Certified Robust Neural Networks: Generalization and Corruption Resistance.

Adversarial training aims to reduce the problematic susceptibility of modern neural networks to small data perturbations. Surprisingly, overfitting is a major concern in adversarial training of neural networks despite being mostly absent in standard training. We provide here theoretical evidence for this peculiar ``robust overfitting'' phenomenon. Subsequently, we advance a novel loss function which we show both theoretically as well as empirically to enjoy a certified level of robustness against data evasion and poisoning attacks while ensuring guaranteed generalization. We indicate through careful numerical experiments that our resulting holistic robust (HR) training procedure yields SOTA performance in terms of adversarial error loss. Finally, we indicate that HR training can be interpreted as a direct extension of adversarial training and comes with a negligible additional computational burden.