# Beyond Similarity through Zero-Token Geometric Graphs for Multi-Hop RAG

arXiv: https://arxiv.org/abs/2609.19622 · HTML: https://mlsanity.com/paper/2609.19622/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Knowledge-graph and structured-knowledge RAG, one of 15 directions in Retrieval-augmented generation.
- Builds on 23 of its 27 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## 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, 23 of 23)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [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)
- [Enhancing Retrieval-Augmented Large Language Models with Iterative Retrieval-Generation Synergy](https://mlsanity.com/paper/2305.15294/) (2023)
- [LightRAG: Simple and Fast Retrieval-Augmented Generation](https://mlsanity.com/paper/2410.05779/) (2024)
- [From RAG to Memory: Non-Parametric Continual Learning for Large Language Models](https://mlsanity.com/paper/2502.14802/) (2025)
- [In Prospect and Retrospect: Reflective Memory Management for Long-term Personalized Dialogue Agents](https://mlsanity.com/paper/2503.08026/) (2025)
- [Re2G: Retrieve, Rerank, Generate](https://mlsanity.com/paper/2207.06300/) (2022)
- [A Survey of Graph Retrieval-Augmented Generation for Customized Large Language Models](https://mlsanity.com/paper/2501.13958/) (2025)
- [Inference Scaling for Long-Context Retrieval Augmented Generation](https://mlsanity.com/paper/2410.04343/) (2024)
- [RAG vs. GraphRAG: A Systematic Evaluation and Key Insights](https://mlsanity.com/paper/2502.11371/) (2025)
- [LinearRAG: Linear Graph Retrieval Augmented Generation on Large-scale Corpora](https://mlsanity.com/paper/2510.10114/) (2025)
- [HybGRAG: Hybrid Retrieval-Augmented Generation on Textual and Relational Knowledge Bases](https://mlsanity.com/paper/2412.16311/) (2024)
- [EfficientRAG: Efficient Retriever for Multi-Hop Question Answering](https://mlsanity.com/paper/2408.04259/) (2024)
- [Mitigating Lost-in-Retrieval Problems in Retrieval Augmented Multi-Hop Question Answering](https://mlsanity.com/paper/2502.14245/) (2025)
- [Efficient Algorithms for Personalized PageRank Computation: A Survey](https://mlsanity.com/paper/2403.05198/) (2024)
- [Meta-Chunking: Learning Text Segmentation and Semantic Completion via Logical Perception](https://mlsanity.com/paper/2410.12788/) (2024)
- [GeAR: Graph-enhanced Agent for Retrieval-augmented Generation](https://mlsanity.com/paper/2412.18431/) (2024)
- [Empowering GraphRAG with Knowledge Filtering and Integration](https://mlsanity.com/paper/2503.13804/) (2025)
- [T-GRAG: A Dynamic GraphRAG Framework for Resolving Temporal Conflicts and Redundancy in Knowledge Retrieval](https://mlsanity.com/paper/2508.01680/) (2025)

## Abstract (arXiv)

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 (G3RAG), a document-only framework whose offline graph construction uses no LLM calls or generated tokens. G3RAG assigns each edge a geometric gain score, cosθ · 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 G3RAG on MusiQue, 2WikiMultiHopQA, and HotpotQA using Nv-embed-v2 and Qwen3-8B-embed. G3RAG 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/