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Joint Graph Rewiring and Feature Denoising via Spectral Resonance
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Proposes JDR, an alternating spectral-interpolation algorithm that jointly denoises node features and rewires the graph by maximizing alignment between graph and feature leading eigenspaces, improving GCN and GPRGNN node classification.
Problem
Node classification with GNNs is hurt by noisy graph structure (spurious and missing edges) and noisy node features; existing rewiring methods use only the graph and do not exploit features to denoise.
Approach
Define graph-feature alignment as the spectral norm of the cosine between leading eigenspaces of the adjacency and feature SVD, and alternately interpolate leading eigenvectors between graph and features and resynthesize graph and features, motivated by the contextual SBM and a proof under a spiked GOE model that interpolation improves alignment with labels.
Key results
- GCN+JDR reaches 79.96% on Cora (sparse split) vs 77.26% for GCN and best on four of five homophilic datasets.
- GPRGNN+JDR reaches 71.00% on Chameleon and 93.85% on Texas in the dense split, outperforming DIGL, FoSR and BORF.
- On Penn94, GCN+JDR improves accuracy from 80.40% to 82.30%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply JDR rewiring and denoising to GCN | GCN · Homophilic datasets, sparse split | accuracy: Cora: 77.26 -> 79.96; CiteSeer: 67.16 -> 69.35; PubMed: 84.22 -> 84.79; Computers: 84.42 -> 85.66; Photo: 91.33 -> 92.52 | Mixed |
| Apply JDR rewiring and denoising to GPRGNN | GPRGNN · Homophilic datasets, sparse split | accuracy: Cora: 79.65 -> 80.77; CiteSeer: 67.50 -> 69.17; PubMed: 84.33 -> 85.05; Computers: 84.06 -> 84.77; Photo: 92.01 -> 92.68 | Mixed |
| Apply JDR rewiring and denoising to GCN | GCN · Heterophilic datasets, dense split | accuracy: Chameleon: 67.65 -> 69.76; Squirrel: 57.94 -> 61.76; Actor: 34.00 -> 40.47; Texas: 75.62 -> 85.12; Cornell: 64.68 -> 84. | Mixed |
| Apply JDR rewiring and denoising to GPRGNN | GPRGNN · Heterophilic datasets, dense split | accuracy: Chameleon: 69.15 -> 71.00; Squirrel: 53.44 -> 60.62; Actor: 39.52 -> 41.89; Texas: 92.82 -> 93.85; Cornell: 87.79 -> 89. | Helped |
| Apply JDR rewiring and denoising to GCN | GCN · Questions, Penn94, Twitch-gamers | accuracy or ROC AUC: Questions: 75.31 -> 77.52; Penn94: 80.40 -> 82.30; Twitch-gamers: 64.56 -> 65.14 | Helped |
| Apply JDR rewiring and denoising to GCN | GCN · Minesweeper | accuracy: 90.08 -> 90.01 | Hurt |
| Use JDR with GCN rather than the strongest baseline rewiring | GCN · Texas, Cornell, sparse homophilic Computers | accuracy: Texas: GCN+DIGL 91.05, GCN+JDR 85.12; Cornell: GCN+DIGL 88.49, GCN+JDR 84.51; Computers: GCN+DIGL 86.00, GCN+JDR 85.66 | Mixed |
| Use JDR with GPRGNN rather than the strongest baseline rewiring | GPRGNN · Computers, sparse split | accuracy: GPRGNN+DIGL 86.25; GPRGNN+JDR 84.77 | Hurt |
| Jointly denoise graph and features with JDR | GCN and GPRGNN · CSBM across different φ | accuracy | Helped |
| Interpolate leading graph and feature spectral vectors toward each other | JDR on the stylized GOE model · Stylized model, large-graph limit | alignment with labels | Helped |
Surprising findings
- DIGL degrades performance on several heterophilic datasets such as Chameleon and Squirrel despite strong results on Actor, Texas and Cornell.
- On Minesweeper none of the rewiring methods improve performance, since the graph carries little label information.
Limitations
- Requires node features; cannot be applied to graphs without features.
- Theoretical proof covers a stylized spiked GOE model with L=1, not the binary cSBM directly.
- Not designed for strong adversarial perturbations and does not compete with graph structure learning methods; does not scale yet to millions of nodes.
Experimental setup
Datasets: Cora CiteSeer PubMed Computers Photo Chameleon Squirrel Actor Texas Cornell Questions Penn94
Benchmarks: Cora CiteSeer PubMed Computers Photo Chameleon Squirrel Actor Texas Cornell Questions Penn94
Metrics: accuracy ROC AUC alignment 95% confidence interval
Baselines: GCN GPRGNN DIGL FoSR BORF AMP-BP MLP
Builds on: contextual stochastic block model FoSR BORF DIGL
Closest papers by meaning
- Mitigating Over-Squashing in Graph Neural Networks by Spectrum-Preserving Sparsification (ICML 2025 · similarity 0.90)
- Locality-Aware Graph Rewiring in GNNs (ICLR 2024 · similarity 0.89)
- SLOG: An Inductive Spectral Graph Neural Network Beyond Polynomial Filter (ICML 2024 · similarity 0.88)
- Improving Expressive Power of Spectral Graph Neural Networks with Eigenvalue Correction (AAAI 2024 · similarity 0.88)
- WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets (AAAI 2024 · similarity 0.88)
- Enhancing Spectral GNNs: From Topology and Perturbation Perspectives (ICML 2025 · similarity 0.88)
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