Towards Understanding Memory buffer based Continual Learning
Keywords: continual learning, memory, catastrophic forgetting, generalization
Abstract: Continual learning (CL) is a paradigm that adapts to and retains knowledge from a stream of tasks. Despite the growing number of experimental methods in CL, there is a lack of rigorous theoretical analysis, particularly in memory-based continual learning (MCL), which remains an open research area. In this paper, we theoretically analyze the impact of memory in CL and derive explicit expressions for expected forgetting and generalization errors under overparameterized linear models. We propose a detailed matrix decomposition of the data to distinguish between current and previous datasets, effectively decoupling the coupled data for different tasks. Additionally, we conduct a comprehensive mathematical analysis for scenarios with a small number of tasks and employ numerical analysis for larger task scenarios to evaluate the overall properties of expected forgetting and generalization errors. Compared with CL, our theoretical analysis suggests that (1) a larger memory buffer must be paired with a larger model to effectively reduce forgetting; (2) training with a larger memory buffer generalizes better when tasks are similar but may perform worse when tasks are dissimilar, while training with a large model can help mitigate this negative effect. Ultimately, our findings here sheds new light on how memory can assist CL in mitigating catastrophic forgetting and improving generalization.
Primary Area: transfer learning, meta learning, and lifelong learning
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Submission Number: 13727
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