Towards Eliminating Catastrophic Forgetting in the Curriculum Learning of Math Reasoning Tasks

2026-09-27

AI Summary

This study addresses catastrophic forgetting in curriculum learning caused by parameter distribution shifts, which fundamentally stem from significant discrepancies among optimal solutions across different tasks. To mitigate this issue, we propose IV-EWC, a method that integrates Elastic Weight Consolidation (EWC) with influence functions. Specifically, influence functions are leveraged to construct a validation set for precisely evaluating sample importance, thereby enabling a dynamic regularization strategy that effectively constrains updates to critical parameters. Experimental results on mathematical reasoning tasks demonstrate that IV-EWC reduces the forgetting rate by an average of 162%, facilitates positive backward transfer, and significantly enhances performance on simpler tasks. Consequently, this work provides an efficient solution for alleviating forgetting problems inherent in curriculum learning paradigms.

Abstract

Curriculum learning has found broad application across numerous domains. Nevertheless, its effectiveness is intrinsically curtailed by catastrophic forgetting, driven by the shifts in model parameter distributions between curriculum tasks. In this paper, we investigate the phenomenon of catastrophic forgetting in this training paradigm, building on the established efficacy of curriculum learning. Our theoretical analyses of parameter update dynamics demonstrate that catastrophic forgetting in curriculum learning stems from the divergence of task optima, which is generally essential to the faster convergence of curriculum learning; therefore, forgetting cannot be completely eliminated. Based on this finding, we augment the training process and propose IV-EWC, which incorporates Elastic Weight Consolidation (EWC) into the curriculum learning objective to curb catastrophic forgetting in mathematical reasoning, a prototypical curriculum learning scenario. IV-EWC employs the influence function to construct a representative validation set from the curriculum's training data, which is used to drive dynamic regularization during training. We further present an extended theoretical analysis to show that EWC-based regularization methods mitigate catastrophic forgetting in curriculum learning, thereby providing theoretical support for IV-EWC. Empirical evaluations on three backbone models and three benchmarks indicate that curriculum learning exhibits catastrophic forgetting. IV-EWC alleviates this issue, reducing forgetting by 162% on average relative to vanilla curriculum learning and yielding positive backward transfer, as evidenced by improved performance on easier tasks after subsequent training on challenging tasks.

Problem

• Catastrophic Forgetting
• Curriculum Learning
• Math Reasoning

Innovation

• Curriculum Learning
• Catastrophic Forgetting
• Elastic Weight Consolidation
• Influence Function
• Math Reasoning