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A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition
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Proposes WaveGC, a graph wavelet convolution that learns admissible wavelets by separately combining odd and even Chebyshev terms, paired with a matrix-valued shared kernel, and reports gains on short- and long-range node/graph benchmarks.
Problem
Spectral graph convolutions using Fourier bases or diagonal vector-valued kernels struggle to model signals across large spatial ranges, and existing learnable graph wavelets often violate wavelet admissibility criteria or have fixed shapes.
Approach
Decompose Chebyshev polynomials into odd terms (forming a scaling function that supplies the DC component) and even terms (forming admissible band-pass wavelets vanishing at zero), learn their coefficients and scales, normalize for tight frames, and use a weight-shared matrix-valued kernel in the wavelet domain.
Key results
- WaveGC reaches 41.63 F1 on PascalVOC-SP versus 35.98 for the best baseline DEFT, the largest reported gain (up to about 15.7% in the intro, 11.83% in experiments).
- WaveGC achieves 95.89 accuracy on CS, 92.26 on Computer, and 73.01 on ogbn-arxiv, best among listed baselines.
- Matrix-valued kernel beats vector-valued on Computer (92.26 vs 89.96 accuracy); weight sharing beats non-sharing (92.26 vs 90.51) with fewer parameters.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace the strongest listed baseline with WaveGC | graph models · CS | accuracy: 95.46±0.33 -> 95.89±0.34 | Helped |
| replace the strongest listed baseline with WaveGC | graph models · Photo | accuracy: 94.45±0.45 -> 95.37±0.44 | Helped |
| replace the strongest listed baseline with WaveGC | graph models · Computer | accuracy: 92.06±0.33 -> 92.26±0.18 | Helped |
| replace the strongest listed baseline with WaveGC | graph models · CoraFull | accuracy: 68.01±0.86 -> 69.14±0.78 | Helped |
| replace the strongest listed baseline with WaveGC | graph models · ogbn-arxiv | accuracy: 72.64±0.21 -> 73.01±0.18 | Helped |
| replace the strongest listed baseline with WaveGC | graph models · VOC | F1 score: 35.98±0.20 -> 41.63±0.19 | Helped |
| replace the strongest listed baseline with WaveGC | graph models · PCQM | MRR: 34.25±0.06 -> 34.50±0.02 | Helped |
| replace the strongest listed baseline with WaveGC | graph models · COCO | F1 score: 32.97±0.53 -> 35.96±0.22 | Helped |
| replace the strongest listed baseline with WaveGC | graph models · Peptides-func | AP: 68.75±0.20 -> 69.73±0.43 | Helped |
| replace the strongest listed baseline with WaveGC | graph models · Peptides-struct | MAE: 25.06±0.13 -> 24.83±0.11 | Helped |
| use a matrix-valued rather than vector-valued kernel (ablation) | WaveGC · Computer | accuracy: 89.96 -> 92.26 | Helped |
| use a matrix-valued rather than vector-valued kernel (ablation) | WaveGC · Peptides-struct | MAE: 25.30 -> 24.83 | Helped |
Surprising findings
- Non-shared frequency-specific kernels degrade performance, attributed to overfitting.
- Removing the wavelet part hurts more than removing the MPNN part in the ablation.
Limitations
- Relies on eigendecomposition with O(N^3) cost, which is expensive for large graphs.
- Theoretical receptive-field analysis uses approximations (Taylor expansion, dropped terms) and bounds rather than exact results.
Experimental setup
Datasets: CS Photo Computer CoraFull ogbn-arxiv PascalVOC-SP PCQM-Contact COCO-SP Peptides-func Peptides-struct
Benchmarks: CS Photo Computer CoraFull ogbn-arxiv PascalVOC-SP PCQM-Contact COCO-SP Peptides-func Peptides-struct
Metrics: accuracy F1 score MRR AP MAE
Baselines: GCN GAT APPNP GINE GatedGCN Scattering Scattering GCN SGWT GWNN UFGConvS UFGConvR WaveShrink-ChebNet
Builds on: spectral graph wavelet transform ChebNet Fourier Neural Operator DEFT UFGConv
Closest papers by meaning
- WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets (AAAI 2024 · similarity 0.93)
- HoloNets: Spectral Convolutions do extend to Directed Graphs (ICLR 2024 · similarity 0.90)
- ASWT-SGNN: Adaptive Spectral Wavelet Transform-Based Self-Supervised Graph Neural Network (AAAI 2024 · similarity 0.90)
- Unifying Homophily and Heterophily for Spectral Graph Neural Networks via Triple Filter Ensembles (NeurIPS 2024 · similarity 0.88)
- SEA-GWNN: Simple and Effective Adaptive Graph Wavelet Neural Network (AAAI 2024 · similarity 0.87)
- Position: Spectral GNNs Rely Less on Graph Fourier Basis than Conceived (ICML 2025 · similarity 0.87)
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