HyperKGR: Knowledge Graph Reasoning in Hyperbolic Space with Graph Neural Network Encoding Symbolic Path

Knowledge graphs (KGs) enable reasoning tasks such as link prediction, question answering, and knowledge discovery. However, real-world KGs are often incomplete, making link prediction both essential and challenging. Existing methods, including embeddingbased and path-based approaches, rely on Euclidean embeddings, which struggle to capture hierarchical structures. GNN-based methods aggregate information through message passing in Euclidean space, but they struggle to effectively encode the recursive treelike structures that emerge in multi-hop reasoning. To address these challenges, instead of learning static entity and relation embeddings, we propose a hyperbolic GNN framework (HYPERKGR) that embeds recursive learning trees in dynamic query-specific hyperbolic space. By incorporating hierarchical message passing, our method naturally aligns with reasoning paths and dynamically adapts to queries, improving prediction accuracy. Unlike static embedding-based approaches, our model learns context-aware embeddings tailored to each query. Experiments on multiple benchmark datasets show that our approach consistently outperforms state-of-the-art methods, demonstrating its effectiveness in KG reasoning. The code can be found in https: //github.com/lihuiliullh/HyperKGR