Information-Theoretic Generalization Bounds of Replay-based Continual Learning

2025-07-16

AI Summary

This work investigates the theoretical mechanisms underlying generalization in replay-based continual learning, specifically addressing how the memory buffer interacts with current tasks to jointly mitigate catastrophic forgetting and enhance generalization. Method: We establish the first unified information-theoretic framework, integrating information-theoretic analysis with stochastic gradient Langevin dynamics (SGLD) modeling to ensure consistency between theoretical derivation and empirical validation. Contribution/Results: We derive two novel generalization bounds—over the hypothesis space and the prediction space—and theoretically prove that finite-sample replay outperforms full-replay. Moreover, we obtain a tight, computationally tractable upper bound on the generalization gap based on low-dimensional variables. Experiments demonstrate that our bounds accurately capture generalization dynamics and exhibit strong explanatory power and cross-scenario generalizability across diverse continual learning settings.

Technology Category

• Machine Learning: Life-Long and Continual Learning
• Natural Language Processing: Learning & Optimization for NLP
• Multiagent Systems: Multiagent Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Social networks and social learning
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

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. In this paper, we establish a unified theoretical framework for replay-based CL, deriving a series of information-theoretic bounds that explicitly characterize how the memory buffer interacts with the current task to affect generalization. Specifically, our hypothesis-based bounds reveal that utilizing the limited exemplars of previous tasks alongside the current task data, rather than exhaustive replay, facilitates improved generalization while effectively mitigating catastrophic forgetting. Furthermore, our prediction-based bounds yield tighter and computationally tractable upper bounds of the generalization gap through the use of low-dimensional variables. Our 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.

Problem

• Theoretical understanding of replay-based continual learning generalization is limited
• Memory buffer interaction with current task affects generalization bounds
• Low-dimensional variables yield tighter generalization gap bounds

Innovation

• Information-theoretic bounds for replay-based CL
• Hypothesis-based bounds using limited exemplars
• Prediction-based bounds with low-dimensional variables