# Rethinking Factor Sharing in Federated LoRA: A Rank-Aware Adaptive Approach

arXiv: https://arxiv.org/abs/2608.09742 · HTML: https://mlsanity.com/paper/2608.09742/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 38 of its 52 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 38)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning](https://mlsanity.com/paper/1807.06629/) (2018)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Improving LoRA in Privacy-preserving Federated Learning](https://mlsanity.com/paper/2403.12313/) (2024)
- [FederatedScope-LLM: A Comprehensive Package for Fine-tuning Large Language Models in Federated Learning](https://mlsanity.com/paper/2309.00363/) (2023)
- [FLoRA: Federated Fine-Tuning Large Language Models with Heterogeneous Low-Rank Adaptations](https://mlsanity.com/paper/2409.05976/) (2024)
- [LoRA-FA: Efficient and Effective Low Rank Representation Fine-tuning](https://mlsanity.com/paper/2308.03303/) (2023)
- [PromptFL: Let Federated Participants Cooperatively Learn Prompts Instead of Models -- Federated Learning in Age of Foundation Model](https://mlsanity.com/paper/2208.11625/) (2022)
- [HydraLoRA: An Asymmetric LoRA Architecture for Efficient Fine-Tuning](https://mlsanity.com/paper/2404.19245/) (2024)
- [Heterogeneous LoRA for Federated Fine-tuning of On-Device Foundation Models](https://mlsanity.com/paper/2401.06432/) (2024)
- [Federated Fine-tuning of Large Language Models under Heterogeneous Tasks and Client Resources](https://mlsanity.com/paper/2402.11505/) (2024)
- [Asymmetry in Low-Rank Adapters of Foundation Models](https://mlsanity.com/paper/2402.16842/) (2024)
- [Selective Aggregation for Low-Rank Adaptation in Federated Learning](https://mlsanity.com/paper/2410.01463/) (2024)
- [Federated Learning of Large Language Models with Parameter-Efficient Prompt Tuning and Adaptive Optimization](https://mlsanity.com/paper/2310.15080/) (2023)
- [Dual-Personalizing Adapter for Federated Foundation Models](https://mlsanity.com/paper/2403.19211/) (2024)

## Abstract (arXiv)

Low-rank adaptation (LoRA) represents large language model (LLM) updates with two compact matrix factors, i.e., A and B, providing an efficient way to fine-tune large models in federated learning paradigm. Inspired by the asymmetric roles of the LoRA factors, we study whether A should be shared across clients while B remains client-specific (Share-A/Local-B), or whether B should instead be shared while A remains client-specific (Share-B/Local-A). With a least-squares surrogate, we reveal that Share-A/Local-B requires the client-specific LoRA update matrices to use a common rank-r input-side space, whereas Share-B/Local-A requires a common rank-r output-side space. The two strategies therefore incur different projection residuals, indicating that the preferred strategy is the one with the smaller aggregate residual across clients. With this insight, we propose Federated Adaptive Factor Sharing Low-Rank Adaptation (FedAS-LoRA), which selects the sharing side before training to enhance fine-tuning performance. To enable adaptive factor selection before training, we design a Rank-Aware Shared-Subspace Sufficiency (RSS) metric, which effectively assesses whether a shared rank-r input subspace is sufficient for the local data distributions using representations extracted from a frozen LLM backbone. Experiments across different tasks, data distributions, LoRA ranks, and participation settings confirm the effectiveness of RSS and the superior performance of FedAS-LoRA.