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Learn Beneficial Noise as Graph Augmentation
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Proposes PiNGDA, which learns positive-incentive (beneficial) noise via trainable topology and attribute noise generators as graph augmentations for graph contrastive learning, and shows predefined augmentations are point estimates of this noise.
Problem
Heuristic graph augmentations (random edge/node dropping) in graph contrastive learning can disrupt important structure and cause unstable GCL performance; the paper seeks learnable, theoretically grounded augmentations.
Approach
Frames GCL loss as task entropy via a Gaussian auxiliary variable, showing standard predefined augmentation corresponds to a point estimate of positive-incentive noise; then learns the noise distribution with a trainable generator over edges (Gumbel-Softmax Bernoulli) and node attributes (Gaussian reparameterization) jointly with the encoder.
Key results
- On node classification over seven datasets, PiNGDA achieves the best average rank (1.4), e.g., 86.25% on Cora and 87.34% on PubMed, outperforming AD-GCL.
- On graph classification, PiNGDA reaches 89.71% on MUTAG and 83.99% on RDT-B, best or near-best among compared methods.
- Adding PiNGDA to GRACE improves Cora accuracy from 83.43% to 84.28% and PubMed from 85.90% to 86.79%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add PiNGDA augmentation to GRACE (ablation) | GRACE · Cora, CiteSeer, PubMed, Amazon-Photo, Coauthor-Phy | accuracy: 83.43 $\pm$ 0.32 -> 84.28 $\pm$ 0.24; 70.93 $\pm$ 0.21 -> 71.47 $\pm$ 0.20; 85.90 $\pm$ 0.24 -> 86.79 $\pm$ 0.27; 93.13 | Helped |
| Add PiNGDA augmentation to Sp$^2$GCL (ablation) | Sp$^2$GCL · Cora, CiteSeer, PubMed, Amazon-Photo, Coauthor-Phy | accuracy: 82.45 $\pm$ 0.35 -> 83.89 $\pm$ 0.48; 65.54 $\pm$ 0.51 -> 67.21 $\pm$ 0.63; 84.26 $\pm$ 0.29 -> 84.73 $\pm$ 0.23; 93.05 | Helped |
| Use learnable feature and edge augmentation instead of no augmentation (ablation) | PiNGDA · Cora, PubMed, Wiki-CS | accuracy: 82.59 $\pm$ 0.66 -> 86.25 $\pm$ 0.25; 85.11 $\pm$ 0.19 -> 87.34 $\pm$ 0.08; 80.34 $\pm$ 0.25 -> 82.17 $\pm$ 0.15 | Helped |
| Use learnable feature and edge augmentation instead of random augmentation (ablation) | PiNGDA · Cora, PubMed, Wiki-CS | accuracy: 85.84 $\pm$ 0.44 -> 86.25 $\pm$ 0.25; 86.89 $\pm$ 0.13 -> 87.34 $\pm$ 0.08; 81.61 $\pm$ 0.19 -> 82.17 $\pm$ 0.15 | Helped |
| Add learnable edge augmentation while using no feature augmentation (ablation) | PiNGDA · PubMed | accuracy: 85.11 $\pm$ 0.19 -> 86.81 $\pm$ 0.23 | Helped |
| Add learnable feature augmentation while using no edge augmentation (ablation) | PiNGDA · Cora, PubMed | accuracy: 82.59 $\pm$ 0.66 -> 83.36 $\pm$ 0.54; 85.11 $\pm$ 0.19 -> 85.37 $\pm$ 0.07 | Mixed |
| Use learnable feature and edge augmentation instead of no augmentation (ablation) | PiNGDA · PROTEINS, DD, NCI1 | accuracy: 72.49 $\pm$ 0.90 -> 73.21 $\pm$ 0.40; 75.24 $\pm$ 0.21 -> 75.70 $\pm$ 0.42; 68.59 $\pm$ 0.75 -> 69.35 $\pm$ 0.63 | Mixed |
| Use learnable feature and edge augmentation instead of random augmentation (ablation) | PiNGDA · PROTEINS, DD, NCI1 | accuracy: 72.38 $\pm$ 0.79 -> 73.21 $\pm$ 0.40; 74.23 $\pm$ 0.82 -> 75.70 $\pm$ 0.42; 68.54 $\pm$ 1.02 -> 69.35 $\pm$ 0.63 | Mixed |
Surprising findings
- Predefined augmentations in standard GCL are shown to be point estimates of pi-noise that may fail to reduce task entropy, suggesting heuristic augmentations are unreliable.
Limitations
- Theory restricted to node-level GCL with a single augmentation and Dirac-delta (point-estimate) assumptions; extension to graph-level left implicit.
- Gaussian attribute noise assumed uncorrelated (diagonal covariance) and Bernoulli edge noise is a simplification.
- Some results are within standard deviation of baselines (e.g., ogbn-arxiv below GCN), and graph classification gains are small.
Experimental setup
Datasets: Cora CiteSeer PubMed Wiki-CS Amazon-Photo Coauthor-Phy ogbn-arxiv NCI1 MUTAG PROTEINS DD RDT-B
Benchmarks: Cora CiteSeer PubMed Wiki-CS Amazon-Photo Coauthor-Phy ogbn-arxiv NCI1 MUTAG PROTEINS DD RDT-B
Metrics: accuracy standard deviation
Baselines: GCN GAT DGI GMI GCA BGRL GREET SGRL GRACEIS GOUDA GASSL AD-GCL
Builds on: GRACE AD-GCL JOAO GCA pi-noise framework
Closest papers by meaning
- Is Noise Conditioning Necessary? A Unified Theory of Unconditional Graph Diffusion Models (NeurIPS 2025 · similarity 0.89)
- Training Robust Graph Neural Networks by Modeling Noise Dependencies (NeurIPS 2025 · similarity 0.88)
- Graph Contrastive Learning with Joint Spectral Augmentation of Attribute and Topology (AAAI 2025 · similarity 0.87)
- Community-Invariant Graph Contrastive Learning (ICML 2024 · similarity 0.87)
- Perfect Alignment May be Poisonous to Graph Contrastive Learning (ICML 2024 · similarity 0.86)
- Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classifications (AAAI 2025 · similarity 0.86)
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