Recent work has shown local convergence of GAN training for absolutely continuous data and generator distributions. In this note we show that the requirement of absolute continuity is necessary: we describe a simple yet prototypical counterexample showing that in the more realistic case of distributions that are not absolutely continuous, unregularized GAN training is generally not convergent. Furthermore, we discuss recent regularization strategies that were proposed to stabilize GAN training. Our analysis shows that while GAN training with instance noise or gradient penalties converges, Wasserstein-GANs and Wasserstein-GANs-GP with a finite number of discriminator updates per generator update do in general not converge to the equilibrium point. We explain these results and show that both instance noise and gradient penalties constitute solutions to the problem of purely imaginary eigenvalues of the Jacobian of the gradient vector field. Based on our analysis, we also propose a simplified gradient penalty with the same effects on local convergence as more complicated penalties.

本文针对GAN训练中绝对连续数据和生成器分布的本地收敛性已经得到证明的观点，进一步阐述了绝对连续性要求的必要性。作者证明了非绝对连续分布情况下，不稳定的GAN训练不一定收敛，提出了各种正则化策略用于稳定GAN训练，并对处于低维流形上的普通GAN进行了更一般的收敛性分析。

什麼訓練方法對於GAN的收斂效果最佳？