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Despite their impressive performance, deep convolutional neural networks(CNNs) have been shown to be sensitive to small adversarial perturbations.These nuisances, which one can barely notice, are powerful enough to foolsophisticated and well performing classifiers, leading to ridiculousmisclassification results. In this paper we analyze the stability ofstate-of-the-art deep-learning classification machines to adversarialperturbations, where we assume that the signals belong to the (possiblymulti-layer) sparse representation model. We start with convolutional sparsityand then proceed to its multi-layered version, which is tightly connected toCNNs. Our analysis links between the stability of the classification to noiseand the underlying structure of the signal, quantified by the sparsity of itsrepresentation under a fixed dictionary. In addition, we offer similarstability theorems for two practical pursuit algorithms, which are posed as twodifferent deep-learning architectures - the layered Thresholding and thelayered Basis Pursuit. Our analysis establishes the better robustness of thelater to adversarial attacks. We corroborate these theoretical results bynumerical experiments on three datasets: MNIST, CIFAR-10 and CIFAR-100.

Adversarial Noise Attacks of Deep Learning Architectures -- Stability Analysis via Sparse Modeled Signals