# Sequential Function-Space Variational Inference via Gaussian Mixture Approximation

arXiv: https://arxiv.org/abs/2503.07114 · HTML: https://mlsanity.com/paper/2503.07114/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [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)
- [On Tiny Episodic Memories in Continual Learning](https://mlsanity.com/paper/1902.10486/) (2019)
- [Online Continual Learning in Image Classification: An Empirical Survey](https://mlsanity.com/paper/2101.10423/) (2021)
- [Online Structured Laplace Approximations For Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1805.07810/) (2018)
- [Towards Robust Evaluations of Continual Learning](https://mlsanity.com/paper/1805.09733/) (2018)
- [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)
- [On Quadratic Penalties in Elastic Weight Consolidation](https://mlsanity.com/paper/1712.03847/) (2017)
- [A Unifying Bayesian View of Continual Learning](https://mlsanity.com/paper/1902.06494/) (2019)
- [Continual Learning via Sequential Function-Space Variational Inference](https://mlsanity.com/paper/2312.17210/) (2023)

## Abstract (arXiv)

Continual learning in neural networks aims to learn new tasks without forgetting old tasks. Sequential function-space variational inference (SFSVI) uses a Gaussian variational distribution to approximate the distribution of the outputs of the neural network corresponding to a finite number of selected inducing points. Since the posterior distribution of a neural network is multi-modal, a Gaussian distribution could only match one mode of the posterior distribution, and a Gaussian mixture distribution could be used to better approximate the posterior distribution. We propose an SFSVI method based on a Gaussian mixture variational distribution. We also compare different types of variational inference methods with a fixed pre-trained feature extractor (where continual learning is performed on the final layer) and without a fixed pre-trained feature extractor (where continual learning is performed on all layers). We find that in terms of final average accuracy, likelihood-focused Gaussian mixture SFSVI outperforms other sequential variational inference methods, especially in the latter case.