论文标题
针对支持向量机的三种类型的对抗扰动的优化模型和解释
Optimization Models and Interpretations for Three Types of Adversarial Perturbations against Support Vector Machines
论文作者
论文摘要
对抗性扰动在各种深层神经网络中引起了极大的关注。其中大多数是通过迭代计算的，不能很好地解释。相比之下，很少注意基本的机器学习模型，例如支持向量机。在本文中，我们研究了针对支持向量机器的三种类型的对抗扰动的优化模型和解释，包括样本 - 逆转扰动（SAP），类 - 普及对抗扰动（CUAP）以及通用的对抗扰动（UAP）。对于线性二进制/多分类支持向量机（SVM），我们得出了SAP，CUAP和UAP（二进制案例）的显式解决方案，以及用于多分类的UAP的近似解决方案。我们还获得了UAP的上限率的上限。这样的结果不仅可以提高三种对抗性扰动的解释性，而且还可以在计算方面提供极大的便利性，因为可以避免迭代过程。数值结果表明，我们的方法可以快速有效地计算三种类型的对抗扰动。
Adversarial perturbations have drawn great attentions in various deep neural networks. Most of them are computed by iterations and cannot be interpreted very well. In contrast, little attentions are paid to basic machine learning models such as support vector machines. In this paper, we investigate the optimization models and the interpretations for three types of adversarial perturbations against support vector machines, including sample-adversarial perturbations (sAP), class-universal adversarial perturbations (cuAP) as well as universal adversarial perturbations (uAP). For linear binary/multi classification support vector machines (SVMs), we derive the explicit solutions for sAP, cuAP and uAP (binary case), and approximate solution for uAP of multi-classification. We also obtain the upper bound of fooling rate for uAP. Such results not only increase the interpretability of the three adversarial perturbations, but also provide great convenience in computation since iterative process can be avoided. Numerical results show that our method is fast and effective in calculating three types of adversarial perturbations.
