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A counter-intuitive property of convolutional neural networks (CNNs) is theirinherent susceptibility to adversarial examples, which severely hinders theapplication of CNNs in security-critical fields. Adversarial examples aresimilar to original examples but contain malicious perturbations. Adversarialtraining is a simple and effective defense method to improve the robustness ofCNNs to adversarial examples. The mechanisms behind adversarial examples andadversarial training are worth exploring. Therefore, this work investigatessimilarities and differences between normally trained CNNs (NT-CNNs) andadversarially trained CNNs (AT-CNNs) in information extraction from the mutualinformation perspective. We show that 1) whether NT-CNNs or AT-CNNs, fororiginal and adversarial examples, the trends towards mutual information arealmost similar throughout training; 2) compared with normal training,adversarial training is more difficult and the amount of information thatAT-CNNs extract from the input is less; 3) the CNNs trained with differentmethods have different preferences for certain types of information; NT-CNNstend to extract texture-based information from the input, while AT-CNNs preferto shape-based information. The reason why adversarial examples mislead CNNsmay be that they contain more texture-based information about other classes.Furthermore, we also analyze the mutual information estimators used in thiswork and find that they outline the geometric properties of the middle layer'soutput.

Exploring Adversarial Examples and Adversarial Robustness of Convolutional Neural Networks by Mutual Information