# Uncertainty Decomposition for Bayes-Filtered Transformers via Bayesian Predictive Inference

arXiv: https://arxiv.org/abs/2602.04596 · HTML: https://mlsanity.com/paper/2602.04596/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2026.

## Built on by (most cited first, 6 of 6)

- [PFN-TS: Thompson Sampling for Contextual Bandits via Prior-Data Fitted Networks](https://mlsanity.com/paper/2605.10137/) (2026)
- [What does a Bayes-filtered transformer believe? A predictive Monte Carlo approach](https://mlsanity.com/paper/2607.17060/) (2026)
- [Concentration and Calibration in Predictive Bayesian Inference](https://mlsanity.com/paper/2605.00455/) (2026)
- [Elicitation without Backpropagation: Steering Model Behavior by Optimizing the Latent Posterior](https://mlsanity.com/paper/2607.18804/) (2026)
- [Can Tabular Foundation Models Amortize Statistical Inference?](https://mlsanity.com/paper/2609.33114/) (2026)
- [How Well Do Prior-Data Fitted Networks Amortize Bayesian Inference?](https://mlsanity.com/paper/2610.13764/) (2026)

## Abstract (arXiv)

Bayes-filtered transformers are transformers meta-learned on sequences from a prior predictive distribution to approximate the corresponding posterior predictive distribution. They output total predictive uncertainty in a single forward pass but never explicitly represent a posterior distribution, making the standard route to separating aleatoric from epistemic uncertainty unavailable. We address this challenge through the lens of Bayesian predictive inference (BPI). Our main result is a predictive Central Limit Theorem (CLT) for supervised settings under conditions that are among the weakest known in the BPI literature. The CLT characterises the posterior of the limiting predictive distribution given an observed context as asymptotically Gaussian; the variance of this Gaussian quantifies epistemic uncertainty. We apply the framework to TabPFN, a Bayes-filtered transformer that is a state-of-the-art foundation model for tabular prediction. The resulting credible bands achieve near-nominal frequentist coverage as context length grows, and the decomposition largely matches standard desiderata: epistemic uncertainty shrinks with context length and is highest in sparsely observed regions within the span of the context data, while aleatoric uncertainty dominates near decision boundaries where classes overlap.