Parameter-efficient fine-tuning methods, such as LoRA, reduces the number of trainable parameters. However, they often suffer from scalability issues and differences between their learning pattern and full fine-tuning. To overcome these limitations, we propose Efficient Weight-Decomposed Low-Rank Adaptation (EDoRA): a novel PEFT method that decomposes pre-trained weights into magnitude and directional components. By freezing low-rank matrices, initializing them by singular value decomposition, and introducing a small trainable matrix between them, EDoRA achieves substantial reduction in trainable parameters while maintaining learning capacity. Experimental results on the GLUE benchmark demonstrate that EDoRA achieves competitive or superior performance compared to state-of-the-art methods, such as LoRA and DoRA, with up to 30x fewer trainable parameters. This makes EDoRA a highly efficient solution for adapting LLMs to diverse tasks under memory-constrained settings. Code is available at https://github.com/Hamid-Nasiri/EDoRA .

Low-rank adapters have become a standard approach for efficiently fine-tuning large language models (LLMs), but they often fall short of achieving the performance of full fine-tuning. We propose a method, LoRA Silver Bullet or LoRA-SB, that approximates full fine-tuning within low-rank subspaces using a carefully designed initialization strategy. We theoretically demonstrate that the architecture of LoRA-XS, which inserts a trainable (r x r) matrix between B and A while keeping other matrices fixed, provides the precise conditions needed for this approximation. We leverage its constrained update space to achieve optimal scaling for high-rank gradient updates while removing the need for hyperparameter tuning. We prove that our initialization offers an optimal low-rank approximation of the initial gradient and preserves update directions throughout training. Extensive experiments across mathematical reasoning, commonsense reasoning, and language understanding tasks demonstrate that our approach exceeds the performance of standard LoRA while using 27-90x fewer parameters, and comprehensively outperforms LoRA-XS. Our findings establish that it is possible to simulate full fine-tuning in low-rank subspaces, and achieve significant efficiency gains without sacrificing performance. Our code is publicly available at https://github.com/RaghavSinghal10/lora-sb.

The recent trend in scaling language models has led to a growing demand for parameter-efficient tuning (PEFT) methods such as LoRA (Low-Rank Adaptation). LoRA consistently matches or surpasses the full fine-tuning baseline with fewer parameters. However, handling numerous task-specific or user-specific LoRA modules on top of a base model still presents significant storage challenges. To address this, we introduce LoRA-XS (Low-Rank Adaptation with eXtremely Small number of parameters), a novel approach leveraging Singular Value Decomposition (SVD) for parameter-efficient fine-tuning. LoRA-XS introduces a small r x r weight matrix between frozen LoRA matrices, which are constructed by SVD of the original weight matrix. Training only r x r weight matrices ensures independence from model dimensions, enabling more parameter-efficient fine-tuning, especially for larger models. LoRA-XS achieves a remarkable reduction of trainable parameters by over 100x in 7B models compared to LoRA. Our benchmarking across various scales, including GLUE, GSM8k, and MATH benchmarks, shows that our approach outperforms LoRA and recent state-of-the-art approaches like VeRA in terms of parameter efficiency while maintaining competitive performance.