  As machine learning (ML) models become more widely deployed in high-stakes
applications, counterfactual explanations have emerged as key tools for
providing actionable model explanations in practice. Despite the growing
popularity of counterfactual explanations, a deeper understanding of these
explanations is still lacking. In this work, we systematically analyze
counterfactual explanations through the lens of adversarial examples. We do so
by formalizing the similarities between popular counterfactual explanation and
adversarial example generation methods identifying conditions when they are
equivalent. We then derive the upper bounds on the distances between the
solutions output by counterfactual explanation and adversarial example
generation methods, which we validate on several real-world data sets. By
establishing these theoretical and empirical similarities between
counterfactual explanations and adversarial examples, our work raises
fundamental questions about the design and development of existing
counterfactual explanation algorithms.
