  Classical adversarial training (AT) frameworks are designed to achieve high
adversarial accuracy against a single attack type, typically $\ell_\infty$
norm-bounded perturbations. Recent extensions in AT have focused on defending
against the union of multiple perturbations but this benefit is obtained at the
expense of a significant (up to $10\times$) increase in training complexity
over single-attack $\ell_\infty$ AT. In this work, we expand the capabilities
of widely popular single-attack $\ell_\infty$ AT frameworks to provide
robustness to the union of ($\ell_\infty, \ell_2, \ell_1$) perturbations while
preserving their training efficiency. Our technique, referred to as Shaped
Noise Augmented Processing (SNAP), exploits a well-established byproduct of
single-attack AT frameworks -- the reduction in the curvature of the decision
boundary of networks. SNAP prepends a given deep net with a shaped noise
augmentation layer whose distribution is learned along with network parameters
using any standard single-attack AT. As a result, SNAP enhances adversarial
accuracy of ResNet-18 on CIFAR-10 against the union of ($\ell_\infty, \ell_2,
\ell_1$) perturbations by 14%-to-20% for four state-of-the-art (SOTA)
single-attack $\ell_\infty$ AT frameworks, and, for the first time, establishes
a benchmark for ResNet-50 and ResNet-101 on ImageNet.
