Learning Hierarchy-Aware Quaternion Knowledge Graph Embeddings with Representing Relations as 3D Rotations

Proceedings of the 29th International Conference on Computational Linguistics, pages 2011–2023 October 12–17, 2022. 2011 Learning Hierarchy-Aware Quaternion Knowledge Graph Embeddings with Representing Relations as 3D Rotations Jinfa Yang, Xianghua Ying*, Yongjie Shi, Xin Tong, Ruibin Wang, Taiyan Chen, Bowei Xing Key Laboratory of Machine Perception (MOE) School of Intelligence Science and Technology, Peking University {jinfayang, xhying, shiyongjie, xin_tong, robin_wang}@pku.edu.cn, chenty@stu.pku.edu.cn, 2017xbw@pku.edu.cn Abstract Knowledge graph embedding aims to repre- sent entities and relations as low-dimensional vectors, which is an effective way for pre- dicting missing links. It is crucial for knowl- edge graph embedding models to model and infer various relation patterns, such as sym- metry/antisymmetry. However, many existing approaches fail to model semantic hierarchies, which are common in the real world. We pro- pose a new model called HRQE, which rep- resents entities as pure quaternions. The re- lational embedding consists of two parts: (a) Using unit quaternions to represent the rotation part in 3D space, where the head entities are rotated by the corresponding relations through Hamilton product. (b) Using scale parameters to constrain the modulus of entities to make them have hierarchical distributions. To the best of our knowledge, HRQE is the first model that can encode symmetry/antisymmetry, inver- sion, composition, multiple relation patterns and learn semantic hierarchies simultaneously. Experimental results demonstrate the effective- ness of HRQE against some of the SOTA meth- ods on four well-established knowledge graph completion benchmarks. 1 Introduction Knowledge graphs represent human knowledge of the real world as structured triples— (head entity, relation, tail entity) also known as (subject, predi- cate, object). There are some outstanding knowl- edge graphs, such as WordNet (Miller, 1995), Free- base (Bollacker et al., 2008), DBpedia (Lehmann et al., 2015). They have gained widespread at- tention for their successful usage in various ap- plications (e.g., question answering, natural lan- guage processing, and recommendation systems). Although millions of entities and billions of facts exist in large-scale knowledge graphs, they still *Corresponding Author suffer from the incompleteness problem. There- fore, knowledge graph completion (also known as link prediction) which aims to predict missing links among entities based on the known triples has gained growing interest. Learning low-dimensional representations of entities and relations for Knowl- edge graphs is an effective solution for this task. Learning knowledge graph embeddings in the complex space C or quaternion space H has been proven to be a highly effective inductive bias, largely owing to their ability to model connectiv- ity patterns of the relations. For example, Com- plEx (Trouillon et al., 2016), which infers new re- lational triplets with the asymmetrical Hermitian product can model the symmetry/antisymmetry pat- terns. RotatE (Sun et al., 2019), which represents entities as points in a complex space and relations as rotations, can model relation patterns including symmetry/antisymmetry, inversion, and composi- tion. DualE (Cao et al., 2021), which combines rotation and translation in dual quaternion space can additionally model the multiple relations pat- tern. However, many existing models fail to model semantic hierarchies in knowledge graphs. Semantic hierarchy is …

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