Robustness Guarantees for Adversarial Training on Non-Separable Data

Yunjuan Wang, Kaibo Zhang, Raman Arora

Primary Area: general machine learning (i.e., none of the above)

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Keywords: Adversarial training, neural networks, convergence and generalization guarantees

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Abstract: Adversarial training has emerged as a popular approach for training models that are robust to inference time attacks. However, our theoretical understanding of why and when it works remains limited. Prior work has offered convergence analysis of adversarial training, but they are either restricted to the Neural Tangent Kernel (NTK) regime or make restrictive assumptions about data such as linearly realizability. In this work, we provide convergence and generalization guarantees for adversarial training of two-layer networks of any width on non-separable data. Our analysis goes beyond the NTK regime and holds for both smooth and non-smooth activation functions. We support our theoretical findings with an empirical study on synthetic and real-world data.

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Submission Number: 3898