@inproceedings{zhang-etal-2026-sdc,
    title = "{SDC}-{L}o{RA}: Singular-Subspace Drift Controlled {L}o{RA} to Mitigate Knowledge Forgetting",
    author = "Zhang, Geyuan  and
      Zhou, Xiaofei  and
      Liu, Shihao  and
      Tian, Jingyuan  and
      Ma, Jizheng",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.findings-acl.1207/",
    pages = "24116--24132",
    ISBN = "979-8-89176-395-1",
    abstract = "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 $W_0$; 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 \textit{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 \textbf{S}ingular-subspace \textbf{D}rift \textbf{C}ontrolled \textbf{LoRA} (SDC-LoRA), which constrains the growth of update energy in the principal singular subspace of $W_0$ and thus mitigate SD. SDC-LoRA proposes \textit{Principal Subspace Energy-Controlled Learning}, using \textit{Spectral Calibration} factor $\gamma_{\mathrm{sc}}$ to selectively downscale gradients along the principal singular subspace of $W_0$ 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."
}