Certifiably robust interpretation

A system for generating an interpretation map, the system comprising:

• a convolutional neural network;
• and
• an apparatus comprising a processor, connected to a memory, operable to:
• add generalized Gaussian noise to an image x to obtain T noisy images, wherein the generalized Gaussian noise constitutes perturbations to the image x;
• provide the T noisy images as input to the convolutional neural network;
• calculate T noisy interpretations of output from the convolutional neural network corresponding to the T noisy images, wherein the T noisy interpretations comprise images that illustrate how important each pixel in the image x is for classification by the convolutional neural network;
• re-scale the T noisy interpretations using a scoring vector u to obtain T re-scaled noisy interpretations;
• and
• generate the interpretation map using the T re-scaled noisy interpretations, wherein the interpretation map is robust against the perturbations, and wherein the perturbations are constrained by an d-norm for any d≥1, including d=∞.

A non-transitory computer program product for generating an interpretation map, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a computer to cause the computer to:

• add generalized Gaussian noise to an image x to obtain T noisy images, wherein the generalized Gaussian noise constitutes perturbations to the image x;
• provide the T noisy images as input to a convolutional neural network;
• calculate T noisy interpretations of output from the convolutional neural network corresponding to the T noisy images, wherein the T noisy interpretations comprise images that illustrate how important each pixel in the image x is for classification by the convolutional neural network;
• re-scale the T noisy interpretations using a scoring vector υ to obtain T re-scaled noisy interpretations;
• and
• generate the interpretation map using the T re-scaled noisy interpretations, wherein the interpretation map is robust against the perturbations, and wherein the perturbations are constrained by an d-norm for any d≥1, including d=∞.