Multi-Hop Reasoning for Question Answering with Hyperbolic Representations

TL;DR

This paper compares hyperbolic and Euclidean representations for multi-hop question answering, demonstrating hyperbolic space's superior performance especially on hierarchical data, and highlights the importance of learnable curvature.

Contribution

It provides a comprehensive experimental comparison between hyperbolic and Euclidean spaces for multi-hop reasoning, introducing learnable curvature to enhance hyperbolic representations.

Findings

Hyperbolic space outperforms Euclidean space in multi-hop reasoning tasks.

Learnable curvature initialized with data hyperbolicity improves results.

Hyperbolic representations are more effective on hierarchical datasets.

Abstract

Hyperbolic representations are effective in modeling knowledge graph data which is prevalently used to facilitate multi-hop reasoning. However, a rigorous and detailed comparison of the two spaces for this task is lacking. In this paper, through a simple integration of hyperbolic representations with an encoder-decoder model, we perform a controlled and comprehensive set of experiments to compare the capacity of hyperbolic space versus Euclidean space in multi-hop reasoning. Our results show that the former consistently outperforms the latter across a diverse set of datasets. In addition, through an ablation study, we show that a learnable curvature initialized with the delta hyperbolicity of the utilized data yields superior results to random initializations. Furthermore, our findings suggest that hyperbolic representations can be significantly more advantageous when the datasets exhibit a more hierarchical structure.