# Kalman Bayesian Transformer

arXiv: https://arxiv.org/abs/2509.10695 · HTML: https://mlsanity.com/paper/2509.10695/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 33 references that are in the map.
- First posted on arXiv 12 Sep 2025.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Bayesian Low-rank Adaptation for Large Language Models](https://mlsanity.com/paper/2308.13111/) (2023)
- [Lightweight Probabilistic Deep Networks](https://mlsanity.com/paper/1805.11327/) (2018)
- [Stochastic gradient Markov chain Monte Carlo](https://mlsanity.com/paper/1907.06986/) (2019)
- [BLoB: Bayesian Low-Rank Adaptation by Backpropagation for Large Language Models](https://mlsanity.com/paper/2406.11675/) (2024)
- [Learnable Uncertainty under Laplace Approximations](https://mlsanity.com/paper/2010.02720/) (2020)
- [Bayesian Transformer Language Models for Speech Recognition](https://mlsanity.com/paper/2102.04754/) (2021)
- [Tractable Inference for Complex Stochastic Processes](https://mlsanity.com/paper/1301.7362/) (2013)
- [BayesFormer: Transformer with Uncertainty Estimation](https://mlsanity.com/paper/2206.00826/) (2022)
- [An Analytic Solution to Covariance Propagation in Neural Networks](https://mlsanity.com/paper/2403.16163/) (2024)
- [Kalman Bayesian Neural Networks for Closed-form Online Learning](https://mlsanity.com/paper/2110.00944/) (2021)

## Abstract (arXiv)

Sequential fine-tuning of transformers is useful when new data arrive sequentially, especially with shifting distributions. Unlike batch learning, sequential learning demands that training be stabilized despite a small amount of data by balancing new information and previously learned knowledge in the pre-trained models. This challenge is further complicated when training is to be completed in latency-critical environments and learning must additionally quantify and be mediated by uncertainty. Motivated by these challenges, we propose a novel method that frames sequential fine-tuning as a posterior inference problem within a Bayesian framework. Our approach integrates closed-form moment propagation of random variables, Kalman Bayesian Neural Networks, and Taylor approximations of the moments of softmax functions. By explicitly accounting for pre-trained models as priors and adaptively balancing them against new information based on quantified uncertainty, our method achieves robust and data-efficient sequential learning. The effectiveness of our method is demonstrated through numerical simulations involving sequential adaptation of a decision transformer to tasks characterized by distribution shifts and limited memory resources.