Local Stability of Adversarial Examples

Neural networks’ lack of stability to “small” perturbations of the input signal is a topic of substantial interest. Recent work has explored a number of properties of these so-called adversarial examples (AE) in an attempt to further understand this phenomenon. The present work continues in this spirit and provides an explicit characterization of stability for AE derived from very small perturbations. We also suggest future directions for how this characterization might be used in practice to mitigate the impact of these AE.