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.

研究GANS是否可以准确学习目标分布，发现当判别器具有有限大小时，GAN的训练目标可能无法防止模态崩溃。通过基于生日悖论的新测试方法，提供了实证证据证明当前的GAN方法不能完全学习目标分布的任何支持度数量的分布。

GANs是否真的学习了数据分布？一项实证研究