Hierarchical Multi-Scale Graph Neural Networks: Scalable Heterophilous Learning with Oversmoothing and Oversquashing Mitigation

The paper introduces Hierarchical Multi-view HAAR (HMH), a novel spectral graph-learning framework designed to address oversmoothing and degree-biased aggregation in GNNs for heterophilous graphs. HMH constructs a soft graph hierarchy and applies learnable spectral filters using sparse, orthonormal Haar bases, achieving near-linear time scalability.