# Replay Can Provably Increase Forgetting

arXiv: https://arxiv.org/abs/2506.04377 · HTML: https://mlsanity.com/paper/2506.04377/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 4 Jun 2025.

## Builds on (most cited first, 23 of 23)

- [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)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Large Scale Incremental Learning](https://mlsanity.com/paper/1905.13260/) (2019)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [Characterizing Implicit Bias in Terms of Optimization Geometry](https://mlsanity.com/paper/1802.08246/) (2018)
- [New Insights on Reducing Abrupt Representation Change in Online Continual Learning](https://mlsanity.com/paper/2104.05025/) (2021)
- [A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix](https://mlsanity.com/paper/2010.04003/) (2020)
- [GCR: Gradient Coreset Based Replay Buffer Selection For Continual Learning](https://mlsanity.com/paper/2111.11210/) (2021)
- [How catastrophic can catastrophic forgetting be in linear regression?](https://mlsanity.com/paper/2205.09588/) (2022)
- [Rehearsal revealed: The limits and merits of revisiting samples in continual learning](https://mlsanity.com/paper/2104.07446/) (2021)
- [Theory on Forgetting and Generalization of Continual Learning](https://mlsanity.com/paper/2302.05836/) (2023)
- [The Ideal Continual Learner: An Agent That Never Forgets](https://mlsanity.com/paper/2305.00316/) (2023)
- [Continual Learning in Linear Classification on Separable Data](https://mlsanity.com/paper/2306.03534/) (2023)
- [Analysis of Catastrophic Forgetting for Random Orthogonal Transformation Tasks in the Overparameterized Regime](https://mlsanity.com/paper/2207.06475/) (2022)
- [Fixed Design Analysis of Regularization-Based Continual Learning](https://mlsanity.com/paper/2303.10263/) (2023)
- [Memory Bounds for Continual Learning](https://mlsanity.com/paper/2204.10830/) (2022)
- [Order parameters and phase transitions of continual learning in deep neural networks](https://mlsanity.com/paper/2407.10315/) (2024)

## Built on by (most cited first, 5 of 5)

- [LibContinual: A Comprehensive Library towards Realistic Continual Learning](https://mlsanity.com/paper/2512.22029/) (2025)
- [Re-Evaluating Continual Learning with Few-Shot Adaptation](https://mlsanity.com/paper/2606.03843/) (2026)
- [From Order to Distribution: An Exact Operator Framework for Forgetting in Continual Learning](https://mlsanity.com/paper/2604.13460/) (2026)
- [The Sequential Price of Continual Learning](https://mlsanity.com/paper/2609.29674/) (2026)
- [Formalizing Forgetting: Theory of Forgetting for Online Continual Learning](https://mlsanity.com/paper/2610.14787/) (2026)

## Abstract (arXiv)

Continual learning seeks to enable machine learning systems to solve an increasing corpus of tasks sequentially. A critical challenge for continual learning is forgetting, where the performance on previously learned tasks decreases as new tasks are introduced. One of the commonly used techniques to mitigate forgetting, sample replay, has been shown empirically to reduce forgetting by retaining some examples from old tasks and including them in new training episodes. In this work, we provide a theoretical analysis of sample replay in an over-parameterized continual linear regression setting, where each task is given by a linear subspace and with enough replay samples, one would be able to eliminate forgetting. Our analysis focuses on sample replay and highlights the role of the replayed samples and the relationship between task subspaces. Surprisingly, we find that, even in a noiseless setting, forgetting can be non-monotonic with respect to the number of replay samples. We present tasks where replay can be harmful with respect to worst-case settings, and also in distributional settings where replay of randomly selected samples increases forgetting in expectation. We also give empirical evidence that harmful replay is not limited to training with linear models by showing similar behavior for a neural networks equipped with SGD. Through experiments on a commonly used benchmark, we provide additional evidence that, even in seemingly benign scenarios, performance of the replay heavily depends on the choice of replay samples and the relationship between tasks.