[Submitted on 15 Jun 2026 (v1), last revised 22 Oct 2026 (this version, v3)]
Abstract: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.
Submission history
From: Junghun Oh [view email]
[v1] Mon, 15 Jun 2026 09:27:50 UTC (1,191 KB)
[v2] Thu, 13 Aug 2026 05:54:55 UTC (1,201 KB)
[v3] Thu, 22 Oct 2026 11:25:52 UTC (1,201 KB)
