In this paper, we analyze the numerics of common algorithms for training Generative Adversarial Networks (GANs). Using the formalism of smooth two-player games we analyze the associated gradient vector field of GAN training objectives. Our findings suggest that the convergence of current algorithms suffers due to two factors: i) presence of eigenvalues of the Jacobian of the gradient vector field with zero real-part, and ii) eigenvalues with big imaginary part. Using these findings, we design a new algorithm that overcomes some of these limitations and has better convergence properties. Experimentally, we demonstrate its superiority on training common GAN architectures and show convergence on GAN architectures that are known to be notoriously hard to train.

本研究通过分析生成对抗网络（GAN）的训练算法的数值特征，使用平滑二人博弈的形式，分析GAN训练目标的梯度向量场的相关性，发现当前算法的收敛性受到两个因素的影响：一是梯度向量场的雅可比矩阵存在具有零实部的特征值，二是存在具有较大虚部的特征值，提出了一种基于这些发现的新算法，克服了一些限制并具有更好的收敛性能。实验表明，该算法在训练常见的GAN结构上具有优越性，且可以收敛于一些已知难以训练的GAN结构。

GAN的数值计算