Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to model high-dimensional distributions, sequential training and stacked architectures are common, increasing the number of tunable hyper-parameters as well as the training time. Nonetheless, the sample complexity of the distance metrics remains one of the factors affecting GAN training. We first show that the recently proposed sliced Wasserstein distance has compelling sample complexity properties when compared to the Wasserstein distance. To further improve the sliced Wasserstein distance we then analyze its `projection complexity' and develop the max-sliced Wasserstein distance which enjoys compelling sample complexity while reducing projection complexity, albeit necessitating a max estimation. We finally illustrate that the proposed distance trains GANs on high-dimensional images up to a resolution of 256x256 easily.

本研究研究生成式对抗网络（GAN）和变分自编码器在分布建模方面的应用，着重研究了可靠性和效率，提出了一种新的距离度量方法：最大切片Wasserstein距离，能够更有效地提高GAN的训练效果。

最大切片 Wasserstein 距离及其在 GAN 中的应用