Geometric Relational Embeddings: Progress and Prospects

Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/symbolic information suitable for symbolic reasoning, typically in low dimensions. Their preservation of relational structures and their appealing properties and interpretability have led to their uptake for multiple neuro-symbolic reasoning tasks such as knowledge graph completion, ontology and hierarchy reasoning, logical query answering, and hierarchical multi-label classification. We survey methods that underly geometric relational embeddings and categorize them based on (i) the embedding geometries that are used to represent the data; and (ii) the relational reasoning tasks that they aim to improve. We identify the desired properties (i.e., inductive biases) of each kind of embedding and discuss some potential future work.