It has recently been shown that neural networks but also other classifiers are vulnerable to so called adversarial attacks e.g. in object recognition an almost non-perceivable change of the image changes the decision of the classifier. Relatively fast heuristics have been proposed to produce these adversarial inputs but the problem of finding the optimal adversarial input, that is with the minimal change of the input, is NP-hard. While methods based on mixed-integer optimization which find the optimal adversarial input have been developed, they do not scale to large networks. Currently, the attack scheme proposed by Carlini and Wagner is considered to produce the best adversarial inputs. In this paper we propose a new attack scheme for the class of ReLU networks based on a direct optimization on the resulting linear regions. In our experimental validation we improve in all except one experiment out of 18 over the Carlini-Wagner attack with a relative improvement of up to 9\%. As our approach is based on the geometrical structure of ReLU networks, it is less susceptible to defences targeting their functional properties.

本文提出了一种基于直接优化的攻击方案，针对ReLU网络进行优化，相比Carlini-Wagner攻击方案，在18个实验中除了一个实验外均有提升，并提高了最多9％。

ReLU网络的随机无梯度攻击