# Information-Theoretic Generalization Bounds of Replay-based Continual Learning

arXiv: https://arxiv.org/abs/2507.12043 · HTML: https://mlsanity.com/paper/2507.12043/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 53 references that are in the map.
- First posted on arXiv 16 Jul 2025.

## Builds on (most cited first, 30 of 37)

- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (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)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Class-incremental learning: survey and performance evaluation on image classification](https://mlsanity.com/paper/2010.15277/) (2020)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Coresets via Bilevel Optimization for Continual Learning and Streaming](https://mlsanity.com/paper/2006.03875/) (2020)
- [Reasoning About Generalization via Conditional Mutual Information](https://mlsanity.com/paper/2001.09122/) (2020)
- [Information-Theoretic Generalization Bounds for SGLD via Data-Dependent Estimates](https://mlsanity.com/paper/1911.02151/) (2019)
- [Tightening Mutual Information Based Bounds on Generalization Error](https://mlsanity.com/paper/1901.04609/) (2019)
- [How much does your data exploration overfit? Controlling bias via information usage](https://mlsanity.com/paper/1511.05219/) (2015)
- [Sharpened Generalization Bounds based on Conditional Mutual Information and an Application to Noisy, Iterative Algorithms](https://mlsanity.com/paper/2004.12983/) (2020)
- [Optimal Continual Learning has Perfect Memory and is NP-hard](https://mlsanity.com/paper/2006.05188/) (2020)
- [Information-Theoretic Generalization Bounds for Stochastic Gradient Descent](https://mlsanity.com/paper/2102.00931/) (2021)
- [How catastrophic can catastrophic forgetting be in linear regression?](https://mlsanity.com/paper/2205.09588/) (2022)
- [Flattening Sharpness for Dynamic Gradient Projection Memory Benefits Continual Learning](https://mlsanity.com/paper/2110.04593/) (2021)
- [Information-theoretic generalization bounds for black-box learning algorithms](https://mlsanity.com/paper/2110.01584/) (2021)
- [Natural continual learning: success is a journey, not (just) a destination](https://mlsanity.com/paper/2106.08085/) (2021)
- [Few-Shot Class-Incremental Learning via Training-Free Prototype Calibration](https://mlsanity.com/paper/2312.05229/) (2023)
- [Reproducibility Report: La-MAML: Look-ahead Meta Learning for Continual Learning](https://mlsanity.com/paper/2102.05824/) (2021)
- [A Unified Approach to Domain Incremental Learning with Memory: Theory and Algorithm](https://mlsanity.com/paper/2310.12244/) (2023)
- [A simple but strong baseline for online continual learning: Repeated Augmented Rehearsal](https://mlsanity.com/paper/2209.13917/) (2022)
- [On the Generalization of Models Trained with SGD: Information-Theoretic Bounds and Implications](https://mlsanity.com/paper/2110.03128/) (2021)
- [Understanding Forgetting in Continual Learning with Linear Regression](https://mlsanity.com/paper/2405.17583/) (2024)
- [On Random Subset Generalization Error Bounds and the Stochastic Gradient Langevin Dynamics Algorithm](https://mlsanity.com/paper/2010.10994/) (2020)
- [A New Family of Generalization Bounds Using Samplewise Evaluated CMI](https://mlsanity.com/paper/2210.06422/) (2022)

## Built on by (most cited first, 2 of 2)

- [Information Theory in Open-world Machine Learning Foundations, Frameworks, and Future Direction](https://mlsanity.com/paper/2510.15422/) (2025)
- [Drift and Dependence: Layer-wise Information-Theoretic Bounds for Replay-Based Continual Learning](https://mlsanity.com/paper/2608.11690/) (2026)

## Abstract (arXiv)

Continual learning (CL) has emerged as a dominant paradigm for acquiring knowledge from sequential tasks while avoiding catastrophic forgetting. Although many CL methods have been proposed to show impressive empirical performance, the theoretical understanding of their generalization behavior remains limited, particularly for replay-based approaches. This paper establishes a unified theoretical framework for replay-based CL, deriving a series of information-theoretic generalization bounds that explicitly elucidate the impact of the memory buffer alongside the current task on generalization performance. Specifically, our hypothesis-based bounds capture the trade-off between the number of selected exemplars and the information dependency between the hypothesis and the memory buffer. Our prediction-based bounds yield tighter and computationally tractable upper bounds on the generalization error by leveraging low-dimensional variables. Theoretical analysis is general and broadly applicable to a wide range of learning algorithms, exemplified by stochastic gradient Langevin dynamics (SGLD) as a representative method. Comprehensive experimental evaluations demonstrate the effectiveness of our derived bounds in capturing the generalization dynamics in replay-based CL settings.