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ASWT-SGNN: Adaptive Spectral Wavelet Transform-Based Self-Supervised Graph Neural Network
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Proposes ASWT-SGNN, a self-supervised graph wavelet GNN that approximates learnable multi-scale wavelet filters via weighted least-squares Chebyshev-style polynomials with KPM spectral density estimation, trained with a contrastive loss, avoiding eigen-decomposition.
Problem
Graph contrastive learning encoders built on GCNs rely on Fourier bases, which are spatially non-localized, need costly eigen-decomposition, and offer inflexible neighborhood control and over-smoothing in deep layers.
Approach
Use an adaptive spectral wavelet (low-pass heat kernel plus band-pass Mexican-hat terms) whose polynomial coefficients are computed by weighted least squares with spectral density estimated via stochastic trace estimation (Hutchinson with Jackson-Chebyshev projectors), and optimize wavelet scales end-to-end with a contrastive objective, combined with residual links to mitigate over-smoothing.
Key results
- ASWT-SGNN(CL) averages 87.0% node classification accuracy across eight datasets, versus 86.2% for the best self-supervised baseline MaskGAE per the paper's reported table (average 86.2).
- ASWT-SGNN(Semi) reaches 88.2% average accuracy, with 88.1% on Cora and 81.5% on CiteSeer.
- The paper reports that the wavelet representation is roughly two orders of magnitude sparser than the Fourier eigenvector matrix (e.g., Cora wavelet density 0.18% vs. eigenvector density 99.15%).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ASWT-SGNN instead of the strongest listed baseline | Node classification · Cora | accuracy: 84.3{$\pm$0.4} -> 86.2{$\pm$0.6} | Helped |
| Use ASWT-SGNN instead of the strongest listed baseline | Node classification · CiteSeer | accuracy: 73.8{$\pm$0.8} -> 73.9{$\pm$0.1} | Helped |
| Use ASWT-SGNN instead of the strongest listed baseline | Node classification · PubMed | accuracy: 83.6{$\pm$0.5} -> 84.9{$\pm$0.3} | Helped |
| Use ASWT-SGNN instead of the strongest listed baseline | Node classification · Computers | accuracy: 89.6{$\pm$0.2} -> 89.2{$\pm$0.3} | Hurt |
| Use ASWT-SGNN instead of the strongest listed baseline | Node classification · Photo | accuracy: 93.8{$\pm$0.3} -> 93.5{$\pm$0.2} | Hurt |
| Use ASWT-SGNN instead of the strongest listed baseline | Node classification · CS | accuracy: 93.1 -> 93.5{$\pm$0.3} | Helped |
| Use ASWT-SGNN instead of the strongest listed baseline | Node classification · Physics | accuracy: 95.2{$\pm$0.2} -> 95.4{$\pm$0.3} | Helped |
| Use ASWT-SGNN instead of the strongest listed baseline | Node classification · WikiCS | accuracy: 79.0{$\pm$0.5} -> 79.5{$\pm$0.3} | Helped |
| Remove residual connections by setting α to 0 (ablation) | ASWT-SGNN · Node classification | accuracy | Hurt |
| Increase α to larger values (ablation) | ASWT-SGNN · Node classification | accuracy | Hurt |
| Set β too low, reducing the graph-wavelet contribution (ablation) | ASWT-SGNN · Node classification | accuracy | Hurt |
| Set β excessively high, reducing global-information contribution (ablation) | ASWT-SGNN · Node classification | accuracy | Hurt |
Limitations
- Experiments limited to eight benchmark datasets and node classification; authors note larger datasets are left for future work
- Theoretical guarantees rely on a Gaussian mixture feature assumption and simplified model without residual connection
- Several hyperparameters (K, alpha, beta, scale intervals) are hand-set and their sensitivity is only partly explored
Experimental setup
Datasets: Cora CiteSeer PubMed Amazon-Computers Amazon-Photo Coauthor-CS Coauthor-Physics WikiCS
Benchmarks: Cora CiteSeer PubMed Computers Photo CS Physics WikiCS
Metrics: accuracy mean absolute error of wavelet operator approximation sparsity
Baselines: GCN GAT GWNN GCNII GMI MVGRL GCA-SSG GRADE AF-GCL MA-GCL GraphMAE MaskGAE
Builds on: GCN ChebyNet GWNN GCNII Hammond et al. wavelet approximation
Closest papers by meaning
- WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets (AAAI 2024 · similarity 0.90)
- SEA-GWNN: Simple and Effective Adaptive Graph Wavelet Neural Network (AAAI 2024 · similarity 0.90)
- A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition (ICML 2025 · similarity 0.90)
- Asymmetric Learning for Spectral Graph Neural Networks (AAAI 2025 · similarity 0.89)
- SLOG: An Inductive Spectral Graph Neural Network Beyond Polynomial Filter (ICML 2024 · similarity 0.89)
- Spectral Graph Neural Networks are Incomplete on Graphs with a Simple Spectrum (NeurIPS 2025 · similarity 0.88)
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