RSF-GLLM: Bridging the Semantic Gap in Multi-Hop Knowledge Graph QA via Recurrent Soft-Flow and Decoupled LLM Generation

Knowledge graph question answering (KGQA) requires navigating from topic entities to an answer several relations away. Recent methods prompt a frontier LLM to explore the graph through a retrieval tool, but their reliance on frontier-scale inference makes them costly to deploy. We present Search-on-Graph-R1 (\sogrone{}), which internalizes this navigation into a compact 8B model through supervised fine-tuning (SFT) followed by reinforcement learning (RL). Our central idea is to scaffold a frontier teacher with each question's gold SPARQL query, so the teacher traverses a known answer-bearing path with a live \texttt{Search} tool rather than having to discover the path itself. Since every call executes against a live Freebase server, the resulting trajectories are grounded in the knowledge graph by construction. On WebQSP, CWQ, and GrailQA, \sogrone{} at 8B surpasses every frozen frontier-LLM system in our comparison and posts the strongest results on CWQ of any system we compare against. It does so using no auxiliary module at inference and no LLM judge during training. Isolating each training stage shows that SFT and RL contribute complementary gains, our approach transfers across model families, and RL learns to reach answers in fewer \texttt{Search} calls than its SFT initialization.

Retrieval-augmented generation built on knowledge graphs (Graph RAG) outperforms flat passage retrieval on multi-hop question answering by leveraging graph structure. In most existing systems, however, the question only sets the seed nodes; the subsequent traversal becomes "query-blind", depending solely on the graph structure. The exception is QAFD-RAG, which implements query-aware traversal via a flow-diffusion solver with combined edge re-weighting. This architecture requires loading the full graph into Python memory and an iterative solver with a variable number of iterations complicating integration with the graph database. We propose a spreading-activation method that achieves the same query-aware traversal with a single per-step semantic gate: the step weight is the cosine similarity between the candidate entity's description and the question, and the number of iterations is fixed. The whole retrieval procedure - seed mapping, propagation, top-K selection and context assembly - is expressed as a single Cypher query executed in one round-trip to Neo4j; the graph never leaves the database. On MuSiQue our method matches QAFD-RAG by exact match (32.80 vs 33.50) and outperforms the strongest purely-structural baseline in our comparison, HippoRAG, by 5.3 EM and 3.4 F1; on 2WikiMultiHopQA HippoRAG and QAFD-RAG retain an advantage due to their phrase-node architectures. An ablation with the gate disabled confirms that the gate is the source of a simultaneous F1 gain of 3.6 to 7.4 points and a retrieval-latency reduction by a factor of 1.5 to 4.9.

Graph-based Retrieval-Augmented Generation (RAG) systems leverage interconnected knowledge structures to capture complex relationships that flat retrieval struggles with, enabling multi-hop reasoning. Yet most existing graph-based methods suffer from (i) heuristic designs lacking theoretical guarantees for subgraph quality or relevance and/or (ii) the use of static exploration strategies that ignore the query's holistic meaning, retrieving neighborhoods or communities regardless of intent. We propose Query-Aware Flow Diffusion RAG (QAFD-RAG), a training-free framework that dynamically adapts graph traversal to each query's holistic semantics. The central innovation is query-aware traversal: during graph exploration, edges are dynamically weighted by how well their endpoints align with the query's embedding, guiding flow along semantically relevant paths while avoiding structurally connected but irrelevant regions. These query-specific reasoning subgraphs enable the first statistical guarantees for query-aware graph retrieval, showing that QAFD-RAG recovers relevant subgraphs with high probability under mild signal-to-noise conditions. The algorithm converges exponentially fast, with complexity scaling with the retrieved subgraph size rather than the full graph. Experiments on question answering and text-to-SQL tasks demonstrate consistent improvements over state-of-the-art graph-based RAG methods.