HolmE: Low-Dimensional Hyperbolic KG Embedding for Better Extrapolation

Past works have shown knowledge graph embedding (KGE) methods learn from facts in the form of triples and extrapolate to unseen triples. KGE in hyperbolic space can achieve impressive performance even in low-dimensional embedding space. However, existing work limitedly studied extrapolation to under-represented data, including under-represented entities and relations. To this end, we propose HolmE, a general form of KGE method on hyperbolic manifolds. HolmE addresses extrapolation to under-represented entities through a special treatment of the bias term, and extrapolation to under-represented relations by supporting strong composition. We provide empirical evidence that HolmE achieves promising performance in modelling unseen triples, underrepresented entities, and under-represented relations. We prove that mainstream KGE methods either: (1) are special cases of HolmE and thus support strong composition; (2) do not support strong composition. The code and data are open-sourced at https://github.com/nsai-uio/HolmE-KGE.