# FLoRG: Federated Fine-tuning with Low-rank Gram Matrices and Procrustes Alignment

arXiv: https://arxiv.org/abs/2602.17095 · HTML: https://mlsanity.com/paper/2602.17095/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 34 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 30 of 32)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [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)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [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)
- [FLoRA: Federated Fine-Tuning Large Language Models with Heterogeneous Low-Rank Adaptations](https://mlsanity.com/paper/2409.05976/) (2024)
- [Heterogeneous LoRA for Federated Fine-tuning of On-Device Foundation Models](https://mlsanity.com/paper/2401.06432/) (2024)
- [SLoRA: Federated Parameter Efficient Fine-Tuning of Language Models](https://mlsanity.com/paper/2308.06522/) (2023)
- [Federated Fine-tuning of Large Language Models under Heterogeneous Tasks and Client Resources](https://mlsanity.com/paper/2402.11505/) (2024)
- [Selective Aggregation for Low-Rank Adaptation in Federated Learning](https://mlsanity.com/paper/2410.01463/) (2024)
- [FedBiOT: LLM Local Fine-tuning in Federated Learning without Full Model](https://mlsanity.com/paper/2406.17706/) (2024)
- [Dual-Personalizing Adapter for Federated Foundation Models](https://mlsanity.com/paper/2403.19211/) (2024)
- [Automated Federated Pipeline for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2404.06448/) (2024)
- [FeDeRA:Efficient Fine-tuning of Language Models in Federated Learning Leveraging Weight Decomposition](https://mlsanity.com/paper/2404.18848/) (2024)
- [FedEx-LoRA: Exact Aggregation for Federated and Efficient Fine-Tuning of Foundation Models](https://mlsanity.com/paper/2410.09432/) (2024)

## Built on by (most cited first, 5 of 5)

- [SeFoRA: Sketch-Aggregated Federated Low-Rank Adaptation with Heterogeneous Client Ranks](https://mlsanity.com/paper/2608.10144/) (2026)
- [Accurate and Resource-Efficient Federated Continual Learning](https://mlsanity.com/paper/2606.11480/) (2026)
- [FraQ: Efficient Coordinate-Space Recompression for Federated Low-Rank Adaptation](https://mlsanity.com/paper/2608.03605/) (2026)
- [FedSubMuon: Communication-Efficient Federated LLM Fine-Tuning via Structured Subspace Muon](https://mlsanity.com/paper/2609.06073/) (2026)
- [CFLoRA: Federated Fine-tuning of LLMs with Complementary Factors for Error-free Aggregation](https://mlsanity.com/paper/2609.33147/) (2026)

## Abstract (arXiv)

Parameter-efficient fine-tuning techniques such as low-rank adaptation (LoRA) enable large language models (LLMs) to adapt to downstream tasks efficiently. Federated learning (FL) further facilitates this process by enabling collaborative fine-tuning across distributed clients without sharing private data. However, the use of two separate low-rank matrices in LoRA for federated fine-tuning introduces two types of challenges. First, aggregation error can arise from separately aggregating the two low-rank matrices. Second, even if the server aggregates the product of two low-rank matrices, it needs to decompose the aggregated matrix back into low-rank matrices. Since the decomposition is not unique, it can lead to decomposition drift. To tackle the aforementioned challenges, we propose federated low-rank Gram-matrix aggregation (FLoRG), a federated fine-tuning framework which employs a single low-rank matrix for fine-tuning and aggregates its Gram matrix (i.e., the matrix of inner products of its column vectors). FLoRG can eliminate the aggregation error and reduce the communication overhead. It also minimizes the decomposition drift by introducing a Procrustes alignment approach which aligns the decomposed matrix between consecutive fine-tuning rounds for consistent updates. We theoretically analyze the convergence of FLoRG and prove that adopting the Procrustes alignment results in a tighter convergence bound. Experimental results across multiple LLM fine-tuning benchmarks demonstrate that FLoRG outperforms five state-of-the-art baseline schemes by providing higher downstream task accuracy and can reduce the communication overhead by up to 2041×.