HyperbolicRAG: Enhancing Retrieval-Augmented Generation with Hyperbolic Representations

TL;DR

HyperbolicRAG addresses the inability of Euclidean graph-based RAG to capture hierarchical structure by embedding passages, entities, and facts in a hyperbolic space. It introduces depth-aware representations, a bidirectional containment alignment, and a dual-space retrieval framework that fuses Euclidean and hyperbolic signals for robust, hierarchy-aware retrieval. Across multiple QA benchmarks, HyperbolicRAG improves retrieval recall and end-to-end QA metrics, particularly on multi-hop tasks, demonstrating the practical value of incorporating hyperbolic geometry into retrieval-augmented generation. The method reduces hubness, enhances evidence coherence, and provides a model-agnostic approach that broadens the applicability of hierarchical representations in RAG systems.

Abstract

Retrieval-augmented generation (RAG) enables large language models (LLMs) to access external knowledge, helping mitigate hallucinations and enhance domain-specific expertise. Graph-based RAG enhances structural reasoning by introducing explicit relational organization that enables information propagation across semantically connected text units. However, these methods typically rely on Euclidean embeddings that capture semantic similarity but lack a geometric notion of hierarchical depth, limiting their ability to represent abstraction relationships inherent in complex knowledge graphs. To capture both fine-grained semantics and global hierarchy, we propose HyperbolicRAG, a retrieval framework that integrates hyperbolic geometry into graph-based RAG. HyperbolicRAG introduces three key designs: (1) a depth-aware representation learner that embeds nodes within a shared Poincare manifold to align semantic similarity with hierarchical containment, (2) an unsupervised contrastive regularization that enforces geometric consistency across abstraction levels, and (3) a mutual-ranking fusion mechanism that jointly exploits retrieval signals from Euclidean and hyperbolic spaces, emphasizing cross-space agreement during inference. Extensive experiments across multiple QA benchmarks demonstrate that HyperbolicRAG outperforms competitive baselines, including both standard RAG and graph-augmented baselines.

Figures (6)

• Figure 1: Comparison of Euclidean and hyperbolic embedding effects on retrieval-augmented multi-hop reasoning. (a) In Euclidean space, embeddings reflect surface-level similarity. General concepts (e.g., stress) act as semantic hubs, making top-$k$ retrieval and graph propagation drift toward broad, generic subgraphs. (b) In hyperbolic space, hierarchical depth is radially encoded: abstract nodes lie near the center, while specific facts align near the boundary. Queries are thus aligned to relevant mechanism nodes (e.g., chronic stress, cortisol release), yielding more precise and causally focused reasoning.
• Figure 2: Indexing pipeline. Given a document collection, the framework first performs chunking to obtain passages, from which an OpenIE extractor derives relational triples and normalized entity mentions. Passages, entities, and facts are then encoded into dense vectors using a pretrained encoder. Finally, a heterogeneous knowledge graph is constructed by linking (i) entity--entity pairs co-occurring in triples, (ii) passage--entity pairs grounded in text, and (iii) synonymy links between semantically similar entities.
• Figure 3: Overview of the hierarchical enhancement process. Given Euclidean embeddings of passages, entities, and facts, the model first extracts a hierarchical signal$\mathbf{u}_v$. This signal serves two roles: it is concatenated with the original semantic embedding $\mathbf{z}_v^{\mathbb{E}}$ to form an enhanced Euclidean representation enriched with hierarchical cues, and it is also used to predict a depth score $d_v$ that reflects the relative granularity of each node. The predicted depth then regulates a radial rescaling of the enhanced embedding, assigning smaller norms to more generic concepts and larger norms to more fine-grained evidence. Finally, the depth-aligned vectors are projected into the Poincaré ball via the exponential map, producing hyperbolic embeddings $\mathbf{z}_v^{\mathbb{H}}$ that jointly encode semantic similarity and hierarchical structure.
• Figure 4: Illustration of the dual-space retrieval framework. The query is processed in parallel Euclidean and hyperbolic spaces. Each branch computes query–fact similarities through different ways, propagates them to entities, and combines them with direct query–passage priors to form a seed distribution for PPR on the passage–entity graph, yielding space-specific rankings ($\mathcal{R}^{\mathbb{E}}$ and $\mathcal{R}^{\mathbb{H}}$). A mutual-ranking fusion then favors passages consistently ranked high in both spaces, balancing Euclidean semantic similarity and hyperbolic hierarchical structure for robust retrieval.
• Figure 5: Comparison of HyperbolicRAG under (a) different embedding encoders and (b) generative backbones.