Compounding Geometric Operations for Knowledge Graph Completion

Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics Volume 1: Long Papers, pages 6947–6965 July 9-14, 2023 ©2023 Association for Computational Linguistics Compounding Geometric Operations for Knowledge Graph Completion Xiou Ge1∗, Yun-Cheng Wang1, Bin Wang2, C.-C. Jay Kuo1 1University of Southern California, Los Angeles, California, USA 2National University of Singapore, Singapore {xiouge, yunchenw, jckuo}@usc.edu, bwang28c@gmail.com Abstract Geometric transformations including transla- tion, rotation, and scaling are commonly used operations in image processing. Besides, some of them are successfully used in developing effective knowledge graph embedding (KGE). Inspired by the synergy, we propose a new KGE model by leveraging all three operations in this work. Since translation, rotation, and scaling operations are cascaded to form a com- posite one, the new model is named Com- poundE. By casting CompoundE in the frame- work of group theory, we show that quite a few distanced-based KGE models are special cases of CompoundE. CompoundE extends the simple distance-based scoring functions to relation-dependent compound operations on head and/or tail entities. To demonstrate the effectiveness of CompoundE, we perform three prevalent KG prediction tasks including link prediction, path query answering, and entity typing, on a range of datasets. CompoundE outperforms extant models consistently, demon- strating its effectiveness and flexibility.1 1 Introduction Knowledge graphs (KGs) such as DBpedia (Auer et al., 2007), YAGO (Suchanek et al., 2007), NELL (Carlson et al., 2010), Wikidata (Vrandeˇci´c and Krötzsch, 2014), Freebase (Bollacker et al., 2008), and ConceptNet (Speer et al., 2017) have been cre- ated and made available to the public to facilitate research on KG modeling and applications. Triples, denoted by (h, r, t), are basic elements of a KG, where h and t are head and tail entities while r is the relation connecting them. KG representation learning, also known as knowledge graph embed- ding (KGE), has been intensively studied in recent years. Yet, it remains one of the most fundamental problems in Artificial Intelligence (AI) research. ∗Corresponding author 1Our source code is available at https://github.c om/hughxiouge/CompoundE KGE is critical to many downstream applications such as question answering (Guu et al., 2015) knowledge integration (Chen et al., 2017), text anal- ysis (Li et al., 2019), entity classification (Zhao et al., 2020; Ge et al., 2022), etc. There are sev- eral challenges in the design of good KGE models. Complex relation patterns (e.g. 1-to-N, N-to-1, and N-to-N, antisymmetric, transitive, hierarchical re- lations, etc.) remain difficult to model. Also, each of extant KGE models has its own strengths and weaknesses. It is desired yet unclear how to de- sign a KGE model that leverages strengths of some models and complements weaknesses of others. Geometric operations such as translation and rotation belong to the family of affine transforma- tions. These operations have been used to build effective KGE models such as TransE, RotatE, and PairRE. Previous KGEs often use a single type of operation to model all relation patterns with dif- ferent properties. This could be problematic since each operator may have modeling limitations. A synergy of different …

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