Localized LoRA: A Structured Low-Rank Approximation for Efficient Fine-Tuning
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914053325062144 |
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| author | Barazandeh, Babak Majumdar, Subhabrata Rajyaguru, Om Michailidis, George |
| author_facet | Barazandeh, Babak Majumdar, Subhabrata Rajyaguru, Om Michailidis, George |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localized LoRA: A Structured Low-Rank Approximation for Efficient Fine-Tuning Barazandeh, Babak Majumdar, Subhabrata Rajyaguru, Om Michailidis, George Machine Learning Artificial Intelligence Computation and Language 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. |
| title | Localized LoRA: A Structured Low-Rank Approximation for Efficient Fine-Tuning |
| topic | Machine Learning Artificial Intelligence Computation and Language |
| url | https://arxiv.org/abs/2506.00236 |