BiQUE: Biquaternionic Embeddings of Knowledge Graphs

Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 8338–8351 November 7–11, 2021. c⃝2021 Association for Computational Linguistics 8338 BiQUE: Biquaternionic Embeddings of Knowledge Graphs Jia Guo and Stanley Kok Department of Information Systems and Analytics, School of Computing National University of Singapore guojia@u.nus.edu, skok@comp.nus.edu.sg Abstract Knowledge graph embeddings (KGEs) com- pactly encode multi-relational knowledge graphs (KGs). Existing KGE models rely on geometric operations to model relational pat- terns. Euclidean (circular) rotation is useful for modeling patterns such as symmetry, but cannot represent hierarchical semantics. In contrast, hyperbolic models are effective at modeling hierarchical relations, but do not per- form as well on patterns on which circular ro- tation excels. It is crucial for KGE models to unify multiple geometric transformations so as to fully cover the multifarious relations in KGs. To do so, we propose BiQUE, a novel model that employs biquaternions to integrate multiple geometric transformations, viz., scal- ing, translation, Euclidean rotation, and hyper- bolic rotation. BiQUE makes the best trade- offs among geometric operators during train- ing, picking the best one (or their best combi- nation) for each relation. Experiments on five datasets show BiQUE’s effectiveness. 1 Introduction Knowledge graphs (KGs) provide an efficient way to represent real-world entities and their intricate connections in the form of (head, relation, tail) triples. Each head/tail entity corresponds to a node in a KG, and each relation represents a di- rected edge between them. Imbued with rich fac- tual knowledge, KGs have demonstrated their ef- fectiveness in a wide range of downstream appli- cations (Wang et al., 2018; Saxena et al., 2020). Although problems due to incompleteness and noise continue to plague KGs, those issues have been ameliorated by knowledge graph embeddings (KGEs) that project entities and relations into low- dimensional dense vectors. Current KGE methods mainly focus on ex- ploiting geometric transformations and embed- ding spaces to model relational patterns such as (anti)symmetry, inversion, and composition. Animals Vertebrates Invertebrates Amphibians Crustacea Insects Birds Plants Bacteria interact_with (hierarchical; blue arrow) interact_with (symmetric; green arrow) affect affect Figure 1: interacts_with is symmetric (green arrows) and hierarchical (blue arrows) in different context. Each affects (red arrow) can be composed from a green- arrow relation followed by a blue-arrow one. TransE (Bordes et al., 2013) represents each re- lation as a translation from a head entity to a tail en- tity. With translations alone, TransE cannot model many relation types such as symmetric ones. In contrast, RotatE (Sun et al., 2019) represents each relation as a rotation in complex space. It proves that it can model (anti)symmetry, inversion, and composition patterns. QuatE (Zhang et al., 2019) extends RotatE’s complex number representation to a hypercomplex number representation. A drawback of rotation-based KGE models is that their representations are entrenched in (Eu- clidean) circular rotation, and hence they are un- able to model hierarchical and tree-like structures (e.g. hypernym and part_of). Such hierarchical relations are common and even pervasive in some KGs. Since, in circular rotation, all rotating points are constrained …

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