# Real-Time Hybrid Retrieval in Hyperbolic Space for Retrieval-Augmented Generation on Edge Devices

arXiv: https://arxiv.org/abs/2608.01450 · HTML: https://mlsanity.com/paper/2608.01450/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Generation and context integration, one of 15 directions in Retrieval-augmented generation.
- Builds on 16 of its 21 references that are in the map.
- First posted on arXiv 2 Aug 2026.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [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)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [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)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [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)
- [SPLADE: Sparse Lexical and Expansion Model for First Stage Ranking](https://mlsanity.com/paper/2107.05720/) (2021)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [The Numerical Stability of Hyperbolic Representation Learning](https://mlsanity.com/paper/2211.00181/) (2022)
- [HELM: Hyperbolic Large Language Models via Mixture-of-Curvature Experts](https://mlsanity.com/paper/2505.24722/) (2025)
- [Low-distortion and GPU-compatible Tree Embeddings in Hyperbolic Space](https://mlsanity.com/paper/2502.17130/) (2025)
- [HypRAG: Hyperbolic Dense Retrieval for Retrieval Augmented Generation](https://mlsanity.com/paper/2602.07739/) (2026)

## Abstract (arXiv)

This paper presents a hybrid document retrieval system designed for retrieval-augmented generation (RAG) that operates entirely within the Lorentz model of hyperbolic geometry. Unlike conventional dense retrievers confined to Euclidean space, this system projects pretrained word embeddings into hyperbolic space through a learned HyTE-H transformation, whose exponential volume growth suits the hierarchical organization of natural language. Documents are segmented into overlapping chunks, indexed by their Lorentz embeddings, and retrieved through a two-stage pipeline that first applies BM25 lexical scoring, then re-ranks candidates using Lorentzian inner-product similarity. A tunable parameter α blends the BM25 score with the hyperbolic similarity score. The system was evaluated on five datasets from the BEIR benchmark suite, SciFact, NFCorpus, ArguAna, SciDocs, and FiQA, achieving NDCG@10 scores of 0.654, 0.304, 0.342, 0.150, and 0.217 respectively with word embeddings alone, without fine-tuned neural encoders or cross-attention rerankers. The system supports real-time indexing of user-supplied documents and resource-efficient querying over tens of thousands of moderately sized documents, so hyperbolic retrieval can run on edge devices at interactive latencies.