# On Sequential Bayesian Inference for Continual Learning

arXiv: https://arxiv.org/abs/2301.01828 · HTML: https://mlsanity.com/paper/2301.01828/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 54 references that are in the map.
- First posted on arXiv 4 Jan 2023.

## Builds on (most cited first, 30 of 35)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [Three scenarios for continual learning](https://mlsanity.com/paper/1904.07734/) (2019)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Re-evaluating Continual Learning Scenarios: A Categorization and Case for Strong Baselines](https://mlsanity.com/paper/1810.12488/) (2018)
- [Task-Free Continual Learning](https://mlsanity.com/paper/1812.03596/) (2018)
- [Online Structured Laplace Approximations For Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1805.07810/) (2018)
- [Uncertainty-based Continual Learning with Adaptive Regularization](https://mlsanity.com/paper/1905.11614/) (2019)
- [Functional Regularisation for Continual Learning with Gaussian Processes](https://mlsanity.com/paper/1901.11356/) (2019)
- [Continual Deep Learning by Functional Regularisation of Memorable Past](https://mlsanity.com/paper/2004.14070/) (2020)
- [Uncertainty-guided Continual Learning with Bayesian Neural Networks](https://mlsanity.com/paper/1906.02425/) (2019)
- [Measuring and regularizing networks in function space](https://mlsanity.com/paper/1805.08289/) (2018)
- [Optimal Continual Learning has Perfect Memory and is NP-hard](https://mlsanity.com/paper/2006.05188/) (2020)
- [Task Agnostic Continual Learning Using Online Variational Bayes](https://mlsanity.com/paper/1803.10123/) (2018)
- [Generalized Variational Continual Learning](https://mlsanity.com/paper/2011.12328/) (2020)
- [Scaling Hamiltonian Monte Carlo Inference for Bayesian Neural Networks with Symmetric Splitting](https://mlsanity.com/paper/2010.06772/) (2020)
- [Continuous Meta-Learning without Tasks](https://mlsanity.com/paper/1912.08866/) (2019)
- [Posterior Meta-Replay for Continual Learning](https://mlsanity.com/paper/2103.01133/) (2021)
- [Class-Incremental Learning with Generative Classifiers](https://mlsanity.com/paper/2104.10093/) (2021)
- [Continual Learning with Adaptive Weights (CLAW)](https://mlsanity.com/paper/1911.09514/) (2019)
- [Radial Bayesian Neural Networks: Beyond Discrete Support In Large-Scale Bayesian Deep Learning](https://mlsanity.com/paper/1907.00865/) (2019)
- [Continual Classification Learning Using Generative Models](https://mlsanity.com/paper/1810.10612/) (2018)

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

- [Continual Learning and Catastrophic Forgetting](https://mlsanity.com/paper/2403.05175/) (2024)
- [IBCL: Zero-shot Model Generation under Stability-Plasticity Trade-offs](https://mlsanity.com/paper/2305.14782/) (2023)
- [Approximate Bayesian Class-Conditional Models under Continuous Representation Shift](https://mlsanity.com/paper/2305.19076/) (2023)
- [Advancing Multiple Instance Learning with Continual Learning for Whole Slide Imaging](https://mlsanity.com/paper/2505.10649/) (2025)
- [The Bayesian Approach to Continual Learning: An Overview](https://mlsanity.com/paper/2507.08922/) (2025)
- [A Neuroscience-Inspired Dual-Process Model of Compositional Generalization](https://mlsanity.com/paper/2507.18868/) (2025)

## Abstract (arXiv)

Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and test whether having access to the true posterior is guaranteed to prevent catastrophic forgetting in Bayesian neural networks. To do this we perform sequential Bayesian inference using Hamiltonian Monte Carlo. We propagate the posterior as a prior for new tasks by fitting a density estimator on Hamiltonian Monte Carlo samples. We find that this approach fails to prevent catastrophic forgetting demonstrating the difficulty in performing sequential Bayesian inference in neural networks. From there we study simple analytical examples of sequential Bayesian inference and CL and highlight the issue of model misspecification which can lead to sub-optimal continual learning performance despite exact inference. Furthermore, we discuss how task data imbalances can cause forgetting. From these limitations, we argue that we need probabilistic models of the continual learning generative process rather than relying on sequential Bayesian inference over Bayesian neural network weights. In this vein, we also propose a simple baseline called Prototypical Bayesian Continual Learning, which is competitive with state-of-the-art Bayesian continual learning methods on class incremental continual learning vision benchmarks.