It is widely acknowledged that trained convolutional neural networks (CNNs)
have different levels of sensitivity to signals of different frequency. In
particular, a number of empirical studies have documented CNNs sensitivity to
low-frequency signals. In this work we show with theory and experiments that
this observed sensitivity is a consequence of the frequency distribution of
natural images, which is known to have most of its power concentrated in
low-to-mid frequencies. Our theoretical analysis relies on representations of
the layers of a CNN in frequency space, an idea that has previously been used
to accelerate computations and study implicit bias of network training
algorithms, but to the best of our knowledge has not been applied in the domain
of model robustness.Comment: Comments welcome