Do GANs actually learn the distribution? An empirical study

TL;DR

This paper empirically investigates whether GANs truly learn the target distribution, revealing that they often learn distributions with low support, which may indicate they do not fully capture the intended data distribution.

Contribution

It introduces a novel support size estimation test based on the birthday paradox and provides empirical evidence on the limitations of GANs in learning full distributions.

Findings

GANs can learn distributions with low support

Training objectives may not prevent mode collapse

Empirical evidence suggests GANs often do not learn the full target distribution

Abstract

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.