Stability-Plasticity Balance via Singular-Vector Selection in LLM Continual Learning

Lingxiang Wang, Hainan Zhang, Liang Pang, Hongwei Zheng, Zhiming Zheng

Domain-specific continual adaptation of LLMs risks catastrophic forgetting, creating a fundamental tension between acquiring new capabilities and preserving those learned during pretraining. PEFT mitigates this problem by restricting the number of trainable parameters, but existing methods lack a principled unit for deciding where plasticity should be allocated and stability should be preserved. We identify the singular-vector channel as a natural unit for managing this trade-off. Each channel represents an input-output transformation, which can be updated to acquire new knowledge or fixed to preserve pretrained capabilities. Based on this perspective, we introduce SVC, a parameter-efficient continual-learning method that selectively updates Singular-Vector Channels. Before fine-tuning, SVC uses domain-specific data to estimate each channel's adaptation benefit and a fixed public general-domain corpus only as a history activation proxy for estimating forgetting cost. It then adaptively selects trainable channels based on these scores via knee-based cost screening, Pareto-front filtering, and Otsu thresholding. Experimental results across four LLM families and eight downstream…