# FedSVD: Adaptive Orthogonalization for Private Federated Learning with LoRA

arXiv: https://arxiv.org/abs/2505.12805 · HTML: https://mlsanity.com/paper/2505.12805/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 41 references that are in the map.
- First posted on arXiv 19 May 2025.

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

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [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)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Differentially Private Fine-tuning of Language Models](https://mlsanity.com/paper/2110.06500/) (2021)
- [Opacus: User-Friendly Differential Privacy Library in PyTorch](https://mlsanity.com/paper/2109.12298/) (2021)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [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)
- [LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation](https://mlsanity.com/paper/2306.11222/) (2023)
- [Selective Aggregation for Low-Rank Adaptation in Federated Learning](https://mlsanity.com/paper/2410.01463/) (2024)
- [Delta-LoRA: Fine-Tuning High-Rank Parameters with the Delta of Low-Rank Matrices](https://mlsanity.com/paper/2309.02411/) (2023)
- [Natural Language Understanding with Privacy-Preserving BERT](https://mlsanity.com/paper/2104.07504/) (2021)
- [Natural Language Understanding with the Quora Question Pairs Dataset](https://mlsanity.com/paper/1907.01041/) (2019)
- [The Value of Collaboration in Convex Machine Learning with Differential Privacy](https://mlsanity.com/paper/1906.09679/) (2019)

## Built on by (most cited first, 11 of 11)

- [An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data](https://mlsanity.com/paper/2509.05213/) (2025)
- [SLGNet: Synergizing Structural Priors and Language-Guided Modulation for Multimodal Object Detection](https://mlsanity.com/paper/2601.02249/) (2026)
- [FedMomentum: Preserving LoRA Training Momentum in Federated Fine-Tuning](https://mlsanity.com/paper/2603.08014/) (2026)
- [Task-Agnostic Federated Continual Learning via Replay-Free Gradient Projection](https://mlsanity.com/paper/2509.21606/) (2025)
- [Adaptive Selection of LoRA Components in Privacy-Preserving Federated Learning](https://mlsanity.com/paper/2605.05769/) (2026)
- [SeFoRA: Sketch-Aggregated Federated Low-Rank Adaptation with Heterogeneous Client Ranks](https://mlsanity.com/paper/2608.10144/) (2026)
- [Personalized Federated Learning for Gradient Alignment](https://mlsanity.com/paper/2605.02143/) (2026)
- [Subspace-Constrained Federated Learning with Low-Rank Adaptation](https://mlsanity.com/paper/2606.22724/) (2026)
- [Priority-Aware Learning-Unlearning Correction for Dynamic Decentralized LoRA Fine-Tuning](https://mlsanity.com/paper/2606.22878/) (2026)
- [Federated LoRA Adaptation of BiomedCLIP Across Four International Chest X-Ray Cohorts](https://mlsanity.com/paper/2609.02101/) (2026)
- [Task-Aware Federated Fine-Tuning for MoE-based Large Language Models](https://mlsanity.com/paper/2609.13395/) (2026)

## Abstract (arXiv)

Low-Rank Adaptation (LoRA), which introduces a product of two trainable low-rank matrices into frozen pre-trained weights, is widely used for efficient fine-tuning of language models in federated learning (FL). However, when combined with differentially private stochastic gradient descent (DP-SGD), LoRA faces substantial noise amplification: DP-SGD perturbs per-sample gradients, and the matrix multiplication of the LoRA update (BA) intensifies this effect. Freezing one matrix (e.g., A) reduces the noise but restricts model expressiveness, often resulting in suboptimal adaptation. To address this, we propose textttFedSVD, a simple yet effective method that introduces a global reparameterization based on singular value decomposition (SVD). In our approach, each client optimizes only the B matrix and transmits it to the server. The server aggregates the B matrices, computes the product BA using the previous A, and refactorizes the result via SVD. This yields a new adaptive A composed of the orthonormal right singular vectors of BA, and an updated B containing the remaining SVD components. This reparameterization avoids quadratic noise amplification, while allowing A to better capture the principal directions of the aggregate updates. Moreover, the orthonormal structure of A bounds the gradient norms of B and preserves more signal under DP-SGD, as confirmed by our theoretical analysis. As a result, textttFedSVD consistently improves stability and performance across a variety of privacy settings and benchmarks, outperforming relevant baselines under both private and non-private regimes.