Generative
Adversarial Nets (GANs) is a framework for training deep generative models, due
to Goodfellow et al'13. It involves a competition between a generator net that
tries to produce realistic images, and a discriminator that tries to
distinguish the output from real images. The framework has been applied to many
settings, but it has been open to quantify how well it does, though the images
often look reasonable. In our paper in ICML'17 (joint with Ge, Liang, Ma,
Zhang) we give an analysis for the case of finite discriminators and
generators. On the positive side, we can show the existence of an equilibrium
where generator succeeds in fooling the discriminator. On the negative side, we
show that in this equilibrium, generator produces a distribution of fairly low
support. This can be seen as a failure mode of the GANs framework. But in
subsequent work in ICLR'18 (joint with Risteski and Zhang) we show that this
failure mode exists in popular GANs frameworks, which we show learn
distributions with fairly small support. We quantify this using our new
"birthday paradox" test.