  Adversarial perturbations have drawn great attentions in various machine
learning models. In this paper, we investigate the sample adversarial
perturbations for nonlinear support vector machines (SVMs). Due to the implicit
form of the nonlinear functions mapping data to the feature space, it is
difficult to obtain the explicit form of the adversarial perturbations. By
exploring the special property of nonlinear SVMs, we transform the optimization
problem of attacking nonlinear SVMs into a nonlinear KKT system. Such a system
can be solved by various numerical methods. Numerical results show that our
method is efficient in computing adversarial perturbations.
