Faster Than SVD, Smarter Than SGD: The OPLoRA Alternating Update

• URL: http://arxiv.org/abs/2509.19977v1
• Date: Wed, 24 Sep 2025 10:32:50 GMT
• Title: Faster Than SVD, Smarter Than SGD: The OPLoRA Alternating Update
• Authors: Abdulla Jasem Almansoori, Maria Ivanova, Andrey Veprikov, Aleksandr Beznosikov, Samuel Horváth, Martin Takáč,
• Abstract summary: Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights.<n>There is still a gap between full training with low-rank projections (SVDLoRA) and LoRA fine-tuning, indicating that LoRA steps can be further improved.
• Score: 50.36542772932594
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights, dramatically reducing trainable parameters and memory. However, there is still a gap between full training with low-rank projections (SVDLoRA) and LoRA fine-tuning, indicating that LoRA steps can be further improved. In this study, we propose OPLoRA, a memory-efficient optimizer that closes this gap by casting LoRA optimization as an interpretable sub-problem and solving it efficiently with alternating least squares updates, where 1-2 alternating steps are empirically found to be sufficient to closely match truncated SVD without ever forming the full matrix. We also retrieve the recently proposed preconditioning methods for LoRA as a special case. OPLoRA supports momentum by maintaining a low-rank estimate using the same subroutine (LoRSum) for computing the step, with a memory budget of 3 times the number of LoRA parameters (i.e., same as Adam). We also propose an experimental scaled variant that uses the K-FAC metric, which could be of interest. Across a linear task, MNIST, CIFAR-100, and RoBERTa-base (MNLI), OPLoRA consistently approaches SVDLoRA's performance using significantly less memory.

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