← 研踪 PaperTrailarXiv:2606.16454 · v4
SDS-LoRA: Overcoming Anisotropic Gradient Scaling in Low-Rank Adaptation
首次提交 2026-06-15 17:27
版本更新 2026-11-06 14:10
雷达观测 2026-11-09 11:19
摘要
Low-Rank Adaptation (LoRA) enables efficient adaptation of large pretrained models to downstream tasks by parameterizing weight updates with low-rank matrices. In this paper, we investigate the limitations of the LoRA parameterization from a geometric perspective. Specifically, we show that when a full fine-tuning gradient is backpropagated to the low-rank matrices, it undergoes anisotropic scaling driven by their singular values. We argue that this phenomenon is undesirable because it distorts the full fine-tuning gradient by skewing it toward dominant singular directions while suppressing others. Our analyses demonstrate that anisotropic gradient scaling reduces the effective rank of the low-rank matrices' gradients and fails to provide the best possible alignment between the full fine-tuning gradient and its low-rank approximation in LoRA for arbitrary gradients, thereby exacerbating the gap to full fine-tuning. To address these limitations, we propose a new low-rank parameterization, SDS-LoRA, which Structurally Decouples Singular values from the backward pass. Our method ensures that the full fine-tuning gradient backpropagates only through the orthonormal bases of the low-rank matrices' subspaces, independent of their scales. Convergence analysis demonstrates that while LoRA's convergence rate degrades with the condition number of the low-rank matrices, that of SDS-LoRA remains independent of it. Experimental results across natural language and vision benchmarks show that SDS-LoRA improves loss convergence and reduces the gap to full fine-tuning, significantly enhancing adaptation performance. The code is available at https://github.com/JungHunOh/SDS-LoRA_NeurIPS2026.
作者备注：Accepted at NeurIPS2026
观测到的版本
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v4 · 2026-11-06 14:10 · 最新观测版本
SDS-LoRA: Overcoming Anisotropic Gradient Scaling in Low-Rank Adaptation
Low-Rank Adaptation (LoRA) enables efficient adaptation of large pretrained models to downstream tasks by parameterizing weight updates with low-rank matrices. In this paper, we investigate the limitations of the LoRA parameterization from a geometric perspective. Specifically, we show that when a full fine-tuning gradient is backpropagated to the low-rank matrices, it undergoes anisotropic scaling driven by their singular values. We argue that this phenomenon is undesirable because it distorts the full fine-tuning gradient by skewing it toward dominant singular directions while suppressing others. Our analyses demonstrate that anisotropic gradient scaling reduces the effective rank of the low-rank matrices' gradients and fails to provide the best possible alignment between the full fine-tuning gradient and its low-rank approximation in LoRA for arbitrary gradients, thereby exacerbating the gap to full fine-tuning. To address these limitations, we propose a new low-rank parameterization, SDS-LoRA, which Structurally Decouples Singular values from the backward pass. Our method ensures that the full fine-tuning gradient backpropagates only through the orthonormal bases of the low-rank matrices' subspaces, independent of their scales. Convergence analysis demonstrates that while LoRA's convergence rate degrades with the condition number of the low-rank matrices, that of SDS-LoRA remains independent of it. Experimental results across natural language and vision benchmarks show that SDS-LoRA improves loss convergence and reduces the gap to full fine-tuning, significantly enhancing adaptation performance. The code is available at https://github.com/JungHunOh/SDS-LoRA_NeurIPS2026.
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