Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in representation learning, a class encompassing many of the previously used embedding targets. This enables us to introduce a new method, the use of Finsler metrics integrated in a Riemannian optimization scheme, that better adapts to dissimilar structures in the graph. We develop a tool to analyze the embeddings and infer structural properties of the data sets. For implementation, we choose Siegel spaces, a versatile family of symmetric spaces. Our approach outperforms competitive baselines for graph reconstruction tasks on various synthetic and real-world datasets. We further demonstrate its applicability on two downstream tasks, recommender systems and node classification.

翻译：学习忠实的图形表达方式,作为一组顶点嵌入,已成为一系列机器学习应用程序中的一个基本中间步骤。我们提议在代表性学习中系统地使用对称空间,这是一个包含许多先前使用的嵌入目标的班级。这使我们能够引入一种新的方法,即使用纳入里曼尼亚优化计划的芬斯勒指标,更好地适应图中不同的结构。我们开发了一个工具,分析数据集的嵌入和推断结构特性。为了实施,我们选择了Siegel空间,一个多功能的对称空间大家庭。我们的方法超越了各种合成和真实世界数据集的图表重建任务的竞争性基线。我们进一步展示了其在两个下游任务、推荐系统和节点分类方面的适用性。