TuckER: Tensor Factorization for Knowledge Graph Completion

Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing, pages 5185–5194, Hong Kong, China, November 3–7, 2019. c⃝2019 Association for Computational Linguistics 5185 TuckER: Tensor Factorization for Knowledge Graph Completion Ivana Balaˇzevi´c1 Carl Allen1 Timothy M. Hospedales1,2 1 School of Informatics, University of Edinburgh, UK 2 Samsung AI Centre, Cambridge, UK {ivana.balazevic, carl.allen, t.hospedales}@ed.ac.uk Abstract Knowledge graphs are structured representa- tions of real world facts. However, they typ- ically contain only a small subset of all pos- sible facts. Link prediction is a task of infer- ring missing facts based on existing ones. We propose TuckER, a relatively straightforward but powerful linear model based on Tucker decomposition of the binary tensor represen- tation of knowledge graph triples. TuckER outperforms previous state-of-the-art models across standard link prediction datasets, act- ing as a strong baseline for more elaborate models. We show that TuckER is a fully ex- pressive model, derive sufficient bounds on its embedding dimensionalities and demonstrate that several previously introduced linear mod- els can be viewed as special cases of TuckER. 1 Introduction Vast amounts of information available in the world can be represented succinctly as entities and rela- tions between them. Knowledge graphs are large, graph-structured databases which store facts in triple form (es, r, eo), with es and eo representing subject and object entities and r a relation. How- ever, far from all available information is currently stored in existing knowledge graphs and manually adding new information is costly, which creates the need for algorithms that are able to automat- ically infer missing facts. Knowledge graphs can be represented as a third-order binary tensor, where each element cor- responds to a triple, 1 indicating a true fact and 0 indicating the unknown (either a false or a miss- ing fact). The task of link prediction is to predict whether two entities are related, based on known facts already present in a knowledge graph, i.e. to infer which of the 0 entries in the tensor are indeed false, and which are missing but actually true. A large number of approaches to link prediction so far have been linear, based on various meth- ods of factorizing the third-order binary tensor (Nickel et al., 2011; Yang et al., 2015; Trouillon et al., 2016; Kazemi and Poole, 2018). Recently, state-of-the-art results have been achieved using non-linear convolutional models (Dettmers et al., 2018; Balaˇzevi´c et al., 2019). Despite achieving very good performance, the fundamental problem with deep, non-linear models is that they are non- transparent and poorly understood, as opposed to more mathematically principled and widely stud- ied tensor decomposition models. In this paper, we introduce TuckER (E stands for entities, R for relations), a straightforward linear model for link prediction on knowledge graphs, based on Tucker decomposition (Tucker, 1966) of the binary tensor of triples, acting as a strong baseline for more elaborate models. Tucker decomposition, used widely in machine learning (Schein et al., 2016; Ben-Younes et al., 2017; …

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