Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equations
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes Latent Graph Neural SDEs (LGNSDE), a latent SDE framework with a GCN drift, Bayesian prior-posterior for epistemic uncertainty and Brownian noise for aleatoric uncertainty, evaluated on node classification, OOD detection, noise robustness, and active learning.
Problem
Traditional GNNs and GNODEs cannot reliably quantify uncertainty in node representations for graph-structured data.
Approach
Extends graph neural ODEs to graph neural SDEs with an OU prior SDE and a GCN-parameterized posterior SDE trained via variational inference (ELBO), with theoretical claims that output variance is bounded by latent variance and that perturbed solutions stay close in expectation.
Key results
- On standard setting, LGNSDE achieves Cora AUROC 0.9659 and Computers AUROC 0.9691, ranking best or second-best on most datasets.
- In OOD detection (label leave-out), LGNSDE achieves the best AUROC on Cora (0.7614), Photo (0.8707) and PubMed (0.6204) among compared models.
- Under test-time Gaussian feature noise, LGNSDE ranks in the top two on all datasets for AUROC, AURC and accuracy.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LGNSDE instead of GNODE | Graph node classification · Cora, Citeseer, Computers, Photo, Pubmed | AUROC: Cora: 0.9664 ± 0.0051 -> 0.9659 ± 0.0038; Citeseer: 0.9146 ± 0.0063 -> 0.9111 ± 0.0072; Computers: 0.9569 ± 0.0067 -> 0. | Mixed |
| Use maximum-entropy rather than random label acquisition | LGNSDE active learning · Cora | Accuracy: 0.8641 to 0.8889 | Helped |
| Use maximum-entropy rather than random label acquisition | LGNSDE active learning · Pubmed | Accuracy: 0.8097 to 0.8208 | Helped |
| Replace the GCN drift backbone with GAT (ablation) | LGNSDE · Cora OOD detection | AUROC: 0.7614 ± 0.0804 -> 0.8249 ± 0.0321 | Helped |
| Replace the GCN drift backbone with GAT (ablation) | LGNSDE · Citeseer OOD detection | AUROC: 0.8258 ± 0.0418 -> 0.8003 ± 0.0488 | Hurt |
| Vary prior drift from -100.0 to 100.0 (ablation) | LGNSDE · Cora | Accuracy: -100.0: 81.29; -10.0: 82.21; -5.0: 80.52; -1.0: 82.17; -0.5: 83.66; 0.0: 82.74; 0.5: 82.58; 1.0: 82.41; 5.0: 80.48; 10.0 | Mixed |
| Vary prior diffusion from 0.1 to 10.0 (ablation) | LGNSDE · Cora | Accuracy: 0.1: 79.45; 0.2: 80.13; 0.5: 81.32; 0.8: 80.52; 1.0: 80.79; 1.5: 78.93; 2.0: 78.47; 5.0: 76.85; 7.0: 68.78; 10.0: 60.54 | Hurt |
Surprising findings
- Plain GNN and GNODE show similar entropy for correct and incorrect predictions; LGNSDE shows a larger gap, though the gains in many tables are small and within standard deviations.
- In the appendix, the GNSD and GPN baselines outperform LGNSDE on several OOD construction benchmarks (e.g., GNSD AUROC 94.76 vs LGNSDE 93.14 on Cora label leave-out).
Limitations
- Theoretical bounds rely on assumptions (Lipschitz, linear growth) and an output-variance bound that treats the output as Lipschitz in the latent state; the proofs contain inconsistencies such as the Var(H(t)) derivation ignoring the drift and the mixing of Itô terms.
- Gains over baselines are often small relative to reported standard deviations.
- Only the diffusion is left as a fixed hyperparameter; the epistemic and aleatoric decomposition is not formally validated.
Experimental setup
Datasets: Cora CiteSeer PubMed Amazon Computers Amazon Photo
Benchmarks: Cora CiteSeer PubMed Amazon Computers Amazon Photo
Metrics: AUROC AURC accuracy entropy
Baselines: GNN GNODE BGCN GCN ensemble Graph GP
Builds on: Graph Neural ODE Latent SDE GCN Bayesian GCN Graph Gaussian Process
Closest papers by meaning
- Uncertainty Estimation on Graphs with Structure Informed Stochastic Partial Differential Equations (NeurIPS 2025 · similarity 0.93)
- A Unified Uncertainty Representation for Graph Neural Networks via Doubly-Spectral Stochastic Expansion (NeurIPS 2026 · similarity 0.92)
- Graph Neural Stochastic Diffusion for Estimating Uncertainty in Node Classification (ICML 2024 · similarity 0.91)
- Accurate and Scalable Estimation of Epistemic Uncertainty for Graph Neural Networks (ICLR 2024 · similarity 0.91)
- Energy-based Epistemic Uncertainty for Graph Neural Networks (NeurIPS 2024 · similarity 0.89)
- Learning Latent Graph Structures and their Uncertainty (ICML 2025 · similarity 0.88)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.