Deep neural networks (DNNs) are known vulnerable to adversarial attacks. That is, adversarial examples, obtained by adding delicately crafted distortions onto original legal inputs, can mislead a DNN to classify them as any target labels. This work provides a solution to hardening DNNs under adversarial attacks through defensive dropout. Besides using dropout during training for the best test accuracy, we propose to use dropout also at test time to achieve strong defense effects. We consider the problem of building robust DNNs as an attacker-defender two-player game, where the attacker and the defender know each others' strategies and try to optimize their own strategies towards an equilibrium. Based on the observations of the effect of test dropout rate on test accuracy and attack success rate, we propose a defensive dropout algorithm to determine an optimal test dropout rate given the neural network model and the attacker's strategy for generating adversarial examples.We also investigate the mechanism behind the outstanding defense effects achieved by the proposed defensive dropout. Comparing with stochastic activation pruning (SAP), another defense method through introducing randomness into the DNN model, we find that our defensive dropout achieves much larger variances of the gradients, which is the key for the improved defense effects (much lower attack success rate). For example, our defensive dropout can reduce the attack success rate from 100% to 13.89% under the currently strongest attack i.e., C&W attack on MNIST dataset.

采用防御性抛弃策略来提高神经网络模型的抵御对抗攻击能力，优化测试抛弃率，并通过攻击方与防御方的博弈过程来确定最优策略。相较于随机激活剪枝等其他防御方法，防御性抛弃在MNIST数据集上的攻击成功率可以由100％降至13.89％。

防御性随机失活用于加固对抗攻击下的深度神经网络