  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.
