Semantic Gain Graphs for Complementarity-Guided Retrieval-Augmented Generation

Multi-hop Retrieval-Augmented Generation (RAG) requires discovering evidence whose value emerges through combination across documents. Dense retrievers rank chunks by isolated query relevance, while graph-based retrievers traverse connections that do not indicate whether neighboring documents contribute useful evidence. We propose SG${}^2$RAG, which reframes graph retrieval around semantic gain, defined as the useful and nonredundant evidence that one document chunk contributes in the context of another. SG${}^2$RAG aggregates these assessments into document-pair strengths in a Semantic Gain Graph, turning cross-document complementarity into an explicit retrieval relation. Starting from query-relevant seeds, controlled Personalized PageRank composes local gain relations into a global multi-hop ranking, following complementary evidence chains while maintaining query focus. This design moves evidence discovery beyond similarity ranking and topology-only traversal. Experiments on three multi-hop benchmarks show that SG${}^2$RAG achieves the best overall performance. Under identical candidate support and propagation, semantic-gain weighting consistently outperforms similarity weighting. Gold-support analysis further validates the gain signal, while improvements across iterative retrieval frameworks demonstrate its modularity.