  Despite its popularity, deep neural networks are easily fooled. To alleviate
this deficiency, researchers are actively developing new training strategies,
which encourage models that are robust to small input perturbations. Several
successful robust training methods have been proposed. However, many of them
rely on strong adversaries, which can be prohibitively expensive to generate
when the input dimension is high and the model structure is complicated. We
adopt a new perspective on robustness and propose a novel training algorithm
that allows a more effective use of adversaries. Our method improves the model
robustness at each local ball centered around an adversary and then, by
combining these local balls through a global term, achieves overall robustness.
We demonstrate that, by maximizing the use of adversaries via focusing on local
balls, we achieve high robust accuracy with weak adversaries. Specifically, our
method reaches a similar robust accuracy level to the state of the art
approaches trained on strong adversaries on MNIST, CIFAR-10 and CIFAR-100. As a
result, the overall training time is reduced. Furthermore, when trained with
strong adversaries, our method matches with the current state of the art on
MNIST and outperforms them on CIFAR-10 and CIFAR-100.
