Position: Hyperbolic Embeddings Are Essential for Health Knowledge Graphs in LLMs and Vector Databases

OU DENG, Qun Jin

TL;DR: Hyperbolic Embeddings Are Essential for Health Knowledge Graphs in LLMs and Vector Databases

Abstract: This position paper contends that hyperbolic embeddings must become a standard for modeling and retrieving hierarchical health knowledge graphs (HKGs) within large language models (LLMs) and their supporting vector databases. While Euclidean or spherical embeddings remain prevalent in biomedical retrieval systems, these geometries cannot adequately capture the deep ontological hierarchies, small-world connections, and rich relational patterns inherent in medical data. By contrast, hyperbolic embeddings exploit negatively curved spaces such as the Poincaré ball to compress hierarchical information with minimal distortion, paving the way for more interpretable retrieval, advanced question answering, and robust clinical decision support. This paper details how negative curvature addresses common bottlenecks in Euclidean-based solutions and calls on the healthcare and ML communities to adopt hyperbolic geometry as a core component of next-generation health informatics pipelines. We present both theoretical underpinnings and practical implementation strategies, supplemented by four in-depth appendices that cover mathematical proofs, comprehensive literature overviews, experiment design frameworks, and real-world policy considerations. Despite engineering and organizational hurdles, we argue that hyperbolic embeddings offer compelling benefits and should be the default choice for hierarchical HKGs in LLM-driven ecosystems.

Primary Area: Research Priorities, Methodology, and Evaluation

Keywords: Hyperbolic embedding, Health knowledge graphs, Large language model, Vector database

Submission Number: 200