MetaHKG: Meta Hyperbolic Learning for Few-shot Temporal Reasoning

This paper investigates the few-shot temporal reasoning capability within the hyperbolic space. The goal is to forecast future events for newly emerging entities within temporal knowledge graphs (TKGs), leveraging only a limited set of initial observations. Hyperbolic space is advantageous for modeling emerging graph entities for two reasons: First, its geometric property of exponential expansion aligns with the rapid growth of new entities in real-world graphs; Second, it excels in capturing power-law patterns and hierarchical structures, well-suitable for new entities distributed at the peripheries of graph hierarchies and loosely connected with others through few links. We therefore propose a meta-learning framework, MetaHKG, to enable few-shot temporal reasoning within a hyperbolic space. Unlike prior hyperbolic learning works, MetaHKG addresses the challenges of effectively representing new entities in TKGs and adapting model parameters by incorporating novel hyperbolic time encodings and temporal attention networks that achieve translational invariance. We also introduce a meta hyperbolic optimization algorithm to enhance model adaptation by learning both global and entity-specific parameters through bi-level optimization. Comprehensive experiments conducted on three real-world temporal knowledge graphs demonstrate the superiority of MetaHKG over a diverse range of baselines, which achieves average 5.2% relative improvements. Compared to its Euclidean counterpart, MetaHKG operates in a lower-dimensional space but yields a more stable and efficient adaptability towards new entities.