DSS-GNN：用双谱随机展开统一图神经网络的不确定性表示
A Unified Uncertainty Representation for Graph Neural Networks via Doubly-Spectral Stochastic Expansion
做图神经网络的可以看看：一个表示同时搞定校准、OOD 检测和分布偏移，14 个基准 Brier score 最低，不用再各训练一个模型。
论文提出把不确定的节点嵌入建模为随机图信号：graph Fourier 滤波器捕捉结构变化，正交多项式混沌坐标捕捉潜在随机变化，构成双谱随机（DSS）展开。单一表示同时支持三类任务：均值系数用于 energy-based OOD 打分，高阶系数编码 logit 变化，求积平均得到用于预测和校准的预测分布。Standalone DSS-GNN 在全部 14 个节点分类基准上取得对比方法中最低 Brier score，无需事后校正；DSS-Hybrid 在多数 node-OOD 设置上取得最高 AUROC，并在全部 7 个 GOOD concept-shift 基准上取得最强偏移精度。论文还给出容量定理，证明在满秩特征假设下其受限子族可匹配任意高斯潜在随机图信号的混沌系数。
A Unified Uncertainty Representation for Graph Neural Networks via Doubly-Spectral Stochastic Expansion
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.