  Geometric relational embeddings map relational data as geometric objects that
combine vector information suitable for machine learning and
structured/relational information for structured/relational reasoning,
typically in low dimensions. Their preservation of relational structures and
their appealing properties and interpretability have led to their uptake for
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.
