HMH GNN tackles heterophily with 7% boost, near-linear scaling
New spectral GNN framework prevents oversmoothing and oversquashing with a hierarchical Haar basis
Graph Neural Networks (GNNs) traditionally struggle with heterophilous graphs—where adjacent nodes often have different labels, common in social networks and molecular interactions. Existing spectral methods suffer from hub-dominated aggregation and oversmoothing due to suboptimal polynomial filters that introduce approximation errors and blend distant signals. These issues degrade performance and limit scalability. The new HMH framework directly addresses these bottlenecks by replacing polynomial filters with a multi-scale, orthonormal Haar basis that preserves locality and prevents signal mixing.
HMH first learns feature- and structure-aware signed affinities via a heterophily-aware encoder. It then constructs a soft graph hierarchy guided by these embeddings. At each level, HMH builds a sparse, orthonormal Haar basis and applies learnable spectral filters in the frequency domain. Skip-connection unpooling layers combine outputs from all levels back into the original graph, effectively preventing hub domination and long-range signal bottlenecks (oversquashing). Experiments show HMH outperforms baselines by up to 3% on node classification and 7% on graph classification, while maintaining near-linear scalability—making it practical for large-scale real-world graphs.
- HMH uses a heterophily-aware encoder to learn signed affinities, capturing whether node relationships are similar or dissimilar.
- A hierarchical Haar wavelet basis with learnable spectral filters prevents oversmoothing and oversquashing while staying sparse and orthonormal.
- Up to 3% improvement on node classification and 7% on graph classification over state-of-the-art spectral GNNs, with near-linear time complexity.
Why It Matters
Enables more accurate, scalable analysis of real-world heterophilous graphs like social networks and molecular interactions.