Hyperbolic RAG (HyRAG) boosts graph AI generalization by fixing geometry mismatch

Graph foundation models (GFMs) have become dominant for cross-domain graph representation learning, but their parameterized knowledge struggles with distribution shifts. Retrieval-augmented generation (RAG) can inject external knowledge at inference, but existing RAG frameworks operate in Euclidean space, which has polynomial volume growth — fundamentally mismatched with the tree-like structure of many knowledge bases. This mismatch leads to loss of semantic granularity and the hubness problem. To address this, the paper introduces HyRAG (Hyperbolic Retrieval-Augmented Generation), which reimagines retrieval in hyperbolic space, where volume grows exponentially — naturally matching tree hierarchies.

The HyRAG pipeline comprises three modules. First, Hyperbolic Knowledge Indexing models external knowledge with tree-like hierarchies in hyperbolic space. Second, Multi-granularity Retrieval fetches both global semantic anchors (coarse-grained) and local semantic nuances (fine-grained) to provide comprehensive context. Third, Dual-path Fusion integrates retrieved knowledge into GFM inference at both feature and structural levels. Experiments on multiple graph benchmarks demonstrate significant improvements in zero-shot settings, validating HyRAG's ability to enhance GFM generalization. The paper has been accepted at KDD 2026.