KR是首屈一指的知识表示和推理国际会议。与一般AI会议相比,KR会议系列为研究人员研究由推理算法操纵的知识的显式表示提供了更为私密的环境,这为从事人工智能,计算机科学和软件工程的大量工作提供了重要基础。会议强调了知识表示和推理的理论原理以及这些原理及其在工作系统中的实施方式之间的关系。 官网地址:


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.