Localized LoRA: A Structured Low-Rank Approximation for Efficient Fine-Tuning

• URL: http://arxiv.org/abs/2506.00236v1
• Date: Fri, 30 May 2025 21:13:23 GMT
• Title: Localized LoRA: A Structured Low-Rank Approximation for Efficient Fine-Tuning
• Authors: Babak Barazandeh,
• Abstract summary: Localized LoRA is a framework that models weight updates as a composition of low-rank approximations applied to structured blocks of the weight matrix.<n>We show that our method consistently achieves lower approximation error under matched parameter budgets.
• Score: 2.0652244993845086
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Parameter-efficient fine-tuning (PEFT) methods, such as LoRA, offer compact and effective alternatives to full model fine-tuning by introducing low-rank updates to pretrained weights. However, most existing approaches rely on global low-rank structures, which can overlook spatial patterns spread across the parameter space. In this work, we propose Localized LoRA, a generalized framework that models weight updates as a composition of low-rank matrices applied to structured blocks of the weight matrix. This formulation enables dense, localized updates throughout the parameter space-without increasing the total number of trainable parameters. We provide a formal comparison between global, diagonal-local, and fully localized low-rank approximations, and show that our method consistently achieves lower approximation error under matched parameter budgets. Experiments on both synthetic and practical settings demonstrate that Localized LoRA offers a more expressive and adaptable alternative to existing methods, enabling efficient fine-tuning with improved performance.

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