### Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach

Joint with Federico López, Beatrice Pozzetti, Michael Strube, and Anna Wienhard

Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learn-ing 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 anew 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 out-performs 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.