Localized LoRA: A Structured Low-Rank Approximation for Efficient Fine-Tuning
This work addresses the need for more expressive fine-tuning methods in machine learning, offering an incremental improvement over existing approaches like LoRA.
The paper tackled the problem of parameter-efficient fine-tuning by proposing Localized LoRA, a framework that models weight updates as low-rank matrices applied to structured blocks, which achieved lower approximation error and improved performance in experiments.
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.