Multiple marginal matching problem aims at learning mappings to match a
source domain to multiple target domains and it has attracted great attention
in many applications, such as multi-domain image translation. However,
addressing this problem has two critical challenges: (i) Measuring the
multi-marginal distance among different domains is very intractable; (ii) It is
very difficult to exploit cross-domain correlations to match the target domain
distributions. In this paper, we propose a novel Multi-marginal Wasserstein GAN
(MWGAN) to minimize Wasserstein distance among domains. Specifically, with the
help of multi-marginal optimal transport theory, we develop a new adversarial
objective function with inner- and inter-domain constraints to exploit
cross-domain correlations. Moreover, we theoretically analyze the
generalization performance of MWGAN, and empirically evaluate it on the
balanced and imbalanced translation tasks. Extensive experiments on toy and
real-world datasets demonstrate the effectiveness of MWGAN.

本文中提出了一种新的多重边际 Wasserstein GAN（MWGAN）来最小化域之间的 Wasserstein 距离，并利用多边际最优传输理论开发了一种新的对抗性目标函数以利用交叉域相关性，并在平衡和不平衡的翻译任务上进行了理论分析和实验证明了 MWGAN 的有效性。

多边沃瑟斯坦生成对抗网络

Multi-marginal Wasserstein GAN

There is a growing interest in designing models that can deal with images
from different visual domains. If there exists a universal structure in
different visual domains that can be captured via a common parameterization,
then we can use a single model for all domains rather than one model per
domain. A model aware of the relationships between different domains can also
be trained to work on new domains with less resources. However, to identify the
reusable structure in a model is not easy. In this paper, we propose a
multi-domain learning architecture based on depthwise separable convolution.
The proposed approach is based on the assumption that images from different
domains share cross-channel correlations but have domain-specific spatial
correlations. The proposed model is compact and has minimal overhead when being
applied to new domains. Additionally, we introduce a gating mechanism to
promote soft sharing between different domains. We evaluate our approach on
Visual Decathlon Challenge, a benchmark for testing the ability of multi-domain
models. The experiments show that our approach can achieve the highest score
while only requiring 50% of the parameters compared with the state-of-the-art
approaches.

本文提出一种基于深度可分离卷积的多领域学习体系结构，以捕获不同视觉领域之间的通用结构，并介绍一个门控机制，促进不同领域之间的软共享。在 Visual Decathlon 挑战赛上，我们的方法可以取得最高分数，比现有方法所需的参数数量少 50％。