CylE: Cylinder Embeddings for Multi-hop Reasoning over Knowledge Graphs

Proceedings of the 17th Conference of the European Chapter of the Association for Computational Linguistics, pages 1736–1751 May 2-6, 2023 ©2023 Association for Computational Linguistics CylE: Cylinder Embeddings for Multi-hop Reasoning over Knowledge Graphs Chau Duc Minh Nguyen∗ and Tim French and Wei Liu and Michael Stewart ARC Centre for Transforming Maintenance through Data Science, Department of Computer Science and Software Engineering The University of Western Australia ∗chau.nguyenducminh@research.uwa.edu.au {tim.french, wei.liu, michael.stewart}@uwa.edu.au Abstract Recent geometric-based approaches have been shown to efficiently model complex logical queries (including the intersection operation) over Knowledge Graphs based on the natu- ral representation of Venn diagram. Existing geometric-based models (using points, boxes embeddings), however, cannot handle the log- ical negation operation. Further, those using cones embeddings are limited to representing queries by two-dimensional shapes, which re- duced their effectiveness in capturing entities query relations for correct answers. To over- come this challenge, we propose unbounded cylinder embeddings (namely CylE), which is a novel geometric-based model based on three- dimensional shapes. Our approach can han- dle a complete set of basic first-order logic op- erations (conjunctions, disjunctions and nega- tions). CylE considers queries as Cartesian products of unbounded sector-cylinders and consider a set of nearest boxes corresponds to the set of answer entities. Precisely, the con- junctions can be represented via the intersec- tions of unbounded sector-cylinders. Trans- forming queries to Disjunctive Normal Form can handle queries with disjunctions. The negations can be represented by consider- ing the closure of complement for an arbi- trary unbounded sector-cylinder. Empirical results show that the performance of multi- hop reasoning task using CylE significantly in- creases over state-of-the-art geometric-based query embedding models for queries without negation. For queries with negation operations, though the performance is on a par with the best performing geometric-based model, CylE significantly outperforms a recent distribution- based model. 1 Introduction Multi-hop Reasoning (MHR) on Knowledge Graphs (KGs) is a primary task in answering queries over large-scale knowledge graphs. Queries can be represented using First-Order-Logic (FOL) connectives (Brachman and Levesque, 2004), in- volving these operations: existential quantification (∃), conjunction (∧), disjunction (∨) and negation (¬). MHR involves learning to answer these FOL queries, which has recently received attention from several studies (Hamilton et al., 2018; Ren et al., 2020; Ren and Leskovec, 2020). A common ap- proach is to first transform the FOL query into a computation graph (see Figure 1), where nodes rep- resent entity constants or variables and edges map to predicates and logical operations. Representing queries in this way enables the learning process to traverse paths of KGs via the computation graph, so as to find a set of answers for a given query. How- ever, large-scale KGs (Bollacker et al., 2008; Vran- deˇci´c and Krötzsch, 2014; Lehmann et al., 2015; Speer et al., 2017; Fellbaum, 2010; Mitchell et al., 2018) are often incomplete and noisy, which makes explicit query mechanism, such as graph traversal incapable of returning correct answers to a query. Motivated by the challenge above, we aim to reason about incomplete …

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