  Despite the great success achieved in machine learning (ML), adversarial
examples have caused concerns with regards to its trustworthiness: A small
perturbation of an input results in an arbitrary failure of an otherwise
seemingly well-trained ML model. While studies are being conducted to discover
the intrinsic properties of adversarial examples, such as their transferability
and universality, there is insufficient theoretic analysis to help understand
the phenomenon in a way that can influence the design process of ML
experiments. In this paper, we deduce an information-theoretic model which
explains adversarial attacks as the abuse of feature redundancies in ML
algorithms. We prove that feature redundancy is a necessary condition for the
existence of adversarial examples. Our model helps to explain some major
questions raised in many anecdotal studies on adversarial examples. Our theory
is backed up by empirical measurements of the information content of benign and
adversarial examples on both image and text datasets. Our measurements show
that typical adversarial examples introduce just enough redundancy to overflow
the decision making of an ML model trained on corresponding benign examples. We
conclude with actionable recommendations to improve the robustness of machine
learners against adversarial examples.
