# Continual Learning with Fully Probabilistic Models

arXiv: https://arxiv.org/abs/2104.09240 · HTML: https://mlsanity.com/paper/2104.09240/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 19 Apr 2021.

## Builds on (most cited first, 27 of 27)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [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)
- [Expert Gate: Lifelong Learning with a Network of Experts](https://mlsanity.com/paper/1611.06194/) (2016)
- [PathNet: Evolution Channels Gradient Descent in Super Neural Networks](https://mlsanity.com/paper/1701.08734/) (2017)
- [Measuring Catastrophic Forgetting in Neural Networks](https://mlsanity.com/paper/1708.02072/) (2017)
- [Overcoming Catastrophic Forgetting by Incremental Moment Matching](https://mlsanity.com/paper/1703.08475/) (2017)
- [Towards Robust Evaluations of Continual Learning](https://mlsanity.com/paper/1805.09733/) (2018)
- [A Wholistic View of Continual Learning with Deep Neural Networks: Forgotten Lessons and the Bridge to Active and Open World Learning](https://mlsanity.com/paper/2009.01797/) (2020)
- [On GANs and GMMs](https://mlsanity.com/paper/1805.12462/) (2018)
- [Deep Generative Dual Memory Network for Continual Learning](https://mlsanity.com/paper/1710.10368/) (2017)
- [Selfless Sequential Learning](https://mlsanity.com/paper/1806.05421/) (2018)
- [Meta-Consolidation for Continual Learning](https://mlsanity.com/paper/2010.00352/) (2020)
- [A comprehensive, application-oriented study of catastrophic forgetting in DNNs](https://mlsanity.com/paper/1905.08101/) (2019)
- [Born to Learn: the Inspiration, Progress, and Future of Evolved Plastic Artificial Neural Networks](https://mlsanity.com/paper/1703.10371/) (2017)
- [Training Discriminative Models to Evaluate Generative Ones](https://mlsanity.com/paper/1806.10840/) (2018)

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

- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Beyond Supervised Continual Learning: a Review](https://mlsanity.com/paper/2208.14307/) (2022)
- [ProtoDepth: Unsupervised Continual Depth Completion with Prototypes](https://mlsanity.com/paper/2503.12745/) (2025)
- [UnCLe: Benchmarking Unsupervised Continual Learning for Depth Completion](https://mlsanity.com/paper/2410.18074/) (2024)
- [CCD: Continual Consistency Diffusion for Lifelong Generative Modeling](https://mlsanity.com/paper/2505.11936/) (2025)
- [Enhancing Memory Recall in LLMs with Gauss-Tin: A Hybrid Instructional and Gaussian Replay Approach](https://mlsanity.com/paper/2508.09510/) (2025)

## Abstract (arXiv)

We present an approach for continual learning (CL) that is based on fully probabilistic (or generative) models of machine learning. In contrast to, e.g., GANs that are "generative" in the sense that they can generate samples, fully probabilistic models aim at modeling the data distribution directly. Consequently, they provide functionalities that are highly relevant for continual learning, such as density estimation (outlier detection) and sample generation. As a concrete realization of generative continual learning, we propose Gaussian Mixture Replay (GMR). GMR is a pseudo-rehearsal approach using a Gaussian Mixture Model (GMM) instance for both generator and classifier functionalities. Relying on the MNIST, FashionMNIST and Devanagari benchmarks, we first demonstrate unsupervised task boundary detection by GMM density estimation, which we also use to reject untypical generated samples. In addition, we show that GMR is capable of class-conditional sampling in the way of a cGAN. Lastly, we verify that GMR, despite its simple structure, achieves state-of-the-art performance on common class-incremental learning problems at very competitive time and memory complexity.