在双曲空间实现实时文档检索，让边缘设备也能高效运行RAG。
Real-Time Hybrid Retrieval in Hyperbolic Space for Retrieval-Augmented Generation on Edge Devices
- 将词向量映射到双曲空间，利用其层级结构适配自然语言。
- 仅用词向量在5个数据集上达到最高0.654的NDCG@10性能。
- 支持边缘设备实时索引与查询，延迟低至交互级别。
本文提出一种完全在洛伦兹模型双曲几何空间中运行的混合文档检索系统，用于检索增强生成（RAG）。不同于受限于欧几里得空间的传统密集检索器，该系统通过可学习的HyTE-H变换将预训练词向量投影至双曲空间，其指数级体积增长特性契合自然语言的层次组织。文档被分块索引，使用洛伦兹嵌入进行存储；检索采用两阶段流程：先以BM25进行词汇评分，再以洛伦兹内积相似度重排候选文档。通过可调参数α融合两种得分。在BEIR基准的五个数据集（SciFact、NFCorpus、ArguAna、SciDocs、FiQA）上评估，仅使用词向量即取得NDCG@10分别为0.654、0.304、0.342、0.150、0.217的成绩，无需微调神经编码器或交叉注意力重排序器。系统支持用户文档的实时索引，可在数十万条中等大小文档上实现资源高效的查询，使双曲检索能在边缘设备上以交互延迟运行。
原文摘要 · Abstract (English)
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.
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