E-MART: An Improved Misclassification Aware Adversarial Training with Entropy-Based Uncertainty Measure

Recently, adversarial training (AT) has been demonstrated to be effective to improve deep neural network (DNN) robustness against adversarial examples. Among them, Misclassification Aware adveRsarial Training (MART) is the most promising one, which incorporates an explicit differentiation of misclassified examples as a regularizer. However, MART uses prediction error for identifying the misclassified examples, and yet it fails to achieve the greatest performance. This crux lies in the fact that the prediction error only focuses on the output probability regarding with the ground-truth label, neglecting the impact of the complement classes. In this paper, we offer a unique insight into the condition that emphasizes learning on misclassified examples, and propose an improved MART method with entropy-based uncertainty measure (termed as E-MART). Specifically, we consider the impact of the outputs from all classes and develop an entropy-based uncertainty measure (EUM) to provide reliable evidence that indicates the impact of the misclassified and correctly classified examples. Moreover, based on EUM, we conduct a soft decision scheme to optimize the loss function of AT, which help to make the efficient training for the model's final robustness. We have carried out experiments on CIFAR-10 dataset, and the experimental results demonstrate the effectiveness of our method.