  We investigate the relationship between the frequency spectrum of image data
and the generalization behavior of convolutional neural networks (CNN). We
first notice CNN's ability in capturing the high-frequency components of
images. These high-frequency components are almost imperceptible to a human.
Thus the observation leads to multiple hypotheses that are related to the
generalization behaviors of CNN, including a potential explanation for
adversarial examples, a discussion of CNN's trade-off between robustness and
accuracy, and some evidence in understanding training heuristics.
