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Deep Hypergraph Neural Networks with Tight Framelets
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Analyzes why deep hypergraph neural networks oversmooth and proposes FrameHGNN, a deep HGNN using tight-framelet hypergraph convolutions with low- and high-pass channels plus initial residual and identity mapping.
Problem
Deep hypergraph neural networks suffer from oversmoothing as depth increases, and its causes in hypergraphs are poorly understood compared with GNNs.
Approach
Theoretically shows high-frequency energy of classic hypergraph convolution decays with depth, then builds a spectral hypergraph convolution using tight framelet decomposition (Haar-type filters, Chebyshev approximation) with both low-pass and high-pass channels, combined with GCNII-style initial residuals and identity mappings.
Key results
- FrameHGNN reaches 81.51% on Cora, 85.18% on Cora-CA and 98.41% on ModelNet40, outperforming all eight baselines on seven of eight datasets.
- On Senate, FrameHGNN achieves 67.61% versus 64.79% for the best baseline (ED-HNN), a gain of nearly 3 points.
- Unlike baselines whose accuracy drops beyond two layers, FrameHGNN improves with depth across datasets; on Senate it gains about 2% from 1 to 32 layers.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use FrameHGNN instead of ED-HNN | Hypergraph node classification · Cora | accuracy: 80.31 -> 81.51 | Helped |
| use FrameHGNN instead of ED-HNN | Hypergraph node classification · CiteSeer | accuracy: 73.70 -> 74.72 | Helped |
| use FrameHGNN instead of AllDeepSets | Hypergraph node classification · Pubmed | accuracy: 88.75 -> 88.73 | Hurt |
| use FrameHGNN instead of ED-HNN | Hypergraph node classification · Cora-CA | accuracy: 83.97 -> 85.18 | Helped |
| use FrameHGNN instead of ED-HNN | Hypergraph node classification · Senate | accuracy: 64.79 -> 67.61 | Helped |
| use FrameHGNN instead of ED-HNN | Hypergraph node classification · House | accuracy: 72.45 -> 72.82 | Helped |
| use FrameHGNN instead of UniGCNII | Hypergraph node classification · NTU2012 | accuracy: 89.30 -> 89.98 | Helped |
| use FrameHGNN instead of AllSetTransformer | Hypergraph node classification · ModelNet40 | accuracy: 98.20 -> 98.41 | Helped |
| add high-pass component (ablation) | FrameHGNN · Cora | accuracy: 80.34 -> 81.51 | Helped |
| add high-pass component (ablation) | FrameHGNN · CiteSeer | accuracy: 74.65 -> 74.72 | No clear effect |
| add high-pass component (ablation) | FrameHGNN · Pubmed | accuracy: 88.67 -> 88.73 | No clear effect |
| add high-pass component (ablation) | FrameHGNN · Senate | accuracy: 66.34 -> 67.61 | Helped |
Surprising findings
- Ablation shows removing the high-pass component improves ModelNet40 accuracy, and removing the low-pass component improves Cora, CiteSeer and Pubmed slightly, suggesting dataset-dependent frequency needs.
- Most classic HGNN baselines degrade once the network exceeds about two layers.
Limitations
- The balance between low-pass and high-pass components is data-dependent and not adaptively learned.
- Evaluation is limited to node classification on eight datasets.
- Standard deviations on Senate and House are large, making some gains less certain.
Experimental setup
Datasets: Cora CiteSeer Pubmed Cora-CA Senate House NTU2012 ModelNet40
Benchmarks: Cora CiteSeer Pubmed Cora-CA Senate House NTU2012 ModelNet40
Metrics: accuracy (%) standard deviation over 10 runs
Baselines: HGNN HCHA HNHN HyperGCN UniGCNII AllDeepSets AllSetTransformer ED-HNN
Builds on: HGNN GCNII framelet transforms on graphs Chebyshev polynomial approximation
Closest papers by meaning
- When Hypergraph Meets Heterophily: New Benchmark Datasets and Baseline (AAAI 2025 · similarity 0.90)
- Graph Neural Networks Do Not Always Oversmooth (NeurIPS 2024 · similarity 0.89)
- K-hop Hypergraph Neural Network: A Comprehensive Aggregation Approach (AAAI 2025 · similarity 0.88)
- Training-Free Message Passing for Learning on Hypergraphs (ICLR 2025 · similarity 0.88)
- LightHGNN: Distilling Hypergraph Neural Networks into MLPs for 100x Faster Inference (ICLR 2024 · similarity 0.88)
- A Signed Graph Approach to Understanding and Mitigating Oversmoothing (NeurIPS 2025 · similarity 0.88)
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