HyperGraphPro: Progress-Aware Reinforcement Learning for Structure-Guided Hypergraph RAG

Large language models (LLMs) have shown strong capabilities, with retrieval-augmented generation (RAG) supporting complex multi-hop reasoning by retrieving evidence distributed across documents. Graph-based approaches exploit connections among evidence, and hypergraph-based retrieval further preserves higher-order entity associations within documents and connects documents through shared entities. However, existing hypergraph retrievers often rely on predefined structural expansion or diffusion, which may miss query-dependent interactions needed to identify relevant evidence. They also leave connections among retrieved evidence implicit, requiring LLMs to reconstruct these connections before reasoning. Therefore, we propose HyperReCo, a framework for retrieving and connecting evidence with a hypergraph neural network (HyperGNN). We represent each document as a hyperedge over its extracted entities, with shared entities connecting the hyperedges. Through hypergraph message passing with joint supervision over documents and entities, the HyperGNN learns query-dependent interactions to retrieve complementary evidence. We further introduce Gradient-Guided Hyper-Path Decoding (GGHD), which uses gradient attribution to interpret the learned interactions and translate them into explicit hyper-paths that help LLMs combine complementary facts for multi-hop reasoning. Experiments on six benchmarks show that HyperReCo achieves the best retrieval performance among the compared methods on all three multi-hop QA datasets, together with strong downstream QA performance. Case studies and further analyses demonstrate the utility of decoded hyper-paths for connecting retrieved evidence.

Graph-based retrieval-augmented generation (RAG) methods, typically built on knowledge graphs (KGs) with binary relational facts, have shown promise in multi-hop open-domain QA. However, their rigid retrieval schemes and dense similarity search often introduce irrelevant context, increase computational overhead, and limit relational expressiveness. In contrast, n-ary hypergraphs encode higher-order relational facts that capture richer inter-entity dependencies and enable shallower, more efficient reasoning paths. To address this limitation, we propose HyperRAG, a RAG framework tailored for n-ary hypergraphs with two complementary retrieval variants: (i) HyperRetriever learns structural-semantic reasoning over n-ary facts to construct query-conditioned relational chains. It enables accurate factual tracking, adaptive high-order traversal, and interpretable multi-hop reasoning under context constraints. (ii) HyperMemory leverages the LLM's parametric memory to guide beam search, dynamically scoring n-ary facts and entities for query-aware path expansion. Extensive evaluations on WikiTopics (11 closed-domain datasets) and three open-domain QA benchmarks (HotpotQA, MuSiQue, and 2WikiMultiHopQA) validate HyperRAG's effectiveness. HyperRetriever achieves the highest answer accuracy overall, with average gains of 2.95% in MRR and 1.23% in Hits@10 over the strongest baseline. Qualitative analysis further shows that HyperRetriever bridges reasoning gaps through adaptive and interpretable n-ary chain construction, benefiting both open and closed-domain QA.

Multi-hop question answering often fails when retrieval treats evidence as isolated matches to the original question, since the facts needed to answer a complex question are usually connected through intermediate entities, relations, and constraints. We propose HyperProve, a retrieval-augmented QA framework that addresses this challenge by coupling question decomposition with answer-conditioned expansion over a hypergraph of atomic facts. HyperProve does not use atomic facts, hypergraphs, or iterative retrieval in isolation; instead, it carries intermediate answers and supporting hyperedges as retrieval state, then uses that state to bias the next local hypergraph expansion. This design enables HyperProve to construct coherent evidence chains for final answer generation while making the retrieval process stateful and fact-centered. Across multi-hop QA benchmarks, HyperProve achieves the best overall performance in our evaluation, outperforming the strongest baselines by an average relative improvement of 6.2% in answer accuracy and 4.9% in F1.