On relating explanations and adversarial examples

The importance of explanations (XP's) of machine learning (ML) model predictions and of adversarial examples (AE's) cannot be overstated, with both arguably being essential for the practical success of ML in different settings. There has been recent work on understanding and assessing the relationship between XP's and AE's. However, such work has been mostly experimental and a sound theoretical relationship has been elusive. This paper demonstrates that explanations and adversarial examples are related by a generalized form of hitting set duality, which extends earlier work on hitting set duality observed in model-based diagnosis and knowledge compilation. Furthermore, the paper proposes algorithms, which enable computing adversarial examples from explanations and vice-versa.