  We evaluate the distribution learning capabilities of generative adversarial
networks by testing them on synthetic datasets. The datasets include common
distributions of points in $R^n$ space and images containing polygons of
various shapes and sizes. We find that by and large GANs fail to faithfully
recreate point datasets which contain discontinous support or sharp bends with
noise. Additionally, on image datasets, we find that GANs do not seem to learn
to count the number of objects of the same kind in an image. We also highlight
the apparent tension between generalization and learning in GANs.
