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

TL;DR

Localized LoRA introduces a structured low-rank approximation framework for parameter-efficient fine-tuning, enabling localized updates that improve expressiveness and performance without increasing trainable parameters.

Contribution

The paper proposes Localized LoRA, a novel structured low-rank approach that models weight updates as localized blocks, outperforming global low-rank methods in approximation error and fine-tuning efficiency.

Findings

Lower approximation error compared to global methods.

Enhanced fine-tuning performance on synthetic and real tasks.

Efficient localized updates without increasing parameters.

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 pre-trained 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.