Despite the wide use of machine learning in adversarial settings including computer security, recent studies have demonstrated vulnerabilities to evasion attacks---carefully crafted adversarial samples that closely resemble legitimate instances, but cause misclassification. In this paper, we examine the adequacy of the leading approach to generating adversarial samples---the gradient descent approach. In particular (1) we perform extensive experiments on three datasets, MNIST, USPS and Spambase, in order to analyse the effectiveness of the gradient-descent method against non-linear support vector machines, and conclude that carefully reduced kernel smoothness can significantly increase robustness to the attack; (2) we demonstrate that separated inter-class support vectors lead to more secure models, and propose a quantity similar to margin that can efficiently predict potential susceptibility to gradient-descent attacks, before the attack is launched; and (3) we design a new adversarial sample construction algorithm based on optimising the multiplicative ratio of class decision functions.
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