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A Unified Uncertainty Representation for Graph Neural Networks via Doubly-Spectral Stochastic Expansion

NeurIPS 2026 · Graph learning › Graph self-supervised learning · approach: Graph out-of-distribution generalization · 0 citations (OpenAlex)

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Proposes DSS-GNN, a GNN that represents node embeddings as polynomial chaos expansions over a scalar Gaussian latent combined with graph-Fourier filtering, yielding one uncertainty representation with standalone and hybrid deployment modes for calibration, OOD detection, and shift robustness.

Problem

Reliable GNN deployment needs calibration, OOD detection, and robustness to distribution shift, but existing methods handle these separately with different models and objectives.

Approach

Model node embeddings as random graph signals expanded jointly over Laplacian eigenmodes (dual low/high-pass Chebyshev filters) and Hermite chaos orders (per-order gates), with deterministic Gauss-Hermite quadrature giving a single predictive distribution for prediction/calibration and mean-logit energy for OOD; a hybrid mode adds it as a residual branch to a GCN.

Key results

• Standalone DSS-GNN achieves the lowest Brier score among compared uncertainty-aware baselines on all 14 node classification datasets without post-hoc calibration (e.g., Cora Brier 0.207 vs 0.226 for G-ΔUQ).
• DSS-Hybrid has the best AUROC on 6 of 9 node-OOD cells (e.g., Cora structure 94.32 vs 90.62 for GNNSafe++) and on Twitch (95.75 vs 95.36).
• DSS-Hybrid attains the best mean shifted accuracy on all 7 GOOD concept-shift settings under ERM (e.g., GOOD-WebKB/university 40.77 vs 30.83 for TAR).

Surprising findings

• The scalar-latent chaos energy has little effect on energy-based OOD AUROC; varying chaos order P in 0-3 leaves AUROC flat, as predicted since the energy score reads only the mean logit.
• Standalone DSS-GNN fails to separate cross-graph OOD inputs on Twitch, where the hybrid is needed.

Limitations

• Scalar Gaussian latent makes all stochasticity perfectly correlated across nodes, so independent per-node noise and joint cross-node uncertainty are not modeled.
• Standalone model requires BatchNorm stabilization in sparse-label regimes; hybrid inherits its GCN encoder's failures.
• Chaos expansion adds compute overhead (2.9x per epoch on Cora at P=2).

Experimental setup

Datasets: Cora Citeseer PubMed Texas Cornell Wisconsin Chameleon Squirrel CS Roman-Empire Amazon-Ratings Minesweeper

Benchmarks: 14 node classification benchmarks GNNSafe OOD benchmark (9 node-OOD settings, Twitch, Arxiv) GOOD concept-shift benchmark (7 settings)

Metrics: accuracy Brier score AUROC AUPR FPR95

Baselines: TFE-GNN G-ΔUQ GNNSafe GNNSafe++ GPN Graph-EBM MC-dropout Deep Ensembles TAR GOOD baselines (ERM, IRM, VREx, Coral, DANN, SRGNN, EERM, FLOOD, CIT, KL-DRO, Gr

Builds on: ChebNet GCN GNNSafe polynomial chaos expansion energy-based OOD detection

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