Interpretation maps of deep neural networks are provided that use Renyi differential privacy to guarantee the robustness of the interpretation. In one aspect, a method for generating interpretation maps with guaranteed robustness includes: perturbing an original digital image by adding Gaussian noise to the original digital image to obtain m noisy images; providing the m noisy images as input to a deep neural network; interpreting output from the deep neural network to obtain m noisy interpretations corresponding to the m noisy images; thresholding the m noisy interpretations to obtain a top-k of the m noisy interpretations; and averaging the top-k of the m noisy interpretations to produce an interpretation map with certifiable robustness.