Bending the Future: Autoregressive Modeling of Temporal Knowledge Graphs in Curvature-Variable Hyperbolic Spaces

TL;DR

This paper introduces HyperVC, a hyperbolic space-based model for temporal knowledge graphs that effectively captures hierarchical structures across time and within individual graphs, leading to improved reasoning performance.

Contribution

The paper proposes HyperVC, a novel approach using hyperbolic embeddings with adjustable curvature to model hierarchies in temporal knowledge graphs, addressing a gap in hierarchical reasoning.

Findings

Significant performance improvements on four benchmark datasets.

Better encoding of hierarchies with hyperbolic space compared to Euclidean.

Enhanced reasoning accuracy on datasets with complex hierarchies.

Abstract

Recently there is an increasing scholarly interest in time-varying knowledge graphs, or temporal knowledge graphs (TKG). Previous research suggests diverse approaches to TKG reasoning that uses historical information. However, less attention has been given to the hierarchies within such information at different timestamps. Given that TKG is a sequence of knowledge graphs based on time, the chronology in the sequence derives hierarchies between the graphs. Furthermore, each knowledge graph has its hierarchical level which may differ from one another. To address these hierarchical characteristics in TKG, we propose HyperVC, which utilizes hyperbolic space that better encodes the hierarchies than Euclidean space. The chronological hierarchies between knowledge graphs at different timestamps are represented by embedding the knowledge graphs as vectors in a common hyperbolic space. Additionally, diverse hierarchical levels of knowledge graphs are represented by adjusting the curvatures of hyperbolic embeddings of their entities and relations. Experiments on four benchmark datasets show substantial improvements, especially on the datasets with higher hierarchical levels.