  Deep Networks have been shown to provide state-of-the-art performance in many
machine learning challenges. Unfortunately, they are susceptible to various
types of noise, including adversarial attacks and corrupted inputs. In this
work we introduce a formal definition of robustness which can be viewed as a
localized Lipschitz constant of the network function, quantified in the domain
of the data to be classified. We compare this notion of robustness to existing
ones, and study its connections with methods in the literature. We evaluate
this metric by performing experiments on various competitive vision datasets.
