With the increasing number of parameters in large pre-trained models, LoRA as a parameter-efficient fine-tuning(PEFT) method is widely used for not adding inference overhead. The LoRA method assumes that weight changes during fine-tuning can be approximated by low-rank matrices. However, the rank values need to be manually verified to match different downstream tasks, and they cannot accommodate the varying importance of different layers in the model. In this work, we first analyze the relationship between the performance of different layers and their ranks using SVD. Based on this, we design the Singular-Value Based Adaptive Low-Rank Adaption(SARA), which adaptively finds the rank during initialization by performing SVD on the pre-trained weights. Additionally, we explore the Mixture-of-SARA(Mo-SARA), which significantly reduces the number of parameters by fine-tuning only multiple parallel sets of singular values controlled by a router. Extensive experiments on various complex tasks demonstrate the simplicity and parameter efficiency of our methods. They can effectively and adaptively find the most suitable rank for each layer of each model.

本研究解决了在大规模预训练模型中，LoRA方法需要手动验证不同层级的秩值匹配不同下游任务的问题。通过奇异值分解分析层与秩之间的关系，提出了SARA方法，能够在初始化时自适应地找到适合的秩；另外，通过探索Mixture-of-SARA方法，大幅度减少参数数量，验证了方法的简单性和参数效率。

基于奇异值的自适应低秩适应