FedHL: Federated Learning for Heterogeneous Low-Rank Adaptation via Unbiased Aggregation

--Federated Learning (FL) facilitates the fine-tuning of Foundation Models (FMs) using distributed data sources, with Low-Rank Adaptation (LoRA) gaining popularity due to its low communication costs and strong performance. While recent work acknowledges the benefits of heterogeneous LoRA in FL and introduces flexible algorithms to support its implementation, our theoretical analysis reveals a critical gap: existing methods lack formal convergence guarantees due to parameter truncation and biased gradient updates. Specifically, adapting client-specific LoRA ranks necessitates truncating global parameters, which introduces inherent truncation errors and leads to subsequent inaccurate gradient updates that accumulate over training rounds, ultimately degrading performance. T o address the above issues, we propose FedHL, a simple yet effective Federated Learning framework tailored for Heterogeneous LoRA. By leveraging the full-rank global model as a calibrated aggregation basis, FedHL eliminates the direct truncation bias from initial alignment with client-specific ranks. Furthermore, we derive the theoretically optimal aggregation weights by minimizing the gradient drift term in the convergence upper bound. Our analysis shows that FedHL guarantees O (1 / T) convergence rate, and experiments on multiple real-world datasets demonstrate a 1-3% improvement over several state-of-the-art methods. Zihao Peng, Jiandian Zeng, and Guo Li are with the Institute of Artificial Intelligence and Future Networks, Beijing Normal University, Zhuhai 519087, China (e-mail: { pzh cs, liguo }@mail.bnu.edu.cn; Boyuan Li is with the School of Computer Science and Artificial Intelligence, Zhengzhou University, Zhengzhou 450001, China (e-mail: l202311841010602@gs.zzu.edu.cn). Shengbo Chen is with the School of Software, Nanchang University, Nanchang 330000, China (e-mail: ccb02kingdom@gmail.com).