@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://aclanthology.org/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."
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<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 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 γ_sc 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.</abstract>
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%0 Conference Proceedings
%T SDC-LoRA: Singular-Subspace Drift Controlled LoRA to Mitigate Knowledge Forgetting
%A Zhang, Geyuan
%A Zhou, Xiaofei
%A Liu, Shihao
%A Tian, Jingyuan
%A Ma, Jizheng
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Findings of the Association for Computational Linguistics: ACL 2026
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-395-1
%F zhang-etal-2026-sdc
%X 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 γ_sc 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.
%U https://aclanthology.org/2026.findings-acl.1207/
%P 24116-24132
Markdown (Informal)
[SDC-LoRA: Singular-Subspace Drift Controlled LoRA to Mitigate Knowledge Forgetting](https://aclanthology.org/2026.findings-acl.1207/) (Zhang et al., Findings 2026)
ACL