Art of Singular Vectors and Universal Adversarial Perturbations

Vulnerability of Deep Neural Networks (DNNs) to adversarial attacks has been attracting a lot of attention in recent studies. It has been shown that for many state of the art DNNs performing image classification there exist universal adversarial perturbations - image-agnostic perturbations mere addition of which to natural images with high probability leads to their misclassification. In this work we propose a new algorithm for constructing such universal perturbations. Our approach is based on computing the so-called (p, q)-singular vectors of the Jacobian matrices of hidden layers of a network. Resulting perturbations present interesting visual patterns, and by using only 64 images we were able to construct universal perturbations with more than 60 % fooling rate on the dataset consisting of 50000 images. We also investigate a correlation between the maximal singular value of the Jacobian matrix and the fooling rate of the corresponding singular vector, and show that the constructed perturbations generalize across networks.