An Efficient Method for Sample Adversarial Perturbations against Nonlinear Support Vector Machines

TL;DR

This paper presents an efficient numerical method to compute adversarial perturbations for nonlinear SVMs by transforming the attack problem into a solvable nonlinear KKT system.

Contribution

It introduces a novel approach that leverages the properties of nonlinear SVMs to efficiently generate adversarial samples, overcoming the challenge of implicit feature mappings.

Findings

Method efficiently computes adversarial perturbations.

Numerical results demonstrate high effectiveness and speed.

Applicable to various nonlinear SVM models.

Abstract

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.