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Interpretability of Deep Learning (DL) is a barrier to trustworthy AI.Despite great efforts made by the Explainable AI (XAI) community, explanationslack robustness -- indistinguishable input perturbations may lead to differentXAI results. Thus, it is vital to assess how robust DL interpretability is,given an XAI method. In this paper, we identify several challenges that thestate-of-the-art is unable to cope with collectively: i) existing metrics arenot comprehensive; ii) XAI techniques are highly heterogeneous; iii)misinterpretations are normally rare events. To tackle these challenges, weintroduce two black-box evaluation methods, concerning the worst-caseinterpretation discrepancy and a probabilistic notion of how robust in general,respectively. Genetic Algorithm (GA) with bespoke fitness function is used tosolve constrained optimisation for efficient worst-case evaluation. SubsetSimulation (SS), dedicated to estimate rare event probabilities, is used forevaluating overall robustness. Experiments show that the accuracy, sensitivity,and efficiency of our methods outperform the state-of-the-arts. Finally, wedemonstrate two applications of our methods: ranking robust XAI methods andselecting training schemes to improve both classification and interpretationrobustness.

SAFARI: Versatile and Efficient Evaluations for Robustness of Interpretability