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Temporal Knowledge Graph Completion with Time-sensitive Relations in Hypercomplex Space

Li Cai, Xin Mao, Zhihong Wang, Shangqing Zhao, Yuhao Zhou, Changxu Wu, Man Lan

TL;DR

This work tackles temporal knowledge graph completion by introducing TQuatE, a quaternion-based model that captures time-sensitive relations through time-aware rotation and periodic time translation in hypercomplex space. It represents $h$, $r$, $t$, and $\tau$ as quaternions, computes a cosine-based score with a rotated relation, and enforces embedding and periodic temporal regularization. Theoretical analyses prove that TQuatE can model symmetric, asymmetric, inverse, compositional, and evolutionary relation patterns, and empirical results on ICEWS14, ICEWS05-15, and GDELT demonstrate SOTA performance, especially on complex temporal data like GDELT. The approach advances temporal reasoning in KGs by leveraging the expressiveness of quaternions and a flexible periodic time component, though it incurs higher computational cost due to quaternion operations.

Abstract

Temporal knowledge graph completion (TKGC) aims to fill in missing facts within a given temporal knowledge graph at a specific time. Existing methods, operating in real or complex spaces, have demonstrated promising performance in this task. This paper advances beyond conventional approaches by introducing more expressive quaternion representations for TKGC within hypercomplex space. Unlike existing quaternion-based methods, our study focuses on capturing time-sensitive relations rather than time-aware entities. Specifically, we model time-sensitive relations through time-aware rotation and periodic time translation, effectively capturing complex temporal variability. Furthermore, we theoretically demonstrate our method's capability to model symmetric, asymmetric, inverse, compositional, and evolutionary relation patterns. Comprehensive experiments on public datasets validate that our proposed approach achieves state-of-the-art performance in the field of TKGC.

Temporal Knowledge Graph Completion with Time-sensitive Relations in Hypercomplex Space

TL;DR

This work tackles temporal knowledge graph completion by introducing TQuatE, a quaternion-based model that captures time-sensitive relations through time-aware rotation and periodic time translation in hypercomplex space. It represents , , , and as quaternions, computes a cosine-based score with a rotated relation, and enforces embedding and periodic temporal regularization. Theoretical analyses prove that TQuatE can model symmetric, asymmetric, inverse, compositional, and evolutionary relation patterns, and empirical results on ICEWS14, ICEWS05-15, and GDELT demonstrate SOTA performance, especially on complex temporal data like GDELT. The approach advances temporal reasoning in KGs by leveraging the expressiveness of quaternions and a flexible periodic time component, though it incurs higher computational cost due to quaternion operations.

Abstract

Temporal knowledge graph completion (TKGC) aims to fill in missing facts within a given temporal knowledge graph at a specific time. Existing methods, operating in real or complex spaces, have demonstrated promising performance in this task. This paper advances beyond conventional approaches by introducing more expressive quaternion representations for TKGC within hypercomplex space. Unlike existing quaternion-based methods, our study focuses on capturing time-sensitive relations rather than time-aware entities. Specifically, we model time-sensitive relations through time-aware rotation and periodic time translation, effectively capturing complex temporal variability. Furthermore, we theoretically demonstrate our method's capability to model symmetric, asymmetric, inverse, compositional, and evolutionary relation patterns. Comprehensive experiments on public datasets validate that our proposed approach achieves state-of-the-art performance in the field of TKGC.
Paper Structure (31 sections, 5 theorems, 20 equations, 3 figures, 5 tables)

This paper contains 31 sections, 5 theorems, 20 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Knowledge Graph Completion
  4. Temporal Knowledge Graph Completion
  5. Problem Formulation and Quaternion
  6. Problem Formulation of TKGC
  7. Quaternion Algebra
  8. Methods
  9. Temporal Reprenstation
  10. Score Function
  11. Regularizer
  12. Loss Function
  13. Relation pattern
  14. Experiments
  15. Datasets and Baselines
  16. ...and 16 more sections

Key Result

Proposition 1

TQuatE can model the symmetric relation pattern. (See proof in Appendix sec:appendix A)

Figures (3)

  • Figure 1: Subgraph example from ICEWS14 dataset for TKGC. Nodes on the graph represent entities, including Obama, Japan, South Korea, North Korea, and edges signify relations (with timestamps in parentheses), encompassing Host a visit, Make a visit, Express intent to meet or negotiate, Engage in negotiation. Solid black arrows denote existing facts, while red dashed arrows indicate missing facts that need to be completed.
  • Figure 2: TKGC performance for different embedding dimensions $d$ on ICEWS14.
  • Figure 3: MRR values for different weight of embedding regularizer $\lambda_e$ and time regularizer $\lambda_\tau$ on ICEWS14.

Theorems & Definitions (10)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Proposition 5