# HyperbolicRAG: Enhancing Retrieval-Augmented Generation with Hyperbolic Representations

arXiv: https://arxiv.org/abs/2511.18808 · HTML: https://mlsanity.com/paper/2511.18808/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge-graph and structured-knowledge RAG, one of 15 directions in Retrieval-augmented generation.
- Builds on 45 of its 61 references that are in the map.
- First posted on arXiv 24 Nov 2025.

## Placed in

- Retrieval-augmented generation / [Knowledge-graph and structured-knowledge RAG](https://mlsanity.com/rag/knowledge-graph-and-structured-knowledge-rag/)

## Builds on (most cited first, 30 of 45)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [Towards General Text Embeddings with Multi-stage Contrastive Learning](https://mlsanity.com/paper/2308.03281/) (2023)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [RAPTOR: Recursive Abstractive Processing for Tree-Organized Retrieval](https://mlsanity.com/paper/2401.18059/) (2024)
- [NV-Embed: Improved Techniques for Training LLMs as Generalist Embedding Models](https://mlsanity.com/paper/2405.17428/) (2024)
- [Large Dual Encoders Are Generalizable Retrievers](https://mlsanity.com/paper/2112.07899/) (2021)
- [A Survey on RAG Meeting LLMs: Towards Retrieval-Augmented Large Language Models](https://mlsanity.com/paper/2405.06211/) (2024)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [LightRAG: Simple and Fast Retrieval-Augmented Generation](https://mlsanity.com/paper/2410.05779/) (2024)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [From RAG to Memory: Non-Parametric Continual Learning for Large Language Models](https://mlsanity.com/paper/2502.14802/) (2025)
- [G-Retriever: Retrieval-Augmented Generation for Textual Graph Understanding and Question Answering](https://mlsanity.com/paper/2402.07630/) (2024)
- [A Survey on Recent Advances in LLM-Based Multi-turn Dialogue Systems](https://mlsanity.com/paper/2402.18013/) (2024)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Hyperbolic Vision Transformers: Combining Improvements in Metric Learning](https://mlsanity.com/paper/2203.10833/) (2022)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [A Comprehensive Survey on Process-Oriented Automatic Text Summarization with Exploration of LLM-Based Methods](https://mlsanity.com/paper/2403.02901/) (2024)
- [A Survey of Graph Retrieval-Augmented Generation for Customized Large Language Models](https://mlsanity.com/paper/2501.13958/) (2025)

## Built on by (most cited first, 2 of 2)

- [HypRAG: Hyperbolic Dense Retrieval for Retrieval Augmented Generation](https://mlsanity.com/paper/2602.07739/) (2026)
- [ISO-RAG: Isoperimetric Noise Control for Retrieval-Augmented Generation](https://mlsanity.com/paper/2609.00513/) (2026)

## Abstract (arXiv)

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.