  Robustness is widely regarded as a fundamental problem in the analysis of
machine learning (ML) models. Most often robustness equates with deciding the
non-existence of adversarial examples, where adversarial examples denote
situations where small changes on some inputs cause a change in the prediction.
The perceived importance of ML model robustness explains the continued progress
observed for most of the last decade. Whereas robustness is often assessed
locally, i.e. given some target point in feature space, robustness can also be
defined globally, i.e. where any point in feature space can be considered. The
importance of ML model robustness is illustrated for example by the existence
of competitions evaluating the progress of robustness tools, namely in the case
of neural networks (NNs) but also by efforts towards robustness certification.
More recently, robustness tools have also been used for computing rigorous
explanations of ML models. In contrast with the observed successes of
robustness, this paper uncovers some limitations with existing definitions of
robustness, both global and local, but also with efforts towards robustness
certification. The paper also investigates uses of adversarial examples besides
those related with robustness.
