发表机构
University of California, Los Angeles; Block, Inc.; Mila, Quebec AI Institute（加州大学洛杉矶分校; Block公司; Mila魁北克人工智能研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出双谱随机展开统一表示图神经网络的不确定性，通过单一模型同时实现校准、OOD检测和分布偏移鲁棒性，并在多个基准上取得最优性能。
AI 中文摘要
图神经网络的可靠部署需要校准、分布外（OOD）检测以及对分布偏移的鲁棒性，然而现有方法通过分离的模型和目标来满足这些需求。我们将不确定的节点嵌入建模为随机图信号：图傅里叶滤波器捕获结构变化，而标量正交多项式混沌坐标捕获潜在的随机变化。由此产生的双谱随机（DSS）展开从单一表示提供任务匹配的读出：均值系数编码能量基OOD评分的类别证据，高阶系数编码结构化logit变化，混沌坐标上的求积平均定义了用于预测和校准的单一预测分布。一个容量定理表明，在满秩特征假设下，受限子族匹配任何高斯潜在随机图信号的混沌系数，在增长条件下具有指数衰减的截断误差；任务级声明通过实验确立。DSS-GNN有两种部署模式：独立模式，或作为确定性编码器旁边的残差分支（DSS-Hybrid）。独立DSS-GNN在所有14个节点分类基准上无需事后校正即可实现所比较的不确定性感知基线中最低的Brier分数；DSS-Hybrid在大多数节点OOD设置中实现最佳AUROC，具有竞争力的跨图OOD检测，并在标准经验风险最小化（ERM）下在所有7个GOOD概念偏移基准上实现最强的偏移精度。在三个任务上交叉评估两种模式表明，每种模式在对方的任务上仍然有效，并记录了例外情况，同时提供了明确的部署指导。
英文摘要
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.
Commentspaper already accepted at Neurips 2026
