Relation Embedding with Dihedral Group in Knowledge Graph

Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 263–272 Florence, Italy, July 28 - August 2, 2019. c⃝2019 Association for Computational Linguistics 263 Relation Embedding with Dihedral Group in Knowledge Graph Canran Xu ∗ eBay Inc. canxu@ebay.com Ruijiang Li ∗ eBay Inc. ruijili@ebay.com Abstract Link prediction is critical for the application of incomplete knowledge graph (KG) in the downstream tasks. As a family of effective approaches for link predictions, embedding methods try to learn low-rank representations for both entities and relations such that the bi- linear form defined therein is a well-behaved scoring function. Despite of their success- ful performances, existing bilinear forms over- look the modeling of relation compositions, resulting in lacks of interpretability for reason- ing on KG. To fulfill this gap, we propose a new model called DihEdral, named after dihe- dral symmetry group. This new model learns knowledge graph embeddings that can capture relation compositions by nature. Furthermore, our approach models the relation embeddings parametrized by discrete values, thereby de- crease the solution space drastically. Our ex- periments show that DihEdral is able to cap- ture all desired properties such as (skew-) sym- metry, inversion and (non-) Abelian compo- sition, and outperforms existing bilinear form based approach and is comparable to or bet- ter than deep learning models such as ConvE (Dettmers et al., 2018). 1 Introduction Large-scale knowledge graph (KG) plays a criti- cal role in the downstream tasks such as semantic search (Berant et al., 2013), dialogue management (He et al., 2017) and question answering (Bordes et al., 2014). In most cases, despite of its large scale, KG is not complete due to the difficulty to enumerate all facts in the real world. The ca- pability of predicting the missing links based on existing dataset is one of the most important re- search topics for years. A common representa- tion of KG is a set of triples (head, relation, tail), and the problem of link prediction can be viewed as predicting new triples from the existing set. A ∗Equal contribution. popular approach is KG embeddings, which maps both entities and relations in the KG to a vec- tor space such that the scoring function of enti- ties and relations for ground truth distinguishes from false facts (Socher et al., 2013; Bordes et al., 2013; Yang et al., 2015). Another family of ap- proaches explicitly models the reasoning process on KG by synthesizing information from paths (Guu et al., 2015). More recently, researchers are applying deep learning methods to KG embed- dings so that non-linear interaction between enti- ties and relations are enabled (Schlichtkrull et al., 2018; Dettmers et al., 2018). The standard task for link prediction is to an- swer queries (h, r, ?) or (? r, t). In this context, recent works on KG embedding focusing on bilin- ear form methods (Trouillon et al., 2016; Nickel et al., 2016; Liu et al., 2017; Kazemi and Poole, 2018) are known to perform reasonably well. The success of this pack …

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