分析LoRA联邦学习中参数聚合的收敛性，揭示不同方法优劣。

Federated Learning (FL) enables collaborative model training across decentralized data sources while preserving data privacy. However, the growing size of Machine Learning (ML) models poses communication and computation challenges in FL. Low-Rank Adaptation (LoRA) has recently been introduced into FL as an efficient fine-tuning method, reducing communication overhead by updating only a small number of trainable parameters. Despite its effectiveness, how to aggregate LoRA-updated local models on the server remains a critical and understudied problem. In this paper, we provide a unified convergence analysis for LoRA-based FL. We first categories the current aggregation method into two major type: Sum-Product (SP) and Product-Sum (PS). Then we formally define the Aggregation-Broadcast Operator (ABO) and derive both weak and strong convergence condition under mild assumptions. Furthermore, we present both weak and strong convergence condition that guarantee convergence of the local model and the global model respectively. These theoretical analyze offer a principled understanding of various aggregation strategies. Notably, we prove that the SP and PS aggregation methods satisfy the weak and strong convergence condition respectively, but differ in their ability to achieve the optimal convergence rate. Extensive experiments on standard benchmarks validate our theoretical findings.