Hyperbolic Temporal Knowledge Graph Embeddings with Relational and Time Curvatures

Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021, pages 3296–3308 August 1–6, 2021. ©2021 Association for Computational Linguistics 3296 Hyperbolic Temporal Knowledge Graph Embeddings with Relational and Time Curvatures Sebastien Montella Orange Labs, Lannion Aix Marseille Univ., CNRS, LIS, Marseille, France sebastien.montella@orange.com Lina Rojas-Barahona Orange Labs, Lannion Johannes Heinecke Orange Labs, Lannion {linamaria.rojasbarahona, johannes.heinecke}@orange.com Abstract Knowledge Graph (KG) completion has been excessively studied with a massive number of models proposed for the Link Prediction (LP) task. The main limitation of such models is their insensitivity to time. Indeed, the tem- poral aspect of stored facts is often ignored. To this end, more and more works consider time as a parameter to complete KGs. In this paper, we first demonstrate that, by sim- ply increasing the number of negative sam- ples, the recent ATTH model can achieve com- petitive or even better performance than the state-of-the-art on Temporal KGs (TKGs), al- beit its nontemporality. We further propose HERCULES, a time-aware extension of ATTH model, which defines the curvature of a Rie- mannian manifold as the product of both re- lation and time. Our experiments show that both HERCULES and ATTH achieve compet- itive or new state-of-the-art performances on ICEWS04 and ICEWS05-15 datasets. There- fore, one should raise awareness when learn- ing TKGs representations to identify whether time truly boosts performances. 1 Introduction The prevalent manner to store factual information is the ⟨s, p, o⟩ triple data structure where s, p and o stand for the subject, predicate and object re- spectively. An entity denotes whether a subject or an object while a relation denote a predicate that links two entities. A collection of triples defines a Knowledge Graph (KG) noted G(E, R) with E the set of entities, i.e. subjects and objects, cor- responding to the nodes in the graph and R the set of predicates corresponding to directed edges. Shedding light on the type of connections between entities, KGs are powerful to work with for numer- ous downstream tasks such as question-answering (Bordes et al., 2014; Hao et al., 2017; Saxena et al., 2020), recommendation system (Yu et al., 2014; Zhang et al., 2016; Zhou et al., 2017), informa- tion retrieval (Lao and Cohen, 2010; Rockt¨aschel et al., 2015; Xiong et al., 2017), or reasoning (Xian et al., 2019; Chen et al., 2020). However, KGs are sometimes incomplete and part of the knowledge is missing. A major concern was therefore raised to predict missing connections between entities, stim- ulating research on the Link Prediction (LP) task. Intuition is to map each entity and relation into a vector space to learn low-dimensional embeddings such that valid triples maximize a defined scoring function and that fallacious triples minimize it. An approach is efficient if it can model multiple re- lational patterns. Some predicates are symmetric (e.g. marriedTo), asymmetric (e.g. fatherOf), an inversion of another relation (e.g. fatherOf and childOf) or a composition (e.g. grandfatherOf). Distinct strategies were introduced by explicitly model those patterns (Bordes et al., 2013; Yang et al., 2015; …

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