Hyperbolic Sheaf Neural Networks for Brain Disorder Classification

Graph learning has emerged as a powerful framework for brain network analysis. However, growing evidence suggest that fundamental brain functions arise from higher-order interactions among multiple regions, which cannot be fully captured by pairwise graph models. Such pairwise representations are may therefore fail to characterize the emergent properties of complex higher-order dynamics. To address this limitation, we propose a novel framework named Hyperbolic Sheaf Neural Networks (HSNN), which integrates sheaf theory with hyperbolic geometry for higher-order brain network representation learning. Specifically, we employ continuity scaling to construct brain simplicial complexes that capture higher-order interactions among brain regions. Based on this structure, we introduce a sheaf diffusion process to infer network representations by propagating information through locally defined sheaf-theoretic relationships. To better represent the hierarchical and scale-free organization of brain networks, we further formulate the sheaf diffusion process to hyperbolic space, enabling more faithful modeling of complex neural interactions in hyperbolic space. Extensive experiments on five real-world neuroimaging datasets demonstrate that the proposed method consistently outperforms Euclidean and pairwise graph-based baselines. These results highlight the effectiveness of hyperbolic sheaf diffusion for brain network analysis and provide new insights into the geometric and topological mechanisms underlying neural function.