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

arXiv: https://arxiv.org/abs/2608.20758 · HTML: https://mlsanity.com/paper/2608.20758/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 78 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 12 of 12)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- ['In-Between' Uncertainty in Bayesian Neural Networks](https://mlsanity.com/paper/1906.11537/) (2019)
- [Variational Bayesian Last Layers](https://mlsanity.com/paper/2404.11599/) (2024)
- [Quality of Uncertainty Quantification for Bayesian Neural Network Inference](https://mlsanity.com/paper/1906.09686/) (2019)
- [A Farewell to the Bias-Variance Tradeoff? An Overview of the Theory of Overparameterized Machine Learning](https://mlsanity.com/paper/2109.02355/) (2021)
- [A statistical theory of cold posteriors in deep neural networks](https://mlsanity.com/paper/2008.05912/) (2020)
- [The Relevance of Bayesian Layer Positioning to Model Uncertainty in Deep Bayesian Active Learning](https://mlsanity.com/paper/1811.12535/) (2018)
- [Evaluating the Robustness of Bayesian Neural Networks Against Different Types of Attacks](https://mlsanity.com/paper/2106.09223/) (2021)
- [How Good is the Bayes Posterior in Deep Neural Networks Really?](https://mlsanity.com/paper/2002.02405/) (2020)

## Abstract (arXiv)

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.