Geometric Gain Graph: Zero-Token Graph Construction for Multi-Hop RAG

Existing Retrieval-Augmented Generation (RAG) systems struggle with multi-hop reasoning due to a fundamental inability to balance relevance and novelty. Traditional dense retrievers are constrained by surface-level matching, falling into a homogenized "Similarity Trap". Conversely, emerging Graph RAGs attempt to explore novel documents via heuristic entity extraction, but they introduce prohibitive Large Language Model (LLM) overhead and easily drift into off-topic "Novelty Traps". To fundamentally resolve this contradiction, we propose Geometric Gain Graph (G$^3$RAG), the novel zero-token graph construction paradigm for RAG. G$^3$RAG completely discards the expensive heuristic extraction by LLMs, aiming instead to directly quantify the information gain between nodes through the native document feature space. To this end, we designed a concise edge weight criterion, $\cos\theta \cdot \sin\theta$, which naturally maps the trade-off between relevance and novelty into a geometric measurement of directional consistency and orthogonality in the vector space, thereby driving the token-free topological construction of the graph. Furthermore, we introduce a topological penalty to suppress the excessive connectivity of high-frequency hubs, forcing the transient diffusion process toward long-tail peripheral nodes that carry critical indirect evidence. Extensive experiments demonstrate that, while entirely eliminating graph construction costs, G$^3$RAG significantly outperforms state-of-the-art Graph RAG baselines on complex multi-hop QA benchmarks.