{"ID":23474974,"CreatedAt":"2026-09-18T01:09:05.407443952Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.19622","arxiv_id":"2609.19622","title":"Beyond Similarity through Zero-Token Geometric Graphs for Multi-Hop RAG","abstract":"Multi-hop retrieval-augmented generation (RAG) requires evidence that remains relevant to a query while introducing enough novelty to bridge semantic gaps. Dense retrieval tends to concentrate on semantically similar documents, whereas graph-based alternatives often depend on costly Large Language Model (LLM) entity extraction and may propagate through noisy connections. We introduce Geometric Gain Graph RAG (G$^3$RAG), a document-only framework whose offline graph construction uses no LLM calls or generated tokens. G$^3$RAG assigns each edge a geometric gain score, $\\cosθ\\cdot \\sinθ$, that jointly captures directional consistency and orthogonality between document representations. A density-aware topological penalty suppresses highly connected hubs, while single-step controlled diffusion expands from filtered query seeds toward complementary evidence. We evaluate G$^3$RAG on MusiQue, 2WikiMultiHopQA, and HotpotQA using Nv-embed-v2 and Qwen3-8B-embed. G$^3$RAG obtains the best average F1 and answer-document hit rate among the evaluated graph-based baselines in both embedding settings, with gains of up to 4.26 F1 points in average performance and 5.76 points on MusiQue. It also removes the graph-construction token cost incurred by entity-based graph methods. These results show that geometric structure can support efficient multi-hop evidence discovery without LLM-based graph construction. Code is available at https://anonymous.4open.science/r/G3RAG-99D9/","short_abstract":"Multi-hop retrieval-augmented generation (RAG) requires evidence that remains relevant to a query while introducing enough novelty to bridge semantic gaps. Dense retrieval tends to concentrate on semantically similar documents, whereas graph-based alternatives often depend on costly Large Language Model (LLM) entity ex...","url_abs":"https://arxiv.org/abs/2609.19622","url_pdf":"https://arxiv.org/pdf/2609.19622v1","authors":"[\"Zeliang Li\",\"Xiaofen Xing\",\"Kailing Guo\",\"Xiangmin Xu\"]","published":"2026-09-17T03:14:30Z","proceeding":"cs.IR","tasks":"[\"cs.IR\"]","methods":"[\"RAG\",\"Diffusion Model\",\"Large Language Model\",\"Language Model\"]","project_urls":"[\"https://anonymous.4open.science/r/G3RAG-99D9/\"]","has_code":false}