Research map / Graph learning / GNN architectures
WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets
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Proposes WaveNet, a spectral GNN that reconstructs graph spectral filters using Haar wavelet scaling functions via multi-resolution analysis, targeting high-frequency graph signals that polynomial-based spectral GNNs fit poorly.
Problem
Polynomial-basis spectral GNNs struggle to capture high-frequency and non-smooth graph spectral filters (and show over-smoothing and performance degradation with increasing order), limiting node classification on heterophilous graphs.
Approach
Perform multi-resolution analysis on graph spectral signals and reconstruct the propagation matrix using Haar wavelet scaling functions (non-polynomial bases) at a truncated resolution J, with learnable coefficients trained by gradient descent.
Key results
- WaveNet achieves the best accuracy on Computers (92.06%) and Photo (94.42%) among compared models, and on Chameleon (72.60%) and Squirrel (62.97%) it improves over the best baseline by roughly 1.2 and 5.3 points.
- On a synthetic high-frequency toy graph, WaveNet reaches 74.29% on sin(10λ)+1 and 68.18% on sin(10λ)e^{-λ}+1, above BernNet and ChebyNetII.
- On 50 synthetic image graphs, WaveNet achieves lower squared error than BernNet on band-rejection and comb filters (e.g., comb 0.0813 vs 0.9982).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Haar-wavelet scaling-function filters instead of polynomial spectral filters | WaveNet · Computers | accuracy: 91.27±0.45 -> 92.06±0.33 | Helped |
| Use Haar-wavelet scaling-function filters instead of polynomial spectral filters | WaveNet · Photo | accuracy: 94.06±0.37 -> 94.42±0.31 | Helped |
| Use Haar-wavelet scaling-function filters instead of polynomial spectral filters | WaveNet · Chameleon | accuracy: 71.37±1.01 -> 72.60±1.18 | Helped |
| Use Haar-wavelet scaling-function filters instead of polynomial spectral filters | WaveNet · Squirrel | accuracy: 57.72±0.59 -> 62.97±0.62 | Helped |
| Use Haar-wavelet scaling-function filters instead of polynomial spectral filters | WaveNet · Cora | accuracy: 89.00±0.72 -> 88.46±0.51 | Hurt |
| Use Haar-wavelet scaling-function filters instead of polynomial spectral filters | WaveNet · CiteSeer | accuracy: 81.79±0.95 -> 80.22±0.71 | Hurt |
| Use Haar-wavelet scaling-function filters instead of polynomial spectral filters | WaveNet · Actor | accuracy: 41.84±1.15 -> 39.69±1.54 | Hurt |
| Use Haar-wavelet scaling-function filters instead of polynomial spectral filters | WaveNet · PubMed | accuracy: 90.74±0.50 -> 90.26±0.22 | Hurt |
| Use wavelet bases instead of polynomial bases | WaveNet · Band-pass filter image graphs | sum of squared error: 0.0213 -> 0.0076 | Helped |
| Use wavelet bases instead of polynomial bases | WaveNet · Band-rejection filter image graphs | sum of squared error: 0.0156 -> 0.0074 | Helped |
| Use wavelet bases instead of polynomial bases | WaveNet · Comb filter image graphs | sum of squared error: 0.2933 -> 0.0813 | Helped |
| Use wavelet bases instead of polynomial bases | WaveNet · Low-pass filter image graphs | sum of squared error: 0.0003 -> 0.0090 | Hurt |
Surprising findings
- Polynomial-based spectral GNNs' performance can decrease as polynomial order increases, and the main contributing bases are often limited to the first few terms.
- The original GWNN produced gradient explosion in the authors' reproduction, yielding near-zero accuracy on Actor.
Limitations
- Underperforms on citation networks (Cora, CiteSeer) and on Actor compared with the best baselines.
- Computational complexity from eigendecomposition is a stated concern for future work.
- Only Haar wavelet is explored; other wavelet families are left to future work.
Experimental setup
Datasets: Cora CiteSeer PubMed Computers Photo Chameleon Squirrel Actor 50 synthetic images (100x100 grid graphs) cSBM synthetic toy graph (50 nodes)
Benchmarks: Cora CiteSeer PubMed Computers Photo Chameleon Squirrel Actor
Metrics: accuracy sum of squared error R2 score
Baselines: GCN GAT MLP GPR-GNN BernNet ChebyNetII SplineCNN ACMII-GCN GWNN ChebyNet JacobiConv
Builds on: ChebyNetII BernNet GPR-GNN GWNN
Closest papers by meaning
- A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition (ICML 2025 · similarity 0.93)
- Position: Spectral GNNs Rely Less on Graph Fourier Basis than Conceived (ICML 2025 · similarity 0.91)
- SLOG: An Inductive Spectral Graph Neural Network Beyond Polynomial Filter (ICML 2024 · similarity 0.90)
- ASWT-SGNN: Adaptive Spectral Wavelet Transform-Based Self-Supervised Graph Neural Network (AAAI 2024 · similarity 0.90)
- SEA-GWNN: Simple and Effective Adaptive Graph Wavelet Neural Network (AAAI 2024 · similarity 0.90)
- Unifying Homophily and Heterophily for Spectral Graph Neural Networks via Triple Filter Ensembles (NeurIPS 2024 · similarity 0.89)
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