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Deep Graph Neural Networks via Posteriori-Sampling-based Node-Adaptative Residual Module
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Proposes PSNR, a posterior-sampling node-adaptive residual module that samples per-node, per-layer residual coefficients from a graph-encoder-learned Gaussian, to alleviate over-smoothing in deep GCN/GAT.
Problem
Over-smoothing in deep GNNs: node representations become indistinguishable as depth grows; existing residual methods use fixed, non-node-adaptive coefficients and lose high-order neighborhood information, and deep GNNs are needed for missing-feature settings.
Approach
Treat node-level residual coefficients as hidden variables with a learned Gaussian posterior produced by a graph encoder (with layer positional embedding), sample them via reparameterization (sigmoid-bounded) at both training and test time, yielding node-adaptive multi-order neighborhood aggregation that decays more slowly at depth.
Key results
- PSNR-GCN achieves the best average rank (1.00) across six fully observed datasets, e.g. 71.51% on Chameleon and 54.95% on Squirrel.
- PSNR-GAT reaches 60.85% on Squirrel versus 47.93% for vanilla GAT, a 12.92-point gain.
- In the missing-feature setting on Pubmed, PSNR boosts GCN and GAT accuracy by 40.6% and 38.8%, respectively.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the PSNR node-adaptive residual module to GCN | GCN · Fully observed node classification across Cora, Citeseer, CS, Photo, Chameleon, and Squirrel | accuracy (%): 81.01$\pm$1.63 vs 80.74$\pm$1.80; 68.06$\pm$2.12 vs 67.76$\pm$2.19; 91.23$\pm$1.00 vs 90.98$\pm$2.04; 91.51$\pm$0.69 vs | Helped |
| Add the PSNR node-adaptive residual module to GCN | GCN · Coauthor-Physics, Flickr, and Ogbn-arxiv | accuracy (%): 95.92 $\pm$ 0.17 vs 95.90 $\pm$ 0.14; 52.47 $\pm$ 0.16 vs 52.18 $\pm$ 0.25; 67.81 $\pm$ 0.57 vs 66.32 $\pm$ 0.59 | Helped |
| Use PSNR residual coefficients | GCN and GAT · Missing-feature Cora, Citeseer, and Pubmed | accuracy: 77.3 vs 76.8; 61.1 vs 61.0; 77.0 vs 76.9; 77.9 vs 77.1; 61.9 vs 61.1; 77.3 vs 76.9 | Helped |
| Use PSNR residual coefficients | GCN and GAT · Fully observed node classification across the six summary-table datasets | accuracy (%) | Mixed |
Surprising findings
- Residual methods like GCNII remain stable across depth but lower overall accuracy, showing depth stability does not imply best performance.
- DenseGCN and Dense-GAT underperform the shallow vanilla baseline on several datasets (e.g. Cora 74.94% vs. GCN 78.56%).
Limitations
- Training deeper GNNs remains challenging, as the authors acknowledge.
- Theoretical advantage relies on a proposition whose proof borrows conclusions from GAT joint-spectral-radius analysis rather than a fully self-contained proof.
- Reported gains are mainly on small benchmark graphs with ten random splits; scalability is shown on only three larger datasets.
Experimental setup
Datasets: Cora Citeseer Pubmed Chameleon Squirrel Coauthor-CS Amazon-Photo Flickr Coauthor-Physics Ogbn-arxiv
Benchmarks: Cora Citeseer Pubmed Chameleon Squirrel Coauthor-CS Amazon-Photo Flickr Coauthor-Physics Ogbn-arxiv
Metrics: classification accuracy average rank memory consumption (MB) training time (ms/epoch)
Baselines: GCN GAT ResGCN GCNII JKNet DenseGCN DropMessage DeProp Half-Hop BatchNorm PairNorm DGN
Builds on: ResGCN APPNP GCNII JKNet DenseGCN
Closest papers by meaning
- Measuring and Relieving the Over-Smoothing Problem for Graph Neural Networks from the Topological View (AAAI 2020 · similarity 0.90)
- MultiNet: Adaptive Multi-Viewed Subgraph Convolutional Networks for Graph Classification (NeurIPS 2025 · similarity 0.90)
- Residual Connections and Normalization Can Provably Prevent Oversmoothing in GNNs (ICLR 2025 · similarity 0.89)
- Curriculum-Enhanced Residual Soft An-Isotropic Normalization for Over-Smoothness in Deep GNNs (AAAI 2024 · similarity 0.89)
- A Flexible, Equivariant Framework for Subgraph GNNs via Graph Products and Graph Coarsening (NeurIPS 2024 · similarity 0.87)
- Graph Neural Networks Do Not Always Oversmooth (NeurIPS 2024 · similarity 0.87)
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