Adversarial Training with Maximal Coding Rate Reduction

Deep convolutional networks can solve various complex tasks in the field of image processing. However, adversarial attacks have been shown to have the ability of fooling deep learning models. Adversarial training is one commonly used strategy to improve the robustness of deep learning models against adversarial examples, which is performed by incorporating adversarial examples into the training process. Traditionally, during this process, cross-entropy loss is used as the loss function. In order to improve the robustness of deep learning models against adversarial examples, we propose in this paper two new methods of adversarial training by applying the principle of Maximal Coding Rate Reduction (MCR<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>). We evaluate the performance of different adversarial training methods by comparing the clean accuracy and adversarial accuracy. It is shown that adversarial training with the MCR<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> loss function yields a more robust network than the traditional adversarial training method. In our experiments, adversarial accuracies are improved by up to 10%. The two loss functions are discussed by using a model.