Exploring the Impact of Parameter Update Magnitude on Forgetting and Generalization of Continual Learning

The magnitude of parameter updates are considered a key factor in continual learning. However, most existing studies focus on designing diverse update strategies, while a theoretical understanding of the underlying mechanisms remains limited. Therefore, we characterize model's forgetting from the perspective of parameter update magnitude and formalize it as knowledge degradation induced by task-specific drift in the parameter space, which has not been fully captured in previous studies due to their assumption of a unified parameter space. By deriving the optimal parameter update magnitude that minimizes forgetting, we unify two representative update paradigms, frozen training and initialized training, within an optimization framework for constrained parameter updates. Our theoretical results further reveals that sequence tasks with small parameter distances exhibit better generalization and less forgetting under frozen training rather than initialized training. These theoretical insights inspire a novel hybrid parameter update strategy that adaptively adjusts update magnitude based on gradient directions. Experiments on deep neural networks demonstrate that this hybrid approach outperforms standard training strategies, providing new theoretical perspectives and practical inspiration for designing efficient and scalable continual learning algorithms.

Understanding the Role of Rehearsal Scale in Continual Learning under Varying Model Capacities

Rehearsal is one of the key techniques for mitigating catastrophic forgetting and has been widely adopted in continual learning algorithms due to its simplicity and practicality. However, the theoretical understanding of how rehearsal scale influences learning dynamics remains limited. To address this gap, we formulate rehearsal-based continual learning as a multidimensional effectiveness-driven iterative optimization problem, providing a unified characterization across diverse performance metrics. Within this framework, we derive a closed-form analysis of adaptability, memorability, and generalization from the perspective of rehearsal scale. Our results uncover several intriguing and counterintuitive findings. First, rehearsal can impair model's adaptability, in sharp contrast to its traditionally recognized benefits. Second, increasing the rehearsal scale does not necessarily improve memory retention. When tasks are similar and noise levels are low, the memory error exhibits a diminishing lower bound. Finally, we validate these insights through numerical simulations and extended analyses on deep neural networks across multiple real-world datasets, revealing statistical patterns of rehearsal mechanisms in continual learning.