Gromov-Wasserstein distance has found many applications in machine learning
due to its ability to compare measures across metric spaces and its invariance
to isometric transformations. However, in certain applications, this invariance
property can be too flexible, thus undesirable. Moreover, the
Gromov-Wasserstein distance solely considers pairwise sample similarities in
input datasets, disregarding the raw feature representations. We propose a new
optimal transport-based distance, called Augmented Gromov-Wasserstein, that
allows for some control over the level of rigidity to transformations. It also
incorporates feature alignments, enabling us to better leverage prior knowledge
on the input data for improved performance. We present theoretical insights
into the proposed metric. We then demonstrate its usefulness for single-cell
multi-omic alignment tasks and a transfer learning scenario in machine
learning.

提出了一种新的基于最优输运的距离度量方法，称为增强型 Gromov-Wasserstein，在保持对几何变换的某种程度刚度的同时，结合特征对齐，以更好地利用输入数据的先验知识，用于单细胞多组学对齐任务和机器学习中的迁移学习场景。

重访 Gromov-Wasserstein 距离中的不变性并引入先验

Revisiting invariances and introducing priors in Gromov-Wasserstein  distances

Unsupervised image semantic segmentation(UISS) aims to match low-level visual
features with semantic-level representations without outer supervision. In this
paper, we address the critical properties from the view of feature alignments
and feature uniformity for UISS models. We also make a comparison between UISS
and image-wise representation learning. Based on the analysis, we argue that
the existing MI-based methods in UISS suffer from representation collapse. By
this, we proposed a robust network called Semantic Attention Network(SAN), in
which a new module Semantic Attention(SEAT) is proposed to generate pixel-wise
and semantic features dynamically. Experimental results on multiple semantic
segmentation benchmarks show that our unsupervised segmentation framework
specializes in catching semantic representations, which outperforms all the
unpretrained and even several pretrained methods.

本研究提出了一种名为语义关注网络（Semantic Attention Network，SAN）的模型，在无监督的图像语义分割（UISS）任务中采用 “语义关注（Semantic Attention）” 模块生成像素级和语义级特征，该模型具有较好的特征一致性和特征匹配性能，在多个数据集上超过已有方法的分割效果。