Dysformer: A Spatial-Spectral Dual-Stream Dynamic Hyperbolic Hypergraph Transformer

Graph representation learning has become a fundamental paradigm for modeling and analyzing complex structured data. In principle, the geometry of the embedding space should be well-aligned with the intrinsic structure of the underlying data to minimize representational distortion. However, most existing methods rely on Euclidean geometry and static graph topologies, which severely limit their ability to capture the hierarchical organization and higher-order dependencies that are prevalent in real-world networks. In addition, deep graph neural networks often suffer from the oversmoothing problem, where node representations become increasingly indistinguishable as network depth grows. To overcome these limitations, we propose Dysformer, a novel spatial–spectral dual-stream fusion framework for graph representation learning. Dysformer integrates a dynamic node–hyperedge–node message-passing mechanism with a Hyperbolic Graph Wavelet Transform, enabling the joint modeling of high-order relational structures and multi-scale spectral information. An adaptive geometric gating mechanism is further introduced to fuse global hierarchical topology with fine-grained local geometric features. Moreover, we design a Dynamic Trainable Curvature Regulation module that allows layer-wise geometric adaptation, enabling the curvature of the hyperbolic manifold to dynamically align with the semantic granularity of features across network depths. Extensive experiments on benchmark datasets demonstrate that Dysformer consistently and substantially outperforms both hyperbolic and Euclidean state-of-the-art baselines. Furthermore, when applied to real-world clinical data, Dysformer effectively disentangles key determinants of anxiety and depression, offering robust data-driven insights to support targeted socio-medical interventions.