  Do GANS (Generative Adversarial Nets) actually learn the target distribution?
The foundational paper of (Goodfellow et al 2014) suggested they do, if they
were given sufficiently large deep nets, sample size, and computation time. A
recent theoretical analysis in Arora et al (to appear at ICML 2017) raised
doubts whether the same holds when discriminator has finite size. It showed
that the training objective can approach its optimum value even if the
generated distribution has very low support ---in other words, the training
objective is unable to prevent mode collapse. The current note reports
experiments suggesting that such problems are not merely theoretical. It
presents empirical evidence that well-known GANs approaches do learn
distributions of fairly low support, and thus presumably are not learning the
target distribution. The main technical contribution is a new proposed test,
based upon the famous birthday paradox, for estimating the support size of the
generated distribution.
