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Driven by massive amounts of data and important advances in computationalresources, new deep learning systems have achieved outstanding results in alarge spectrum of applications. Nevertheless, our current theoreticalunderstanding on the mathematical foundations of deep learning lags far behindits empirical success. Towards solving the vulnerability of neural networks,however, the field of adversarial robustness has recently become one of themain sources of explanations of our deep models. In this article, we provide anin-depth review of the field of adversarial robustness in deep learning, andgive a self-contained introduction to its main notions. But, in contrast to themainstream pessimistic perspective of adversarial robustness, we focus on themain positive aspects that it entails. We highlight the intuitive connectionbetween adversarial examples and the geometry of deep neural networks, andeventually explore how the geometric study of adversarial examples can serve asa powerful tool to understand deep learning. Furthermore, we demonstrate thebroad applicability of adversarial robustness, providing an overview of themain emerging applications of adversarial robustness beyond security. The goalof this article is to provide readers with a set of new perspectives tounderstand deep learning, and to supply them with intuitive tools and insightson how to use adversarial robustness to improve it.

Optimism in the Face of Adversity: Understanding and Improving Deep Learning through Adversarial Robustness