This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an arbitrary metric space into the l2 space, while preserving their pairwise distance distribution. Not only does this metric embedding determine the dimensionality of the latent space automatically, it also enables us to construct a mixture of Gaussians to draw latent space random vectors. We use the Gaussian mixture model in tandem with a simple augmentation of the objective function to train GANs. Every major step of our method is supported by theoretical analysis, and our experiments on real and synthetic data confirm that the generator is able to produce samples spreading over most of the modes while avoiding unwanted samples, outperforming several recent GAN variants on a number of metrics and offering new features.

本文讨论了生成对抗网络（GANs）中的模式坍塌问题，提出了一种基于度量空间的几何视角来嵌入数据，以解决自动确定潜在空间维度和构造高斯混合模型的方法，进而改进目标函数，通过理论分析支持每个方法步骤，并验证了该方法能够在真实和合成数据上产生分布于大多数模式中的样本，避免不需要的样本，性能优于现有GAN变体。

BourGAN: 具有度量嵌入的生成网络