Simple but Effective Compound Geometric Operations for Temporal Knowledge Graph Completion (2024)

Abstract: Temporal knowledge graph completion aims to infer the missing facts in temporal knowledge graphs. Current approaches usually embed factual knowledge into continuous vector space and apply geometric operations to learn potential patterns in temporal knowledge graphs. However, these methods only adopt a single operation, which may have limitations in capturing the complex temporal dynamics present in temporal knowledge graphs. Therefore, we propose a simple but effective method, i.e. TCompoundE, which is specially designed with two geometric operations, including time-specific and relation-specific operations. We provide mathematical proofs to demonstrate the ability of TCompoundE to encode various relation patterns. Experimental results show that our proposed model significantly outperforms existing temporal knowledge graph embedding models. Our code is available at https://github.com/nk-ruiying/TCompoundE.

## introduction a knowledge graph (kg) comprises a collection of structured knowledge presented in triples, offering a simple and effective means of describing factual information @xcite . in a kg, a triplet is conventionally represented as (s, r, o), where s, o and r correspond to the head entity, tail entity and the relation linking between the head and tail entities, respectively. however, knowledge is not static in the real world @xcite . temporal knowledge graph (tkg) represents knowledge (s, r, o) occurring at timestamp τ , denoted as a quadruple (s, r, o, τ ), thereby adding a temporal dimension to knowledge graphs. the introduction of the timestamp τ enables tkg to delineate the temporal scope of knowledge more accurately and helps us better uncover the potential information within it @xcite . therefore, tkg is widely applied in downstream tasks * mengting hu is the corresponding author. ## background and notation in subsequent sections of this article, the com-pounde @xcite methodology is employed to elucidate translation, scaling, and rotation operations. the ensuing discussion provides a comprehensive account of the representation of these operations, followed by an introduction to the com-pounde model. ## conclusion this paper introduces a novel method, tcom-pounde, designed to address the challenge of 11081 knowledge graph completion in tkgs. tcom-pounde applies a compound of translation and scaling as relation-specific and time-specific operations. our experimental results demonstrate that tcom-pounde effectively manages both relation and time information in tkgs. furthermore, we provide mathematical evidence supporting tcompounde's capability to handle various relational patterns. additionally, we explore the effectiveness of different combinations of relation-specific and time-specific operations.