aiqbench analysis
This research introduces a doubly-spectral stochastic expansion that unifies uncertainty quantification, out-of-distribution detection, and calibration into a single graph neural network representation. By leveraging graph Fourier filters and orthogonal-polynomial chaos coordinates, the method achieves superior Brier scores and AUROC metrics across 14 benchmarks without requiring post-hoc corrections. The work provides a rigorous capacity theorem for Gaussian-latent signals and offers practical deployment strategies for both standalone and hybrid architectures.
A Unified Uncertainty Representation for Graph Neural Networks via Doubly-Spectral Stochastic Expansion
arXiv:2609.35703v1 Announce Type: new 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.
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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2609.35703 [cs.LG]
(or arXiv:2609.35703v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.35703 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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