HMH: A Scalable Graph Neural Network for Heterophilous Learning
The paper arXiv:2605.10975 presents a new framework called Hierarchical Multi-view HAAR (HMH) aimed at classifying heterophilous graphs. These types of graphs, where neighboring nodes frequently have differing labels, are prevalent in social networking and molecular interactions. Current spectral GNN methods face challenges such as hub-dominated aggregation and oversmoothing, resulting from inadequate polynomial filters that cause approximation inaccuracies and merge distant signals. HMH resolves these challenges by initially learning signed affinities that are aware of both features and structures through a heterophily-aware encoder, followed by creating a soft graph hierarchy based on these embeddings. At each level of hierarchy, HMH constructs a sparse, orthonormal, and locality-sensitive Haar basis for implementing learnable spectral filters. The framework operates in nearly linear time, making it ideal for large-scale uses. The full paper can be found on arXiv under ID 2605.10975.
Key facts
- arXiv:2605.10975 presents HMH, a spectral graph-learning framework.
- HMH targets heterophilous graph classification.
- Heterophily means adjacent nodes often have different labels.
- Existing spectral GNNs suffer from hub-dominated aggregation and oversmoothing.
- Suboptimal polynomial filters cause approximation errors in prior methods.
- HMH uses a heterophily-aware encoder to learn signed affinities.
- A soft graph hierarchy is constructed from learned embeddings.
- HMH builds a sparse, orthonormal, locality-aware Haar basis at each level.
- The framework scales in near-linear time.
Entities
Institutions
- arXiv