# Subspace-Constrained Federated Learning with Low-Rank Adaptation

arXiv: https://arxiv.org/abs/2606.22724 · HTML: https://mlsanity.com/paper/2606.22724/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 13 references that are in the map.
- First posted on arXiv 21 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Fine-tuning of Large Language Models under Heterogeneous Tasks and Client Resources](https://mlsanity.com/paper/2402.11505/) (2024)
- [Guarantees of Riemannian Optimization for Low Rank Matrix Completion](https://mlsanity.com/paper/1603.06610/) (2016)
- [FedSVD: Adaptive Orthogonalization for Private Federated Learning with LoRA](https://mlsanity.com/paper/2505.12805/) (2025)
- [Exploring Gradient Subspaces: Addressing and Overcoming LoRA's Limitations in Federated Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2410.23111/) (2024)
- [Convergence Analysis of Aggregation-Broadcast in LoRA-enabled Distributed Fine-Tuning](https://mlsanity.com/paper/2508.01348/) (2025)

## Abstract (arXiv)

Federated low-rank adaptation methods are attractive for fine-tuning large models under communication and privacy constraints, but heterogeneous client data can induce geometric misalignment between local low-rank updates. We study whether this subspace misalignment leads to destructive aggregation and slower convergence in LoRA-based federated learning. We propose a subspace-regularized federated LoRA objective that encourages local client updates to remain close to a shared global reference subspace. We present a complete empirical evaluation on two pretrained models, RoBERTa-large and SmolLM-360M, over HellaSwag in a non-IID 10-client federated setting, across 3 random seeds (42, 43, 44), yielding 24 total experimental runs (4 methods x 3 seeds x 2 models). On RoBERTa-large, Subspace-Reg achieves the strongest mean best accuracy (0.454 +/- 0.023), mean final accuracy (0.429 +/- 0.011), and lowest final loss (1.363) across all three seeds, outperforming FedAvg, SVD redistribution, and FedSVD baselines by a large margin. On SmolLM-360M, FedAvg leads on accuracy, revealing that accuracy gains are model-dependent. Crucially, Subspace-Reg achieves near-perfect basis overlap, approximately 0.9999, on both models and across all seeds, versus 0.958 to 0.991 for all baselines, providing robust support for the geometric alignment hypothesis. The code is publicly available at https://github.com/sadia-sigma-lab/Subspace-Constrained-Federated-learning-with-Lora.