# HypRAG: Hyperbolic Dense Retrieval for Retrieval Augmented Generation

arXiv: https://arxiv.org/abs/2602.07739 · HTML: https://mlsanity.com/paper/2602.07739/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Generation and context integration, one of 15 directions in Retrieval-augmented generation.
- Builds on 53 of its 59 references that are in the map.
- First posted on arXiv 8 Feb 2026.

## Placed in

- Retrieval-augmented generation / [Generation and context integration](https://mlsanity.com/rag/generation-and-context-integration/)

## Builds on (most cited first, 30 of 53)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection](https://mlsanity.com/paper/2310.11511/) (2023)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [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)
- [Approximate Nearest Neighbor Negative Contrastive Learning for Dense Text Retrieval](https://mlsanity.com/paper/2007.00808/) (2020)
- [Towards General Text Embeddings with Multi-stage Contrastive Learning](https://mlsanity.com/paper/2308.03281/) (2023)
- [Smarter, Better, Faster, Longer: A Modern Bidirectional Encoder for Fast, Memory Efficient, and Long Context Finetuning and Inference](https://mlsanity.com/paper/2412.13663/) (2024)
- [NV-Embed: Improved Techniques for Training LLMs as Generalist Embedding Models](https://mlsanity.com/paper/2405.17428/) (2024)
- [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)
- [Nomic Embed: Training a Reproducible Long Context Text Embedder](https://mlsanity.com/paper/2402.01613/) (2024)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [mGTE: Generalized Long-Context Text Representation and Reranking Models for Multilingual Text Retrieval](https://mlsanity.com/paper/2407.19669/) (2024)
- [Generative Representational Instruction Tuning](https://mlsanity.com/paper/2402.09906/) (2024)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Retrieval-Augmented Generation with Graphs (GraphRAG)](https://mlsanity.com/paper/2501.00309/) (2024)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [EmbeddingGemma: Powerful and Lightweight Text Representations](https://mlsanity.com/paper/2509.20354/) (2025)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [RAGBench: Explainable Benchmark for Retrieval-Augmented Generation Systems](https://mlsanity.com/paper/2407.11005/) (2024)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Embedding Text in Hyperbolic Spaces](https://mlsanity.com/paper/1806.04313/) (2018)

## Built on by (most cited first, 1 of 1)

- [Real-Time Hybrid Retrieval in Hyperbolic Space for Retrieval-Augmented Generation on Edge Devices](https://mlsanity.com/paper/2608.01450/) (2026)

## Abstract (arXiv)

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.