# Posterior Meta-Replay for Continual Learning

arXiv: https://arxiv.org/abs/2103.01133 · HTML: https://mlsanity.com/paper/2103.01133/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 71 of its 112 references that are in the map.
- First posted on arXiv 1 Mar 2021.

## Builds on (most cited first, 30 of 71)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Three scenarios for continual learning](https://mlsanity.com/paper/1904.07734/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Class-incremental learning: survey and performance evaluation on image classification](https://mlsanity.com/paper/2010.15277/) (2020)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)

## Built on by (most cited first, 30 of 45)

- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Repulsive Deep Ensembles are Bayesian](https://mlsanity.com/paper/2106.11642/) (2021)
- [A Brief Review of Hypernetworks in Deep Learning](https://mlsanity.com/paper/2306.06955/) (2023)
- [A Theoretical Study on Solving Continual Learning](https://mlsanity.com/paper/2211.02633/) (2022)
- [Continual Learning and Catastrophic Forgetting](https://mlsanity.com/paper/2403.05175/) (2024)
- [A Comprehensive Survey of Forgetting in Deep Learning Beyond Continual Learning](https://mlsanity.com/paper/2307.09218/) (2023)
- [Learnability and Algorithm for Continual Learning](https://mlsanity.com/paper/2306.12646/) (2023)
- [How to Reuse and Compose Knowledge for a Lifetime of Tasks: A Survey on Continual Learning and Functional Composition](https://mlsanity.com/paper/2207.07730/) (2022)
- [A Multi-Head Model for Continual Learning via Out-of-Distribution Replay](https://mlsanity.com/paper/2208.09734/) (2022)
- [Catastrophic Forgetting in Deep Learning: A Comprehensive Taxonomy](https://mlsanity.com/paper/2312.10549/) (2023)
- [Open-World Continual Learning: Unifying Novelty Detection and Continual Learning](https://mlsanity.com/paper/2304.10038/) (2023)
- [Bottom-up and top-down approaches for the design of neuromorphic processing systems: Tradeoffs and synergies between natural and artificial intelligence](https://mlsanity.com/paper/2106.01288/) (2021)
- [OVOR: OnePrompt with Virtual Outlier Regularization for Rehearsal-Free Class-Incremental Learning](https://mlsanity.com/paper/2402.04129/) (2024)
- [A Unified and General Framework for Continual Learning](https://mlsanity.com/paper/2403.13249/) (2024)
- [Class Incremental Learning via Likelihood Ratio Based Task Prediction](https://mlsanity.com/paper/2309.15048/) (2023)
- [Two Complementary Perspectives to Continual Learning: Ask Not Only What to Optimize, But Also How](https://mlsanity.com/paper/2311.04898/) (2023)
- [Magnitude Invariant Parametrizations Improve Hypernetwork Learning](https://mlsanity.com/paper/2304.07645/) (2023)
- [Prediction Error-based Classification for Class-Incremental Learning](https://mlsanity.com/paper/2305.18806/) (2023)
- [Rethinking the Stability-Plasticity Trade-off in Continual Learning from an Architectural Perspective](https://mlsanity.com/paper/2506.03951/) (2025)
- [Replay-and-Forget-Free Graph Class-Incremental Learning: A Task Profiling and Prompting Approach](https://mlsanity.com/paper/2410.10341/) (2024)
- [Are Bayesian neural networks intrinsically good at out-of-distribution detection?](https://mlsanity.com/paper/2107.12248/) (2021)
- [Meta-Learning via Classifier(-free) Diffusion Guidance](https://mlsanity.com/paper/2210.08942/) (2022)
- [Continual Learning with Neuromorphic Computing: Foundations, Methods, and Emerging Applications](https://mlsanity.com/paper/2410.09218/) (2024)
- [On the Discrimination and Consistency for Exemplar-Free Class Incremental Learning](https://mlsanity.com/paper/2501.15454/) (2025)
- [Partial Hypernetworks for Continual Learning](https://mlsanity.com/paper/2306.10724/) (2023)
- [Knowledge Retention for Continual Model-Based Reinforcement Learning](https://mlsanity.com/paper/2503.04256/) (2025)
- [On out-of-distribution detection with Bayesian neural networks](https://mlsanity.com/paper/2110.06020/) (2021)
- [On Sequential Bayesian Inference for Continual Learning](https://mlsanity.com/paper/2301.01828/) (2023)
- [Continual Learning From a Stream of APIs](https://mlsanity.com/paper/2309.00023/) (2023)
- [Uncertainty Prioritized Experience Replay](https://mlsanity.com/paper/2506.09270/) (2025)

## Abstract (arXiv)

Learning a sequence of tasks without access to i.i.d. observations is a widely studied form of continual learning (CL) that remains challenging. In principle, Bayesian learning directly applies to this setting, since recursive and one-off Bayesian updates yield the same result. In practice, however, recursive updating often leads to poor trade-off solutions across tasks because approximate inference is necessary for most models of interest. Here, we describe an alternative Bayesian approach where task-conditioned parameter distributions are continually inferred from data. We offer a practical deep learning implementation of our framework based on probabilistic task-conditioned hypernetworks, an approach we term posterior meta-replay. Experiments on standard benchmarks show that our probabilistic hypernetworks compress sequences of posterior parameter distributions with virtually no forgetting. We obtain considerable performance gains compared to existing Bayesian CL methods, and identify task inference as our major limiting factor. This limitation has several causes that are independent of the considered sequential setting, opening up new avenues for progress in CL.