Modeling Heterogeneous Hierarchies with Relation-specific Hyperbolic Cones

Hierarchical relations are prevalent and indispensable for organizing human captured by a knowledge graph (KG). The key property of hierarchical is that they induce a partial ordering over the entities, which needs be modeled in order to allow for hierarchical reasoning. However, current KG can model only a single global hierarchy (single global partial) and fail to model multiple heterogeneous hierarchies that exist in a KG. Here we present ConE (Cone Embedding), a KG embedding model that is to simultaneously model multiple hierarchical as well as non-hierarchical in a knowledge graph. ConE embeds entities into hyperbolic cones and relations as transformations between the cones. In particular, ConE uses containment constraints in different subspaces of the hyperbolic embedding to capture multiple heterogeneous hierarchies. Experiments on standard graph benchmarks show that ConE obtains state-of-the-art performance hierarchical reasoning tasks as well as knowledge graph completion task on graphs. In particular, our approach yields new state-of-the-art@1 of 45. 3% on WN18RR and 16. 1% on DDB14 (0. 231 MRR). As for hierarchical task, our approach outperforms previous best results by an average of20% across the three datasets.