  We show that adversarial examples, i.e., the visually imperceptible
perturbations that result in Convolutional Neural Networks (CNNs) fail, can be
alleviated with a mechanism based on foveations---applying the CNN in different
image regions. To see this, first, we report results in ImageNet that lead to a
revision of the hypothesis that adversarial perturbations are a consequence of
CNNs acting as a linear classifier: CNNs act locally linearly to changes in the
image regions with objects recognized by the CNN, and in other regions the CNN
may act non-linearly. Then, we corroborate that when the neural responses are
linear, applying the foveation mechanism to the adversarial example tends to
significantly reduce the effect of the perturbation. This is because,
hypothetically, the CNNs for ImageNet are robust to changes of scale and
translation of the object produced by the foveation, but this property does not
generalize to transformations of the perturbation. As a result, the accuracy
after a foveation is almost the same as the accuracy of the CNN without the
adversarial perturbation, even if the adversarial perturbation is calculated
taking into account a foveation.
