A new algorithmic framework is proposed for learning autoencoders of data distributions. We minimize the discrepancy between the model and target distributions, with a \emph{relational regularization} on the learnable latent prior. This regularization penalizes the fused Gromov-Wasserstein (FGW) distance between the latent prior and its corresponding posterior, allowing one to flexibly learn a structured prior distribution associated with the generative model. Moreover, it helps co-training of multiple autoencoders even if they have heterogeneous architectures and incomparable latent spaces. We implement the framework with two scalable algorithms, making it applicable for both probabilistic and deterministic autoencoders. Our relational regularized autoencoder (RAE) outperforms existing methods, $e.g.$, the variational autoencoder, Wasserstein autoencoder, and their variants, on generating images. Additionally, our relational co-training strategy for autoencoders achieves encouraging results in both synthesis and real-world multi-view learning tasks.

提出了一种新的算法框架用于学习数据分布的自编码器，该框架最小化模型与目标分布的差异，通过对可学习潜在先验的关系正则化，惩罚潜在先验与其对应后验之间的融合Gromov-Wasserstein（FGW）距离，从而允许灵活地学习与生成模型相关的结构化先验分布，帮助多个自编码器的联合训练，即使它们具有异构的体系结构和无法比较的潜在空间，通过两种可扩展的算法实现该框架，适用于概率和确定性自编码器，我们的关系正则化自编码器（RAE）在生成图像方面优于现有方法，例如变分自编码器，Wasserstein自编码器及其变体，此外，我们的关系联合训练策略也取得了在合成和真实世界多视图学习任务中鼓舞人心的结果。

关系正则化的自动编码器学习