Proper Measure for Adversarial Robustness
Authors: Hyeongji Kim, Ketil Malde
Keywords: adversarial examples, adversarial robustness, adversarial accuracy, nearest neighbor classifiers
Abstract: This paper analyzes the problems of adversarial accuracy and adversarial training. We argue that standard adversarial accuracy fails to properly measure the robustness of classifiers. Its definition has a tradeoff with standard accuracy even when we neglect generalization. In order to handle the problems of the standard adversarial accuracy, we introduce a new measure for the robustness of classifiers called genuine adversarial accuracy. It can measure the adversarial robustness of classifiers without trading off accuracy on clean data and accuracy on the adversarially perturbed samples. In addition, it does not favor a model with invariance-based adversarial examples, samples whose predicted classes are unchanged even if the perceptual classes are changed. We prove that a single nearest neighbor (1-NN) classifier is the most robust classifier according to genuine adversarial accuracy for given data and a norm-based distance metric when the class for each data point is unique. Based on this result, we suggest that using poor distance metrics might be one factor for the tradeoff between test accuracy and $l_p$ norm-based test adversarial robustness.