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

2026-09-28

AI Summary

This study addresses the limitation of existing graph neural networks (GNNs) that require separate models for calibration, out-of-distribution (OOD) detection, and robustness tasks. To this end, we propose DSS-GNN, a unified framework that leverages dual spectral stochastic expansion—integrating graph Fourier filtering with orthogonal polynomial chaos expansion—to characterize uncertainty comprehensively. Coupled with energy-based scoring, this approach enables a single model to jointly perform prediction, calibration, and OOD detection within a hybrid deployment setting. Extensive experiments demonstrate that DSS-GNN achieves the lowest Brier scores across 14 benchmarks and attains state-of-the-art shifted accuracy on 7 GOOD benchmarks. These results confirm that the proposed framework effectively resolves the multi-model fragmentation problem in GNN uncertainty quantification, offering a cohesive and highly performant solution for reliable graph representation learning.

Abstract

Reliable deployment of graph neural networks requires calibration, out-of-distribution (OOD) detection, and robustness to distribution shift, yet existing methods address these needs with separate models and objectives. We model uncertain node embeddings as random graph signals: graph Fourier filters capture structural variation, and a scalar orthogonal-polynomial chaos coordinate captures latent stochastic variation. The resulting doubly-spectral stochastic (DSS) expansion supplies task-matched readouts from one representation: the mean coefficient encodes class evidence for the energy-based OOD score, the higher-order coefficients encode structured logit variation, and quadrature averaging over the chaos coordinate defines the single predictive distribution used for prediction and calibration. A capacity theorem shows that, under a full-rank feature assumption, a restricted subfamily matches the chaos coefficients of any Gaussian-latent random graph signal, with exponentially decaying truncation error under a growth condition; the task-level claims are established empirically. DSS-GNN has two deployment modes: standalone, or as a residual branch beside a deterministic encoder (DSS-Hybrid). Standalone DSS-GNN achieves the lowest Brier score among the compared uncertainty-aware baselines on all 14 node classification benchmarks without post-hoc correction; DSS-Hybrid achieves the best AUROC on most node-OOD settings, competitive cross-graph OOD detection, and the strongest shifted accuracy on all 7 GOOD concept-shift benchmarks under standard empirical risk minimization (ERM). Cross-evaluating both modes on all three tasks shows that each remains effective on the other's tasks, with documented exceptions, and yields explicit deployment guidance.

Problem

• Graph Neural Networks
• Uncertainty Representation
• Out-of-Distribution Detection
• Calibration
• Distribution Shift

Innovation

• Graph Neural Networks
• Uncertainty Representation
• Doubly-Spectral Stochastic Expansion
• Polynomial Chaos
• Out-of-Distribution Detection