aiqbench analysis
This paper is a theoretical machine learning study of catastrophic forgetting in continual learning, using algorithmic stability to bound forgetting under SGD without assuming a specific architecture or convexity. Its main contribution is showing how training set size, updates per task, number of tasks, learning-rate schedule, and cumulative gradient alignment enter the forgetting bound, with experiments on Split CIFAR-100 and Split MiniImageNet as a check. For practitioners, the value lies in clearer guidance on whether restarting learning-rate decay at task boundaries helps or hurts retention, though the empirical validation is limited to standard benchmarks.
Fine-Grained Analysis of Catastrophic Forgetting in Continual Learning via Algorithmic Stability
arXiv:2610.31551v1 Announce Type: new Abstract: Understanding catastrophic forgetting, in which learning new tasks degrades performance on previously learned tasks, remains a fundamental challenge in continual learning (CL). Existing theoretical analyses often rely on specific model or task structures and offer limited insight into how iterative optimization affects forgetting. To address this gap, we develop an algorithmic stability framework for expected population forgetting under SGD without prescribing a particular model architecture. Specifically, we decompose forgetting into intra-task and cross-task generalization gaps and empirical forgetting. To bound the generalization gaps, we track how a sample perturbation affects updates within a task and propagates through subsequent tasks. We consider constant, intra-task decaying, and continuously decaying learning-rate schedules. Comparing the two decaying schedules allows us to characterize how restarting learning-rate decay at task boundaries affects the propagation of historical sample perturbations. For empirical forgetting, we derive bounds for all three schedules by retaining cumulative gradient alignment along the optimization trajectory, without requiring convexity. Combining these results yields upper bounds on expected forgetting that capture the effects of training set size, the number of updates per task, the total number of tasks, learning-rate schedules, and cumulative gradient alignment. Finally, we conduct experiments on Split CIFAR-100 and Split MiniImageNet to examine the empirical implications of our theoretical findings.
Abstract:Understanding catastrophic forgetting, in which learning new tasks degrades performance on previously learned tasks, remains a fundamental challenge in continual learning (CL). Existing theoretical analyses often rely on specific model or task structures and offer limited insight into how iterative optimization affects forgetting. To address this gap, we develop an algorithmic stability framework for expected population forgetting under SGD without prescribing a particular model architecture. Specifically, we decompose forgetting into intra-task and cross-task generalization gaps and empirical forgetting. To bound the generalization gaps, we track how a sample perturbation affects updates within a task and propagates through subsequent tasks. We consider constant, intra-task decaying, and continuously decaying learning-rate schedules. Comparing the two decaying schedules allows us to characterize how restarting learning-rate decay at task boundaries affects the propagation of historical sample perturbations. For empirical forgetting, we derive bounds for all three schedules by retaining cumulative gradient alignment along the optimization trajectory, without requiring convexity. Combining these results yields upper bounds on expected forgetting that capture the effects of training set size, the number of updates per task, the total number of tasks, learning-rate schedules, and cumulative gradient alignment. Finally, we conduct experiments on Split CIFAR-100 and Split MiniImageNet to examine the empirical implications of our theoretical findings.
Machine Learning (cs.LG)
arXiv:2610.31551 [cs.LG]
(or arXiv:2610.31551v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.31551 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 301 words