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Adversarial Learning Guarantees for Linear Hypotheses and Neural Networks
Pranjal Awasthi · Natalie Frank · Mehryar Mohri

Tue Jul 14 07:00 AM -- 07:45 AM & Tue Jul 14 06:00 PM -- 06:45 PM (PDT) @ Virtual
Adversarial or test time robustness measures the susceptibility of a classifier to perturbations to the test input. While there has been a flurry of recent work on designing defenses against such perturbations, the theory of adversarial robustness is not well understood. In order to make progress on this, we focus on the problem of understanding generalization in adversarial settings, via the lens of Rademacher complexity. We give upper and lower bounds for the adversarial empirical Rademacher complexity of linear hypotheses with adversarial perturbations measured in $l_r$-norm for an arbitrary $r \geq 1$. We then extend our analysis to provide Rademacher complexity lower and upper bounds for a single ReLU unit. Finally, we give adversarial Rademacher complexity bounds for feed-forward neural networks with one hidden layer.

Author Information

Pranjal Awasthi (Rutgers University)
Natalie Frank (NYU)
Mehryar Mohri (Google Research and Courant Institute of Mathematical Sciences)

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