# Convergence Analysis of Aggregation-Broadcast in LoRA-enabled Distributed Fine-Tuning

arXiv: https://arxiv.org/abs/2508.01348 · HTML: https://mlsanity.com/paper/2508.01348/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 35 references that are in the map.
- First posted on arXiv 2 Aug 2025.

## Builds on (most cited first, 29 of 29)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Fair Resource Allocation in Federated Learning](https://mlsanity.com/paper/1905.10497/) (2019)
- [Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning](https://mlsanity.com/paper/1807.06629/) (2018)
- [Client Selection in Federated Learning: Convergence Analysis and Power-of-Choice Selection Strategies](https://mlsanity.com/paper/2010.01243/) (2020)
- [Towards Building the Federated GPT: Federated Instruction Tuning](https://mlsanity.com/paper/2305.05644/) (2023)
- [Improving LoRA in Privacy-preserving Federated Learning](https://mlsanity.com/paper/2403.12313/) (2024)
- [QA-LoRA: Quantization-Aware Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2309.14717/) (2023)
- [FLoRA: Federated Fine-Tuning Large Language Models with Heterogeneous Low-Rank Adaptations](https://mlsanity.com/paper/2409.05976/) (2024)
- [A Kernel-Based View of Language Model Fine-Tuning](https://mlsanity.com/paper/2210.05643/) (2022)
- [Heterogeneous LoRA for Federated Fine-tuning of On-Device Foundation Models](https://mlsanity.com/paper/2401.06432/) (2024)
- [Selective Aggregation for Low-Rank Adaptation in Federated Learning](https://mlsanity.com/paper/2410.01463/) (2024)
- [Edge Intelligence: The Confluence of Edge Computing and Artificial Intelligence](https://mlsanity.com/paper/1909.00560/) (2019)
- [LoRA-FAIR: Federated LoRA Fine-Tuning with Aggregation and Initialization Refinement](https://mlsanity.com/paper/2411.14961/) (2024)
- [AutoLoRA: Automatically Tuning Matrix Ranks in Low-Rank Adaptation Based on Meta Learning](https://mlsanity.com/paper/2403.09113/) (2024)
- [Towards Robust and Efficient Federated Low-Rank Adaptation with Heterogeneous Clients](https://mlsanity.com/paper/2410.22815/) (2024)
- [FedEx-LoRA: Exact Aggregation for Federated and Efficient Fine-Tuning of Foundation Models](https://mlsanity.com/paper/2410.09432/) (2024)
- [Towards Efficient Communication and Secure Federated Recommendation System via Low-rank Training](https://mlsanity.com/paper/2401.03748/) (2024)
- [Robust Federated Finetuning of Foundation Models via Alternating Minimization of LoRA](https://mlsanity.com/paper/2409.02346/) (2024)
- [Federated Low-Rank Adaptation for Foundation Models: A Survey](https://mlsanity.com/paper/2505.13502/) (2025)
- [RBLA: Rank-Based-LoRA-Aggregation for Fine-tuning Heterogeneous Models in FLaaS](https://mlsanity.com/paper/2408.08699/) (2024)

## Built on by (most cited first, 2 of 2)

- [Subspace-Constrained Federated Learning with Low-Rank Adaptation](https://mlsanity.com/paper/2606.22724/) (2026)
- [FedFit: Federated Fine-Tuning of LLMs via Vector-Bank Parameterization and Quantization](https://mlsanity.com/paper/2610.01537/) (2026)

## Abstract (arXiv)

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.