Chongjie Si

Chongjie Si, Xiaokang Yang, Wei Shen

The rapid expansion of large foundation models within the pre-training and fine-tuning framework has underscored that larger models often yield better results. However, the scaling up of large foundation models has led to soaring costs in fine-tuning and parameter storage, rendering extensive adaptations impractical. This challenge has sparked the development of parameter-efficient fine-tuning (PEFT), which focuses on optimizing a select subset of parameters while keeping the rest fixed, significantly lowering computational and storage overheads. While recent years have witnessed a significant success in PEFT, a deep understanding of the fundamental principles behind these methods remains unexplored. To this end, here we take the first step to unify all approaches by dissecting them from a decomposition perspective. We initiate a comprehensive mathematical analysis of these methods, allowing us to delve deeply into their underlying mechanisms, and we explore the reasons behind the variations in performance among different techniques. Furthermore, inspired by our theoretical analysis, we introduce two novel PEFT methods alongside a simple yet effective framework designed to enhance the performance of PEFT techniques across various applications. Our empirical validations, conducted across multiple datasets, demonstrate the efficacy of these methods, showcasing both theoretical validity and practical performance improvements under the guidance of our analytical findings. We believe our work will deepen researchers' understanding of PEFT and other techniques, prompting further contemplation and advancing the research across the whole community.

Chongjie Si, Xuankun Yang, Muqing Liu et al.

Large-scale foundation models have demonstrated remarkable versatility across a wide range of downstream tasks. However, fully fine-tuning these models incurs prohibitive computational costs, motivating the development of Parameter-Efficient Fine-Tuning (PEFT) methods such as LoRA, which introduces low-rank updates to pre-trained weights. Despite their empirical success, the underlying mechanisms by which PEFT modifies model parameters remain underexplored. In this work, we present a systematic investigation into the structural changes of weight matrices during fully fine-tuning. Through singular value decomposition (SVD), we reveal that fine-tuning predominantly amplifies the top singular values while leaving the remainder largely intact, suggesting that task-specific knowledge is injected into a low-dimensional subspace. Furthermore, we find that the dominant singular vectors are reoriented in task-specific directions, whereas the non-dominant subspace remains stable. Building on these insights, we propose a novel method that leverages learnable rescaling of top singular directions, enabling precise modulation of the most influential components without disrupting the global structure. Our approach achieves consistent improvements over strong baselines across multiple tasks, highlighting the efficacy of structurally informed fine-tuning.

Chongjie Si, Zhiyi Shi, Yadao Wang et al.

The rapid development of large language models has revolutionized natural language processing, but their fine-tuning remains computationally expensive, hindering broad deployment. Parameter-efficient fine-tuning (PEFT) methods, such as LoRA, have emerged as solutions. Recent work like DoRA attempts to further decompose weight adaptation into direction and magnitude components. However, existing formulations often define direction heuristically at the column level, lacking a principled geometric foundation. In this paper, we propose MAP, a novel framework that reformulates weight matrices as high-dimensional vectors and decouples their adaptation into direction and magnitude in a rigorous manner. MAP normalizes the pre-trained weights, learns a directional update, and introduces two scalar coefficients to independently scale the magnitude of the base and update vectors. This design enables more interpretable and flexible adaptation, and can be seamlessly integrated into existing PEFT methods. Extensive experiments show that MAP significantly improves performance when coupling with existing methods, offering a simple yet powerful enhancement to existing PEFT methods. Given the universality and simplicity of MAP, we hope it can serve as a default setting for designing future PEFT methods.