Abstract: 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.