In inverse problems, many conditional generative models approximate the
posterior measure by minimizing a distance between the joint measure and its
learned approximation. While this approach also controls the distance between
the posterior measures in the case of the Kullback Leibler divergence, it does
not hold true for the Wasserstein distance. We will introduce a conditional
Wasserstein distance with a set of restricted couplings that equals the
expected Wasserstein distance of the posteriors. By deriving its dual, we find
a rigorous way to motivate the loss of conditional Wasserstein GANs. We outline
conditions under which the vanilla and the conditional Wasserstein distance
coincide. Furthermore, we will show numerical examples where training with the
conditional Wasserstein distance yields favorable properties for posterior
sampling.

逆问题中，通过最小化联合度量与其学习近似度量之间的距离，许多条件生成模型近似后验测度。尽管这种方法对于 KL 散度的情况也控制了后验测度之间的距离，但对于 Wasserstein 距离则不成立。我们引入一种带有一组受限耦合的条件 Wasserstein 距离，它等于后验分布的期望 Wasserstein 距离。通过推导其对偶性，我们找到了正式推动条件 Wasserstein GAN 损失的方法。我们概述了条件 Wasserstein 距离和普通 Wasserstein 距离重合的条件，并且还展示了使用条件 Wasserstein 距离训练时获得有利的后验抽样性质的数值示例。

Y - 对角耦合：用条件瓦砾均衡距离近似后验

Y-Diagonal Couplings: Approximating Posteriors with Conditional  Wasserstein Distances

Conventional zero-shot learning (ZSL) methods generally learn an embedding,
e.g., visual-semantic mapping, to handle the unseen visual samples via an
indirect manner. In this paper, we take the advantage of generative adversarial
networks (GANs) and propose a novel method, named leveraging invariant side GAN
(LisGAN), which can directly generate the unseen features from random noises
which are conditioned by the semantic descriptions. Specifically, we train a
conditional Wasserstein GANs in which the generator synthesizes fake unseen
features from noises and the discriminator distinguishes the fake from real via
a minimax game. Considering that one semantic description can correspond to
various synthesized visual samples, and the semantic description, figuratively,
is the soul of the generated features, we introduce soul samples as the
invariant side of generative zero-shot learning in this paper. A soul sample is
the meta-representation of one class. It visualizes the most
semantically-meaningful aspects of each sample in the same category. We
regularize that each generated sample (the varying side of generative ZSL)
should be close to at least one soul sample (the invariant side) which has the
same class label with it. At the zero-shot recognition stage, we propose to use
two classifiers, which are deployed in a cascade way, to achieve a
coarse-to-fine result. Experiments on five popular benchmarks verify that our
proposed approach can outperform state-of-the-art methods with significant
improvements.

使用生成对抗网络，提出了一种名为 LisGAN 的新方法，可以通过条件噪声直接生成未见过的特征。灵魂样本被引入生成式零样本学习中作为不变的一面，具有类别的元表示，并且通过联合部署两个分类器来实现粗分类和细分类，超过了现有方法的表现。

利用生成式零样本学习的不变侧面

Leveraging the Invariant Side of Generative Zero-Shot Learning

In this study, a novel topology optimization approach based on conditional
Wasserstein generative adversarial networks (CWGAN) is developed to replicate
the conventional topology optimization algorithms in an extremely
computationally inexpensive way. CWGAN consists of a generator and a
discriminator, both of which are deep convolutional neural networks (CNN). The
limited samples of data, quasi-optimal planar structures, needed for training
purposes are generated using the conventional topology optimization algorithms.
With CWGANs, the topology optimization conditions can be set to a required
value before generating samples. CWGAN truncates the global design space by
introducing an equality constraint by the designer. The results are validated
by generating an optimized planar structure using the conventional algorithms
with the same settings. A proof of concept is presented which is known to be
the first such illustration of fusion of CWGANs and topology optimization.

本文提出一种基于条件瓦瑟斯坦生成对抗网络的优化拓扑结构方法，与传统算法相比，该方法计算代价极低，只需要通过深度卷积神经网络模拟限定拓扑优化条件的全局设计空间，且得到的优化方案可以得到验证。