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Graph Neural Stochastic Diffusion for Estimating Uncertainty in Node Classification
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Proposes GNSD, a GNN parameterization of a graph stochastic diffusion SPDE with a Q-Wiener process that yields aleatoric and epistemic uncertainty estimates for semi-supervised node classification.
Problem
Uncertainty estimation for GNN node predictions is under-explored; existing methods either need intractable Bayesian posteriors or fixed prior specifications, hurting OOD and misclassification detection.
Approach
Model node representations as a stochastic diffusion SPDE driven by a graph-domain Q-Wiener process; a continuous-depth GAT-style drift network gives accurate predictions while a stochastic forcing network (using the self-loop-augmented Laplacian) models epistemic uncertainty propagation among nodes, sampled in a single model.
Key results
- On Amazon-Computers label leave-out OOD detection, GNSD reaches 94.06 AUROC versus 90.50 for the best baseline GNNsafe.
- Averaged over three datasets, GNSD increases misclassification-detection AUROC by 6.5% over GPN.
- Averaged over two OOD scenarios, GNSD raises AUROC by 5.6% and reduces FPR95 by 48.3% relative to prior SOTA baselines.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the dynamic drift-network attention with fixed attention weights (ablation) | GNSD · Amazon-Computers, label leave-out OOD | AUROC: 94.06 -> 92.53 | Hurt |
| Replace the dynamic drift-network attention with fixed attention weights (ablation) | GNSD · Amazon-Computers, feature perturbation OOD | AUROC: 95.95 -> 94.72 | Hurt |
| Use the Stochastic Runge-Kutta SDE solver instead of Euler (ablation) | GNSD · Amazon-Computers, label leave-out OOD | AUROC: 94.06 -> 93.20 | Hurt |
| Use the Stochastic Runge-Kutta SDE solver instead of Euler (ablation) | GNSD · Amazon-Computers, feature perturbation OOD | AUROC: 95.95 -> 94.58 | Hurt |
| Use exact Q-Wiener process discretization sampling instead of the approximation (ablation) | GNSD · Amazon-Computers, label leave-out OOD | AUROC: 94.06 -> 95.11 | Helped |
| Use exact Q-Wiener process discretization sampling instead of the approximation (ablation) | GNSD · Amazon-Computers, feature perturbation OOD | AUROC: 95.95 -> 96.58 | Helped |
| Use exact Q-Wiener process discretization sampling instead of the approximation (ablation) | GNSD · Cora, label leave-out OOD | AUROC: 94.76 -> 94.87 | No clear effect |
| Use exact Q-Wiener process discretization sampling instead of the approximation (ablation) | GNSD · CiteSeer, label leave-out OOD | AUROC: 82.95 -> 83.02 | No clear effect |
| Use exact Q-Wiener process discretization sampling instead of the approximation (ablation) | GNSD · Pubmed, label leave-out OOD | AUROC: 78.81 -> 78.44 | Hurt |
| Use exact Q-Wiener process discretization sampling instead of the approximation (ablation) | GNSD · Cora, feature perturbation OOD | AUROC: 94.41 -> 94.58 | Helped |
| Use exact Q-Wiener process discretization sampling instead of the approximation (ablation) | GNSD · CiteSeer, feature perturbation OOD | AUROC: 86.82 -> 88.06 | Helped |
Surprising findings
- The linear variant GNSD-L performs worse than the nonlinear GNSD, indicating attention-based diffusion helps detection.
- An approximate Q-Wiener sampling (Laplacian with self-loops) performs comparably to exact sampling, avoiding eigendecomposition.
Limitations
- Evaluated only under homophily assumption; authors note need for architectures handling heterophily.
- Scaling to large-scale graphs is left as future work; exact Q-Wiener sampling runs out of memory on OGBN-Arxiv.
- Relies on approximations (first-order Taylor on sqrt of eigenvalues) justified only loosely.
Experimental setup
Datasets: Amazon-Computers Cora CiteSeer Pubmed OGBN-Arxiv
Benchmarks: Amazon-Computers Cora CiteSeer Pubmed OGBN-Arxiv
Metrics: AUROC AUPR FPR95 DET ACC ID ACC
Baselines: GCN GAT GRAND GREAD MSP ODIN Mahalanobis GNNsafe GCN-Ensemble BGCN GKDE GPN
Builds on: GRAND GREAD GPN GNNsafe Neural ODEs
Closest papers by meaning
- Uncertainty Estimation on Graphs with Structure Informed Stochastic Partial Differential Equations (NeurIPS 2025 · similarity 0.93)
- Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equations (ICLR 2025 · similarity 0.91)
- Accurate and Scalable Estimation of Epistemic Uncertainty for Graph Neural Networks (ICLR 2024 · similarity 0.91)
- A Unified Uncertainty Representation for Graph Neural Networks via Doubly-Spectral Stochastic Expansion (NeurIPS 2026 · similarity 0.90)
- Energy-based Epistemic Uncertainty for Graph Neural Networks (NeurIPS 2024 · similarity 0.87)
- Enhancing Trustworthiness of Graph Neural Networks with Rank-Based Conformal Training (AAAI 2025 · similarity 0.87)
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