FlorE: Integrating Full Lorentz Group and Directional Offsets for Effective Knowledge Graph Embedding

Abstract Knowledge Graph Embedding (KGE) aims to map entities and relationships into a continuous vector space to facilitate reasoning and downstream tasks. Although previous KGE methods based on Euclidean, complex spaces, or hyperbolic spaces have performed well, they still struggle to effectively model Z-Paradox relation patterns which account for a large proportion in each knowledge graph. To address this issue, we propose a novel KGE method **FlorE** which integrates full Lorentz Group and directional offset operation in hyperbolic space for KGE task. Specifically, we incorporates the full Lorentz Group to enable the same relation in knowledge graph (KG) to perform indefinite isometry, thus avoiding the overlapping of entities. Meanwhile, we implement directional offset operation via exponential mapping to transform the relations to the same Lorentz manifold of the entities, thus maintaining geometric consistency for the relations and entities in KG. By integrating these two techniques, FlorE can effectively model the Z-Paradox relation patterns and improve the representation learning ability for KGs. Experiments on the five benchmark datasets demonstrate that our method achieves state-of-the-art performance. For the Z-Paradox relation patterns, the improvement achieves **26.7%**, **15.6%**, **35.4%**, **33.7%**, and **31.5%** on FB15k-237, WN18RR, CoDEx-S, CoDEx-M and CoDEx-L, respectively.