  Robustness of machine learning models to various adversarial and
non-adversarial corruptions continues to be of interest. In this paper, we
introduce the notion of the boundary thickness of a classifier, and we describe
its connection with and usefulness for model robustness. Thick decision
boundaries lead to improved performance, while thin decision boundaries lead to
overfitting (e.g., measured by the robust generalization gap between training
and testing) and lower robustness. We show that a thicker boundary helps
improve robustness against adversarial examples (e.g., improving the robust
test accuracy of adversarial training) as well as so-called out-of-distribution
(OOD) transforms, and we show that many commonly-used regularization and data
augmentation procedures can increase boundary thickness. On the theoretical
side, we establish that maximizing boundary thickness during training is akin
to the so-called mixup training. Using these observations, we show that
noise-augmentation on mixup training further increases boundary thickness,
thereby combating vulnerability to various forms of adversarial attacks and OOD
transforms. We can also show that the performance improvement in several lines
of recent work happens in conjunction with a thicker boundary.
