Retrieving Complementary Evidence for Multi-Hop RAG with Semantic Gain Graphs

Multi-hop retrieval-augmented generation (RAG) requires finding documents whose evidence is useful in combination. Query relevance and graph connectivity help locate related content, but neither directly measures the additional information one document contributes given another. We introduce SG2RAG, a framework that represents this complementarity through semantic gain. Offline, a large language model assesses the relevant and nonredundant information contributed by one chunk given another within neighborhoods proposed by semantic similarity. These ordered assessments are aggregated into symmetric edge weights to construct a reusable Semantic Gain Graph. Online, controlled Personalized PageRank starts from query-relevant seeds and ranks complementary evidence beyond the initial retrieval set. Experiments on MuSiQue, 2Wiki, and HotpotQA with two language model backbones show that SG2RAG achieves the best average EM, F1, and Recall@10 among the evaluated single-retrieval methods. Under identical candidate support and propagation, semantic gain improves average F1 and Recall@10 over similarity weighting by 4.08 and 4.31 points. Analyses of supporting documents and improvements in three iterative retrieval frameworks further support its effectiveness as a reusable retrieval component.