Motivated by the recent discovery that the interpretation maps of CNNs could easily be manipulated by adversarial attacks against network interpretability, we study the problem of interpretation robustness from a new perspective of Renyi differential privacy (RDP). The advantages of our Renyi-Robust-Smooth (RDP-based interpretation method) are three-folds. First, it can offer provable and certifiable top-$k$ robustness. That is, the top-$k$ important attributions of the interpretation map are provably robust under any input perturbation with bounded $ell_d$-norm (for any $dgeq 1$, including $d = infty$). Second, our proposed method offers $sim10%$ better experimental robustness than existing approaches in terms of the top-$k$ attributions. Remarkably, the accuracy of Renyi-Robust-Smooth also outperforms existing approaches. Third, our method can provide a smooth tradeoff between robustness and computational efficiency. Experimentally, its top-$k$ attributions are {em twice} more robust than existing approaches when the computational resources are highly constrained.
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