to adversarial attacks
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Certified defenses against adversarial examples
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Adversarially robust generalization requires more data
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Robust regression and Lasso
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Are adversarial examples inevitable?
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Provable defenses against adversarial examples via the convex outer adversarial polytope
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