Evaluating the distribution learning capabilities of GANs

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.