Interpretation maps of convolutional neural networks having certifiable robustness using Rényi differential privacy are provided. In one aspect, a method for generating an interpretation map includes: adding generalized Gaussian noise to an image x to obtain T noisy images, wherein the generalized Gaussian noise constitutes perturbations to the image x; providing the T noisy images as input to a convolutional neural network; calculating T noisy interpretations of output from the convolutional neural network corresponding to the T noisy images; re-scaling the T noisy interpretations using a scoring vector υ to obtain T re-scaled noisy interpretations; and generating the interpretation map using the T re-scaled noisy interpretations, wherein the interpretation map is robust against the perturbations.