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Adversarial perturbations have drawn great attentions in various deep neuralnetworks. Most of them are computed by iterations and cannot be interpretedvery well. In contrast, little attentions are paid to basic machine learningmodels such as support vector machines. In this paper, we investigate theoptimization models and the interpretations for three types of adversarialperturbations against support vector machines, including sample-adversarialperturbations (sAP), class-universal adversarial perturbations (cuAP) as wellas universal adversarial perturbations (uAP). For linear binary/multiclassification support vector machines (SVMs), we derive the explicit solutionsfor sAP, cuAP and uAP (binary case), and approximate solution for uAP ofmulti-classification. We also obtain the upper bound of fooling rate for uAP.Such results not only increase the interpretability of the three adversarialperturbations, but also provide great convenience in computation sinceiterative process can be avoided. Numerical results show that our method isfast and effective in calculating three types of adversarial perturbations.

Optimization Models and Interpretations for Three Types of Adversarial Perturbations against Support Vector Machines