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SEA-GWNN: Simple and Effective Adaptive Graph Wavelet Neural Network
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Proposes SEA-GWNN, an adaptive graph wavelet network that applies a locally defined tree-based lifting scheme on multi-hop computation trees to preserve graph topology, and fuses high/low-pass components for node classification.
Problem
Existing wavelet GNNs use fixed wavelet filters, and prior adaptive lifting-based wavelet methods require bipartite splitting that alters graph topology, producing undesirable wavelet filters for node classification on homophilic and heterophilic graphs.
Approach
Apply the lifting scheme locally on acyclic multi-hop computation trees built from powers of the adjacency matrix (diagonal as root, off-diagonal as leaves), so the bipartite condition holds without altering the global graph; fuse the predict (high-pass) and update (low-pass) outputs, use GAT-style attention for lifting operators, and induce higher-order operators from first-order ones to cut cost
Key results
- Full-supervised: SEA-GWNN reaches 88.75% on Cora and 72.57% on Chameleon, best among compared methods in Table 1.
- Semi-supervised: SEA-GWNN achieves 84.4% on Cora, 72.8% on Citeseer, 80.7% on PubMed, outperforming LGWNN (83.4/71.1/79.5).
- Large-scale: SEA-GWNN attains 84.4% on Penn94 and 90.5% on Genius, the best in Table 2.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use SEA-GWNN instead of APPNP | node classification · Cora | accuracy: 87.87 ±0.2 -> 88.75 ±0.1 | Helped |
| use SEA-GWNN instead of D-GCN | node classification · Citeseer | accuracy: 76.83 ±1.2 -> 77.13 ±0.2 | Helped |
| use SEA-GWNN instead of BM-GCN | node classification · PubMed | accuracy: 90.25 ±0.7 -> 89.75 ±0.1 | Hurt |
| use SEA-GWNN instead of D-GCN | node classification · Film | accuracy: 37.07 ±0.8 -> 37.10 ±1.8 | Helped |
| use SEA-GWNN instead of D-GCN | node classification · Chameleon | accuracy: 70.90 ±1.1 -> 72.57 ±0.18 | Helped |
| use SEA-GWNN instead of D-GCN | node classification · Squirrel | accuracy: 62.56 ±1.3 -> 63.13 ±0.13 | Helped |
| use SEA-GWNN instead of D-GCN | node classification · Cornell | accuracy: 85.95 ±2.7 -> 85.95 ±4.6 | No clear effect |
| use SEA-GWNN instead of D-GCN | node classification · Wisconsin | accuracy: 87.06 ±3.4 -> 87.25 ±3.3 | Helped |
| use SEA-GWNN instead of GCNII | node classification · Penn94 | accuracy: 82.9 ±0.5 -> 84.4 ±0.3 | Helped |
| use SEA-GWNN instead of GCNII | node classification · Genius | accuracy: 90.2 ±0.1 -> 90.5 ±0.1 | Helped |
| use SEA-GWNN instead of GCNII | node classification · Ogbn-Arxiv | accuracy: 72.7 ±0.2 -> 72.9 ±0.5 | Helped |
| use SEA-GWNN instead of UFGConvR | semi-supervised node classification · Cora | accuracy: 83.6 ±0.6 -> 84.4 ±0.6 | Helped |
Limitations
- Excessively large hop sizes degrade performance due to overfitting (Cora and PubMed, k=32).
- Hyperparameters chosen by grid search; baselines taken from their papers' settings.
- Heterophilic results on Film and Wisconsin/Cornell show overlapping standard deviations with baselines.
Experimental setup
Datasets: Cora Citeseer PubMed Cornell Wisconsin Film Chameleon Squirrel Penn94 Genius Ogbn-Arxiv
Benchmarks: Cora Citeseer PubMed Film Chameleon Squirrel Cornell Wisconsin Penn94 Genius Ogbn-Arxiv
Metrics: node classification accuracy
Baselines: DeepWalk GCN GWNN GAT APPNP G-GCN MixHop H2GCN AM-GCN CPGNN GPR-GNN BM-GCN
Builds on: GWNN LGWNN (lifting-based adaptive graph wavelet network) GAT APPNP GA-GWNN
Closest papers by meaning
- ASWT-SGNN: Adaptive Spectral Wavelet Transform-Based Self-Supervised Graph Neural Network (AAAI 2024 · similarity 0.90)
- WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets (AAAI 2024 · similarity 0.90)
- Kumaraswamy Wavelet for Heterophilic Scene Graph Generation (AAAI 2024 · similarity 0.88)
- A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition (ICML 2025 · similarity 0.87)
- Diffusing to the Top: Boost Graph Neural Networks with Minimal Hyperparameter Tuning (ICLR 2025 · similarity 0.86)
- SLOG: An Inductive Spectral Graph Neural Network Beyond Polynomial Filter (ICML 2024 · similarity 0.86)
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