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Vulnerability of Deep Neural Networks (DNNs) to adversarial attacks has beenattracting a lot of attention in recent studies. It has been shown that formany state of the art DNNs performing image classification there existuniversal adversarial perturbations --- image-agnostic perturbations mereaddition of which to natural images with high probability leads to theirmisclassification. In this work we propose a new algorithm for constructingsuch universal perturbations. Our approach is based on computing the so-called$(p, q)$-singular vectors of the Jacobian matrices of hidden layers of anetwork. Resulting perturbations present interesting visual patterns, and byusing only 64 images we were able to construct universal perturbations withmore than 60 \% fooling rate on the dataset consisting of 50000 images. We alsoinvestigate a correlation between the maximal singular value of the Jacobianmatrix and the fooling rate of the corresponding singular vector, and show thatthe constructed perturbations generalize across networks.

Art of singular vectors and universal adversarial perturbations