Revisiting Weight Regularization for Low-Rank Continual Learning

Continual Learning (CL) with large-scale pre-trained models (PTMs) has recently gained wide attention, shifting the focus from training from scratch to continually adapting PTMs. This has given rise to a promising paradigm: parameter-efficient continual learning (PECL), where task interference is typically mitigated by assigning a task-specific module during training, such as low-rank adapters. However, weight regularization techniques, such as Elastic Weight Consolidation (EWC)—a key strategy in CL—remain underexplored in this new paradigm. In this paper, we revisit weight regularization in low-rank CL as a new perspective for mitigating task interference in PECL. Unlike existing low-rank CL methods, we mitigate task interference by regularizing a shared low-rank update through EWC, thereby keeping the storage requirement constant regardless of the number of tasks. Moreover, we provide the first systematic investigation of EWC in low-rank CL, showing that it achieves a better stability–plasticity trade-off than other low-rank methods and enables competitive performance across a wide range of trade-off points. Building on these insights, we propose EWC-LoRA, which leverages a low-rank representation to estimate parameter importance over the full-dimensional space. This design offers a practical, computational- and memory-efficient solution for CL with PTMs, and provides insights that may inform the broader application of regularization techniques within PECL. Extensive experiments on various benchmarks demonstrate the effectiveness of EWC-LoRA. On average, EWC-LoRA improves over vanilla LoRA by 8.92\% and achieves comparable or even superior performance to other state-of-the-art low-rank CL methods.