发表机构
Korea Institute of Science and Technology; Clean Energy Research Center（韩国科学技术研究院; 清洁能源研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对带贝叶斯输出层的图神经网络，发现潜在-后验对齐现象，提出对齐引导学习方法，可降低预测不确定性并改善结构校准，为不确定性动力学提供新视角。
AI 中文摘要
带贝叶斯输出层的贝叶斯神经网络（BNNs）提供了一种原则性且易处理的框架，用于量化预测不确定性，但塑造该不确定性的机制仍不清楚。传统理论将不确定性减少归因于后验收缩，但相应假设不一定适用于深度模型。在本文研究的带贝叶斯输出层的图神经网络（GNNs）中，我们观察到，即使后验方差没有收缩，预测不确定性也会随着潜在表示向低方差后验方向移动而降低。我们将这种行为称为潜在-后验对齐（LPA），并进行了干预实验，这些实验支持其在塑造预测不确定性中的功能作用。基于这一见解，我们提出了对齐引导学习（AGL），它在训练过程中明确促进这种对齐。AGL有效降低了预测不确定性，同时保持了准确率并改善了结构校准，确保模型置信度忠实地反映潜在数据密度。这些发现为带平均场贝叶斯输出层的GNNs中的不确定性动力学提供了新视角，将重点从后验的大小转移到潜在空间与参数空间之间的几何相互作用上。
英文摘要
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.
Comments56 pages, 14 figures. Includes Supplementary Information
