Jizheng Ma
2026
SDC-LoRA: Singular-Subspace Drift Controlled LoRA to Mitigate Knowledge Forgetting
Geyuan Zhang | Xiaofei Zhou | Shihao Liu | Jingyuan Tian | Jizheng Ma
Findings of the Association for Computational Linguistics: ACL 2026
Geyuan Zhang | Xiaofei Zhou | Shihao Liu | Jingyuan Tian | Jizheng Ma
Findings of the Association for Computational Linguistics: ACL 2026
Knowledge forgetting is a central challenge when adapting LLMs to new tasks. Prior studies indicate that pretrained knowledge is concentrated in the principal singular subspace of pretrained weight W0; so recent Low-Rank Adaptation (LoRA) variants initialize LoRA in the minor subspace to steer early updates away from principal directions and mitigate forgetting. However, we observe that during fine-tuning, the update direction progressively shifts from the minor to the principal subspace, which is called as Singular-subspace Drift (SD), thereby allocating more energy to the directions that carry pretrained knowledge and leaving a persistent risk of forgetting. To address this issue, we propose Singular-subspace Drift Controlled LoRA (SDC-LoRA), which constrains the growth of update energy in the principal singular subspace of W0 and thus mitigate SD. SDC-LoRA proposes Principal Subspace Energy-Controlled Learning, using Spectral Calibration factor 𝛾sc to selectively downscale gradients along the principal singular subspace of W0 while keeping minor-subspace updates unchanged. Across extensive experiments with LLaMA-3.1-8B-Instruct and Qwen2.5-7B-Chat on MetaMathQA and CodeFeedback, SDC-LoRA mitigates forgetting on MMLU, TruthfulQA, and HellaSwag while matching or improving GSM8K and HumanEval, offering a practical route to adapt LLMs without sacrificing prior knowledge.