针对异构数据下的联邦LoRA微调，区分方向与幅度敏感性实现全局共享与本地个性化协同优化。

Federated efficient fine-tuning has emerged as an approach that leverages distributed data and computational resources across nodes to address the challenges of large-scale fine-tuning and privacy preservation. The Low-Rank Adaptation (LoRA) enables efficient fine-tuning of large-scale pre-trained models by introducing trainable low-rank matrices into weight updates.However, in heterogeneous data scenarios, client drift weakens the generalization of the global model, and local models often fail to meet the personalized needs of individual clients.Moreover, existing federated LoRA efficient fine-tuning techniques overlook fine-grained analysis of the tuning matrices. To address this, we conducted preliminary experiments and found that different LoRA matrices exhibit different sensitivity to changes in the direction and magnitude of their vectors.We thus propose a fine-grained federated LoRA tuning method. By fine-tuning the more sensitive directional vectors in the A matrix, which encode shared knowledge, our method learns shared features more effectively across clients and enhances global generalization. Simultaneously, by fine-tuning the more sensitive magnitude vectors in the B matrix, which encode personalized knowledge, our method better captures personalized knowledge, enabling detailed adaptation to local data. The method uses a pipeline combining global and local optimizers. Global optimization further improves local models, achieving collaborative optimization between global and local levels. This improves both the generalization ability of the global model and the personalized adaptation of local models under heterogeneous data scenarios. Experiments on Databricks-Dolly-15k and Natural Instructions with LLaMA2-7B and Deepseek-7B confirm that our method improves global performance by 0.39% and local performance by 0.59%.