  Adversarial examples have raised questions regarding the robustness and
security of deep neural networks. In this work we formalize the problem of
adversarial images given a pretrained classifier, showing that even in the
linear case the resulting optimization problem is nonconvex. We generate
adversarial images using shallow and deep classifiers on the MNIST and ImageNet
datasets. We probe the pixel space of adversarial images using noise of varying
intensity and distribution. We bring novel visualizations that showcase the
phenomenon and its high variability. We show that adversarial images appear in
large regions in the pixel space, but that, for the same task, a shallow
classifier seems more robust to adversarial images than a deep convolutional
network.
