Modeling Heterogeneous Hierarchies with Relation-specific Hyperbolic Cones

NeurIPS 2021  ·  Yushi Bai, Rex Ying, Hongyu Ren, Jure Leskovec ·

Hierarchical relations are prevalent and indispensable for organizing human knowledge captured by a knowledge graph (KG). The key property of hierarchical relations is that they induce a partial ordering over the entities, which needs to be modeled in order to allow for hierarchical reasoning. However, current KG embeddings can model only a single global hierarchy (single global partial ordering) and fail to model multiple heterogeneous hierarchies that exist in a single KG. Here we present ConE (Cone Embedding), a KG embedding model that is able to simultaneously model multiple hierarchical as well as non-hierarchical relations in a knowledge graph. ConE embeds entities into hyperbolic cones and models relations as transformations between the cones. In particular, ConE uses cone containment constraints in different subspaces of the hyperbolic embedding space to capture multiple heterogeneous hierarchies. Experiments on standard knowledge graph benchmarks show that ConE obtains state-of-the-art performance on hierarchical reasoning tasks as well as knowledge graph completion task on hierarchical graphs. In particular, our approach yields new state-of-the-art Hits@1 of 45.3% on WN18RR and 16.1% on DDB14 (0.231 MRR). As for hierarchical reasoning task, our approach outperforms previous best results by an average of 20% across the three datasets.

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FB15k WN18 FB15k-237 WN18RR
Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Link Prediction DDB14 ConE MRR 0.231 # 1
Hits@1 0.161 # 1
Hits@3 0.252 # 1
Hits@10 0.364 # 1
Link Prediction FB15k-237 ConE MRR 0.345 # 35
Hits@10 0.54 # 24
Hits@3 0.381 # 28
Hits@1 0.247 # 34
Link Prediction GO21 ConE MRR 0.211 # 1
Hit@1 0.14 # 1
Hits@3 0.237 # 1
Hits@10 0.347 # 1
Ancestor-descendant prediction WN18RR ConE mAP-0% 0.895 # 1
mAP-50% 0.801 # 1
mAP-100% 0.679 # 1
Link Prediction WN18RR ConE MRR 0.496 # 12
Hits@10 0.579 # 22
Hits@3 0.515 # 12
Hits@1 0.453 # 12


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