论文标题
在gans中的瓦斯汀距离进行广义实施
Towards Generalized Implementation of Wasserstein Distance in GANs
论文作者
论文摘要
Wasserstein Gans（Wgans）建于Wasserstein距离的Kantorovich-Rubinstein（KR）二重性上，是理论上声音最合理的模型之一。但是，在实践中，它并不总是比甘恩斯的其他变体。这主要是由于KR二元性要求的Lipschitz条件的实现不完善。在社区中，通过Lipschitz约束的不同实现进行了广泛的工作，但是，在实践中仍然很难完全满足限制。在本文中，我们认为强大的Lipschitz约束可能不需要优化。取而代之的是，我们退后一步，尝试放松Lipschitz的约束。从理论上讲，我们首先展示了一种更通用的双重形式的Wasserstein距离，称为Sobolev二元性，它放松了Lipschitz的约束，但仍然保持了Wasserstein距离的有利梯度性能。此外，我们表明KR二元性实际上是Sobolev二元性的特殊情况。基于放松的二元性，我们进一步提出了一种名为Sobolev Wasserstein Gan（Swgan）的广义卫生训练方案，并通过广泛的实验表明了Swgan对现有方法的改善。
Wasserstein GANs (WGANs), built upon the Kantorovich-Rubinstein (KR) duality of Wasserstein distance, is one of the most theoretically sound GAN models. However, in practice it does not always outperform other variants of GANs. This is mostly due to the imperfect implementation of the Lipschitz condition required by the KR duality. Extensive work has been done in the community with different implementations of the Lipschitz constraint, which, however, is still hard to satisfy the restriction perfectly in practice. In this paper, we argue that the strong Lipschitz constraint might be unnecessary for optimization. Instead, we take a step back and try to relax the Lipschitz constraint. Theoretically, we first demonstrate a more general dual form of the Wasserstein distance called the Sobolev duality, which relaxes the Lipschitz constraint but still maintains the favorable gradient property of the Wasserstein distance. Moreover, we show that the KR duality is actually a special case of the Sobolev duality. Based on the relaxed duality, we further propose a generalized WGAN training scheme named Sobolev Wasserstein GAN (SWGAN), and empirically demonstrate the improvement of SWGAN over existing methods with extensive experiments.
