HypRAG: Hyperbolic Dense Retrieval for Retrieval Augmented Generation

TL;DR

This paper introduces hyperbolic dense retrieval models for retrieval-augmented generation, leveraging hyperbolic geometry to better capture hierarchical language structures and improve retrieval quality over Euclidean methods.

Contribution

It develops two hyperbolic transformer models and a geometry-aware pooling operator, demonstrating superior performance and hierarchical encoding in retrieval tasks.

Findings

HyTE-FH outperforms Euclidean baselines on MTEB.

HyTE-H achieves up to 29% gains on RAGBench.

Hyperbolic embeddings encode document specificity through norm-based separation.

Abstract

Embedding geometry plays a fundamental role in retrieval quality, yet dense retrievers for retrieval-augmented generation (RAG) remain largely confined to Euclidean space. However, natural language exhibits hierarchical structure from broad topics to specific entities that Euclidean embeddings fail to preserve, causing semantically distant documents to appear spuriously similar and increasing hallucination risk. To address these limitations, we introduce hyperbolic dense retrieval, developing two model variants in the Lorentz model of hyperbolic space: HyTE-FH, a fully hyperbolic transformer, and HyTE-H, a hybrid architecture projecting pre-trained Euclidean embeddings into hyperbolic space. To prevent representational collapse during sequence aggregation, we introduce the Outward Einstein Midpoint, a geometry-aware pooling operator that provably preserves hierarchical structure. On MTEB, HyTE-FH outperforms equivalent Euclidean baselines, while on RAGBench, HyTE-H achieves up to 29% gains over Euclidean baselines in context relevance and answer relevance using substantially smaller models than current state-of-the-art retrievers. Our analysis also reveals that hyperbolic representations encode document specificity through norm-based separation, with over 20% radial increase from general to specific concepts, a property absent in Euclidean embeddings, underscoring the critical role of geometric inductive bias in faithful RAG systems.