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

arXiv: https://arxiv.org/abs/2506.00236 · HTML: https://mlsanity.com/paper/2506.00236/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 24 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 20 of 20)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [LoraHub: Efficient Cross-Task Generalization via Dynamic LoRA Composition](https://mlsanity.com/paper/2307.13269/) (2023)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [The Expressive Power of Low-Rank Adaptation](https://mlsanity.com/paper/2310.17513/) (2023)
- [LoRAMoE: Alleviate World Knowledge Forgetting in Large Language Models via MoE-Style Plugin](https://mlsanity.com/paper/2312.09979/) (2023)
- [A Survey on LoRA of Large Language Models](https://mlsanity.com/paper/2407.11046/) (2024)
- [MoRAL: MoE Augmented LoRA for LLMs' Lifelong Learning](https://mlsanity.com/paper/2402.11260/) (2024)
- [INSTRUCTEVAL: Towards Holistic Evaluation of Instruction-Tuned Large Language Models](https://mlsanity.com/paper/2306.04757/) (2023)
- [VB-LoRA: Extreme Parameter Efficient Fine-Tuning with Vector Banks](https://mlsanity.com/paper/2405.15179/) (2024)
- [K-LoRA: Unlocking Training-Free Fusion of Any Subject and Style LoRAs](https://mlsanity.com/paper/2502.18461/) (2025)
- [DoRA: Enhancing Parameter-Efficient Fine-Tuning with Dynamic Rank Distribution](https://mlsanity.com/paper/2405.17357/) (2024)
- [Hyperbolic Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2410.04010/) (2024)
- [Keeping Yourself is Important in Downstream Tuning Multimodal Large Language Model](https://mlsanity.com/paper/2503.04543/) (2025)
- [GoRA: Gradient-driven Adaptive Low Rank Adaptation](https://mlsanity.com/paper/2502.12171/) (2025)
- [SVFit: Parameter-Efficient Fine-Tuning of Large Pre-Trained Models Using Singular Values](https://mlsanity.com/paper/2409.05926/) (2024)
- [Enhancing Multi-hop Reasoning through Knowledge Erasure in Large Language Model Editing](https://mlsanity.com/paper/2408.12456/) (2024)
- [LoLDU: Low-Rank Adaptation via Lower-Diag-Upper Decomposition for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2410.13618/) (2024)
- [LoR2C : Low-Rank Residual Connection Adaptation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2503.00572/) (2025)

## Built on by (most cited first, 1 of 1)

- [Localized LoRA-MoE: Block-wise Low-Rank Experts With Adaptive Routing](https://mlsanity.com/paper/2607.05114/) (2026)

## Abstract (arXiv)

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.