# FraQ: Efficient Coordinate-Space Recompression for Federated Low-Rank Adaptation

arXiv: https://arxiv.org/abs/2608.03605 · HTML: https://mlsanity.com/paper/2608.03605/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 30 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 21 of 21)

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- [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)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Efficient Intent Detection with Dual Sentence Encoders](https://mlsanity.com/paper/2003.04807/) (2020)
- [An Evaluation Dataset for Intent Classification and Out-of-Scope Prediction](https://mlsanity.com/paper/1909.02027/) (2019)
- [Benchmarking Natural Language Understanding Services for building Conversational Agents](https://mlsanity.com/paper/1903.05566/) (2019)
- [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)
- [Federated Fine-tuning of Large Language Models under Heterogeneous Tasks and Client Resources](https://mlsanity.com/paper/2402.11505/) (2024)
- [Accurate and Efficient Low-Rank Model Merging in Core Space](https://mlsanity.com/paper/2509.17786/) (2025)
- [Towards Robust and Efficient Federated Low-Rank Adaptation with Heterogeneous Clients](https://mlsanity.com/paper/2410.22815/) (2024)
- [FLoRG: Federated Fine-tuning with Low-rank Gram Matrices and Procrustes Alignment](https://mlsanity.com/paper/2602.17095/) (2026)
- [FedMomentum: Preserving LoRA Training Momentum in Federated Fine-Tuning](https://mlsanity.com/paper/2603.08014/) (2026)
- [Spectral Transformation for Layer-wise Global Rank Discovery in Federated LoRA for Vision Transformers](https://mlsanity.com/paper/2607.21074/) (2026)

## Abstract (arXiv)

Federated fine-tuning with Low-Rank Adaptation (LoRA) enables efficient collaborative adaptation of Large Language Models (LLMs) without centralizing private data. However, LoRA's two-factor parameterization creates an aggregation mismatch across clients: naively averaging the factors does not recover the average of their induced updates. This mismatch can be avoided by forming the exact aggregate in the full weight space and then recompressing it, but decomposing the resulting dense matrix is computationally expensive and memory-intensive. We propose FraQ, an efficient coordinate-space recompression method for federated LoRA. Starting from stacked factors that exactly represent the aggregate, FraQ factorizes it into an orthonormal basis and a compact coordinate matrix. It then recovers the singular spectrum from a small Gram matrix, selects the smallest rank satisfying a prescribed energy threshold, and maps the selected coordinate subspace back through the basis to construct the global adapter. Experiments on text classification and commonsense reasoning benchmarks show that FraQ achieves accuracy close to uncompressed baselines while substantially reducing downlink communication with low server-side recompression overhead.