T e AST : Temporal Knowledge Graph Embedding via Archimedean Spiral Timeline (2023)

Abstract: Temporal knowledge graph embedding (TKGE) models are commonly utilized to infer the missing facts and facilitate reasoning and decision-making in temporal knowledge graph based systems. However, existing methods fuse temporal information into entities, potentially leading to the evolution of entity information and limiting the link prediction performance of TKG. Meanwhile, current TKGE models often lack the ability to simultaneously model important relation patterns and provide interpretability, which hinders their effectiveness and potential applications. To address these limitations, we propose a novel TKGE model which encodes T emporal knowledge graph e mbeddings via A rchimedean S piral T imeline (TeAST), which maps relations onto the corresponding Archimedean spiral timeline and transforms the quadruples completion to 3th-order tensor completion problem. Specifically, the Archimedean spiral timeline ensures that relations that occur simultaneously are placed on the same timeline, and all relations evolve over time. Meanwhile, we present a novel temporal spiral regularizer to make the spiral timeline orderly. In addition, we provide mathematical proofs to demonstrate the ability of TeAST to encode various relation patterns. Experimental results show that our proposed model significantly outperforms existing TKGE methods. Our code is available at https://github.com/IMU-MachineLearningSXD/TeAST .

## introduction knowledge graph (kg) expresses the relations of real-world entities and allows for reasoning new facts, which enables a wide range of applications in natural language processing @xcite @xcite . it stores a vast amount of knowledge in the form of triplets. these triplets are typically denoted as (s, r, o), * corresponding author where s, r and o represent the subject, the relation, and the object. since knowledge changes over time, researchers introduced timestamps into knowledge graphs to create temporal knowledge graphs (tkgs). in tkgs, each knowledge fact is represented as a quadruple (s, r, o, τ ), where τ denotes the timestamp at which the fact was true. this allows for more precise representation and querying of information in knowledge graphs, enabling applications that require an understanding of the evolution of knowledge over time. given the inherent incompleteness of most kgs and tkgs, knowledge graph embedding (kge) and temporal knowledge graph embedding (tkge) have been widely investigated to infer the missing facts using the existing ones. in particular, tkge has gained significant attention for its ability to represent and analyze knowledge over time. this work focuses on tkge. with the advancement of deep learning, researchers have proposed a number of kge approaches. these approaches typically involve learning low-dimensional embeddings of entities and relations, and then using a score function to measure the plausibility of triplets @xcite . while existing kge approaches have been shown to be effective on static knowledge graphs, they cannot be directly applied to tkgs due to the fact that real-world knowledge is dynamic and changes over time. to address this issue, researchers have designed tkge models that are capable of capturing the temporal information and dynamic nature of real-world facts. recent tkge models @xcite @xcite have shown very impressive completion performance on tkgs. nevertheless, there are two problems with these tkge models. firstly, the fusion of temporal information into entities led to a potential evolution of entity information, thus limiting the link prediction performance on tkg. in fact, the meaning of entities in quadruples does not change over time, whereas the relations between connected entities do. secondly, existing tkge models are not capable of simultaneously encoding important relation patterns and providing interpretability, which hinders their effectiveness and potential applications. to tackle these issues, we draw inspiration from the archimedean spiral and design temporal knowledge graph embeddings via archimedean spiral timeline (teast). specifically, we first map relations onto the corresponding archimedean spiral timeline and form a unified representation for the timestamp and the relation. as shown in figure 1 , we expect relations at the same time to be on the same timeline and relations evolve over time. that is, we simplify the quadruples (s, r, o, τ ) to a triplet (s, r τ, o), where denotes archimedean spiral operation. as a result, we transform the tkg embedding as 3th-order tensor completion problem in the complex space. next, we optimize the graph embeddings through tensor factorization. in addition, we propose a new temporal spiral regularizer to constrain the time representation and make the spiral timeline orderly. we further provide mathematical proofs to demonstrate the ability of teast to encode various relation patterns. experiments show that our method significantly outperforms the existing methods on tkge benchmarks. different from the existing tkge models, we map relations onto the archimedean spiral timeline and avoid incorporating temporal information into the entities. it ensures that the relations can evolve over time and the entities remain unchanged in tkgs. this is consistent with real-world facts. ## conclusion this paper proposes a novel and interesting tkge method teast, which maps relations onto the corresponding archimedean spiral timeline. the experimental results fully illustrate that teast can better model tkg than previous methods and learn the relation information over time. we also provide formal mathematical proofs to demonstrate that teast can encode the key relation patterns. in addition, the temporal spiral regularizer learns the latent information about the order between months better and improves the link prediction performances. this work will hopefully stimulate further research on tkge models and provide a novel perspective on the subject.