arXiv:2608.20758cs.LG2026-08

发现图神经网络不确定性由隐层与后验方向对齐决定,非传统后验收缩。

Hidden Axis of Uncertainty: Latent-Posterior Alignment in Graph Neural Networks with Bayesian Output Layers

论文配图:Hidden Axis of Uncertainty: Latent-Posterior Alignment in Graph Neural Networks with Bayesian Output Layers
图 1 · 摘自论文原文
  • 通过隐层向低方差后验方向对齐来降低预测不确定性
  • 即使后验方差未缩小,不确定性仍显著下降
  • 提出对齐引导学习,提升校准性且不损失精度

带有贝叶斯输出层的贝叶斯神经网络为量化预测不确定性提供了合理且可操作的框架,但其不确定性形成机制仍不清晰。在研究的图神经网络中,我们发现预测不确定性随隐表示向低方差后验方向移动而降低,即使后验方差未收缩。我们称此现象为隐层-后验对齐(LPA),并通过干预实验验证其在塑造不确定性中的功能作用。基于此,提出对齐引导学习(AGL),在训练中显式促进该对齐。AGL有效降低预测不确定性,保持精度,并改善结构校准性,使模型置信度真实反映数据密度。该发现为均场贝叶斯输出层的图神经网络不确定性动态提供了新视角,将关注点从后验幅度转向隐层与参数空间间的几何交互。

原文摘要 · Abstract (English)

Bayesian Neural Networks (BNNs) with Bayesian output layers provide a principled and tractable framework for quantifying predictive uncertainty, yet the mechanisms shaping that uncertainty remain unclear. While conventional theory attributes uncertainty reduction to posterior contraction, the corresponding assumptions need not hold for deep models. In the Graph Neural Networks (GNNs) with Bayesian output layers studied here, we observe that predictive uncertainty decreases as latent representations shift toward lower-variance posterior directions, even though the posterior variance does not contract. We term this behavior Latent-Posterior Alignment (LPA) and conduct interventional experiments that support its functional role in shaping predictive uncertainty. Building on this insight, we propose Alignment-Guided Learning (AGL), which explicitly promotes this alignment during training. AGL effectively reduces predictive uncertainty while preserving accuracy and improves structural calibration, ensuring that the model confidence faithfully mirrors underlying data density. These findings provide a new perspective on uncertainty dynamics in GNNs with mean-field Bayesian output layers, shifting the focus from the magnitude of the posterior to the geometric interplay between latent and parameter spaces.

图神经网络不确定性量化贝叶斯学习

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。