  As the success of Generative Adversarial Networks (GANs) on natural images
quickly propels them into various real-life applications across different
domains, it becomes more and more important to clearly understand their
limitations. Specifically, understanding GANs' capability across the full
spectrum of spatial frequencies, i.e. beyond the low-frequency dominant
spectrum of natural images, is critical for assessing the reliability of GAN
generated data in any detail-sensitive application (e.g. denoising, filling and
super-resolution in medical and satellite images). In this paper, we show that
the ability of convolutional GANs to learn a distribution is significantly
affected by the spatial frequency of the underlying carrier signal, that is,
GANs have a bias against learning high spatial frequencies. Crucially, we show
that this bias is not merely a result of the scarcity of high frequencies in
natural images, rather, it is a systemic bias hindering the learning of high
frequencies regardless of their prominence in a dataset. Furthermore, we
explain why large-scale GANs' ability to generate fine details on natural
images does not exclude them from the adverse effects of this bias. Finally, we
propose a method for manipulating this bias with minimal computational
overhead. This method can be used to explicitly direct computational resources
towards any specific spatial frequency of interest in a dataset, extending the
flexibility of GANs.
