Hierarchical Multi-Scale Graph Neural Networks: Scalable Heterophilous Learning with Oversmoothing and Oversquashing Mitigation
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| Format: | Preprint |
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2026
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| _version_ | 1866910209727791104 |
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| author | Hossen, Md Sazzad Sahoo, Avimanyu |
| author_facet | Hossen, Md Sazzad Sahoo, Avimanyu |
| contents | Graphs with heterophily, where adjacent nodes carry different labels, are prevalent in real-world applications, from social networks to molecular interactions. However, existing spectral Graph Neural Network (GNN) approaches tailored for heterophilous graph classification suffer from hub-dominated (node with large degree) aggregation and oversmoothing, as their suboptimal polynomial filters introduce approximation errors and blend distant signals. To address the degree-biased aggregation and suboptimal polynomial filtering, we introduce a Hierarchical Multi-view HAAR (HMH), a novel spectral graph-learning framework that scales in near-linear time . HMH first learns feature- and structure-aware signed affinities via a heterophily-aware encoder, then constructs a soft graph hierarchy guided by these embeddings. At each hierarchical level, HMH constructs a sparse, orthonormal, and locality-aware Haar basis to apply learnable spectral filters in the frequency domain. Finally, skip-connection unpooling layers combine outputs from all hierarchical levels back into the original graph, effectively preventing hub domination and long-range signal bottleneck (over-squashing). Experimentation shows that HMH outperforms state-of-the-art spectral baselines, achieving up to a 3% improvement on node classification and 7% points on graph classification datasets, all while maintaining linear scalability. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_10975 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hierarchical Multi-Scale Graph Neural Networks: Scalable Heterophilous Learning with Oversmoothing and Oversquashing Mitigation Hossen, Md Sazzad Sahoo, Avimanyu Machine Learning Artificial Intelligence Graphs with heterophily, where adjacent nodes carry different labels, are prevalent in real-world applications, from social networks to molecular interactions. However, existing spectral Graph Neural Network (GNN) approaches tailored for heterophilous graph classification suffer from hub-dominated (node with large degree) aggregation and oversmoothing, as their suboptimal polynomial filters introduce approximation errors and blend distant signals. To address the degree-biased aggregation and suboptimal polynomial filtering, we introduce a Hierarchical Multi-view HAAR (HMH), a novel spectral graph-learning framework that scales in near-linear time . HMH first learns feature- and structure-aware signed affinities via a heterophily-aware encoder, then constructs a soft graph hierarchy guided by these embeddings. At each hierarchical level, HMH constructs a sparse, orthonormal, and locality-aware Haar basis to apply learnable spectral filters in the frequency domain. Finally, skip-connection unpooling layers combine outputs from all hierarchical levels back into the original graph, effectively preventing hub domination and long-range signal bottleneck (over-squashing). Experimentation shows that HMH outperforms state-of-the-art spectral baselines, achieving up to a 3% improvement on node classification and 7% points on graph classification datasets, all while maintaining linear scalability. |
| title | Hierarchical Multi-Scale Graph Neural Networks: Scalable Heterophilous Learning with Oversmoothing and Oversquashing Mitigation |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2605.10975 |