# Rethinking LoRA for Data Heterogeneous Federated Learning: Subspace and State Alignment

arXiv: https://arxiv.org/abs/2602.01746 · HTML: https://mlsanity.com/paper/2602.01746/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 70 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 30 of 55)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Federated Learning with Matched Averaging](https://mlsanity.com/paper/2002.06440/) (2020)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Bayesian Nonparametric Federated Learning of Neural Networks](https://mlsanity.com/paper/1905.12022/) (2019)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [A Field Guide to Federated Optimization](https://mlsanity.com/paper/2107.06917/) (2021)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (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)
- [OpenFedLLM: Training Large Language Models on Decentralized Private Data via Federated Learning](https://mlsanity.com/paper/2402.06954/) (2024)

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

- [SeFoRA: Sketch-Aggregated Federated Low-Rank Adaptation with Heterogeneous Client Ranks](https://mlsanity.com/paper/2608.10144/) (2026)
- [FedSmoothLoRA: Toward Smoother and Faster Convergence in Federated Low-Rank Adaptation](https://mlsanity.com/paper/2605.29460/) (2026)

## Abstract (arXiv)

Low-Rank Adaptation (LoRA) is widely used for federated fine-tuning. Yet under non-IID settings, it can substantially underperform full-parameter fine-tuning. Through with-high-probability robustness analysis, we uncover that this gap can be attributed to two coupled mismatches: (i) update-space mismatch, where clients optimize in a low-rank subspace but aggregation occurs in the full space; and (ii) optimizer-state mismatch, where unsynchronized adaptive states amplify drift across rounds. We propose FedGaLore, which combines client-side GaLore-style gradient-subspace optimization with server-side drift-robust synchronization of projected second-moment states via spectral shared-signal extraction, to address this challenge. Across NLU, vision, and NLG benchmarks, FedGaLore improves robustness and accuracy over state-of-the-art federated LoRA baselines in non-IID settings.