# Differentially Private Federated Low Rank Adaptation Beyond Fixed-Matrix

arXiv: https://arxiv.org/abs/2507.09990 · HTML: https://mlsanity.com/paper/2507.09990/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 44 references that are in the map.
- First posted on arXiv 14 Jul 2025.

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

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [Analyzing Leakage of Personally Identifiable Information in Language Models](https://mlsanity.com/paper/2302.00539/) (2023)
- [MM-SafetyBench: A Benchmark for Safety Evaluation of Multimodal Large Language Models](https://mlsanity.com/paper/2311.17600/) (2023)
- [Subsampled R'enyi Differential Privacy and Analytical Moments Accountant](https://mlsanity.com/paper/1808.00087/) (2018)
- [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)
- [FederatedScope-LLM: A Comprehensive Package for Fine-tuning Large Language Models in Federated Learning](https://mlsanity.com/paper/2309.00363/) (2023)
- [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)
- [SLoRA: Federated Parameter Efficient Fine-Tuning of Language Models](https://mlsanity.com/paper/2308.06522/) (2023)
- [Hypothesis Testing Interpretations and Renyi Differential Privacy](https://mlsanity.com/paper/1905.09982/) (2019)
- [SPA-VL: A Comprehensive Safety Preference Alignment Dataset for Vision Language Model](https://mlsanity.com/paper/2406.12030/) (2024)
- [Selective Aggregation for Low-Rank Adaptation in Federated Learning](https://mlsanity.com/paper/2410.01463/) (2024)
- [Differentially Private Federated Learning on Heterogeneous Data](https://mlsanity.com/paper/2111.09278/) (2021)
- [Differentially Private Low-Rank Adaptation of Large Language Model Using Federated Learning](https://mlsanity.com/paper/2312.17493/) (2023)
- [Concentrated Differentially Private Gradient Descent with Adaptive per-Iteration Privacy Budget](https://mlsanity.com/paper/1808.09501/) (2018)
- [Safe RLHF-V: Safe Reinforcement Learning from Multi-modal Human Feedback](https://mlsanity.com/paper/2503.17682/) (2025)

## 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)
- [Stable-Plastic Subspace Construction for Differentially Private Continual LoRA](https://mlsanity.com/paper/2610.17904/) (2026)

## Abstract (arXiv)

Large language models (LLMs) typically require fine-tuning for domain-specific tasks, and LoRA offers a computationally efficient approach by training low-rank adapters. LoRA is also communication-efficient for federated LLMs when multiple users collaboratively fine-tune a global LLM model without sharing their proprietary raw data. However, even the transmission of local adapters between a server and clients risks serious privacy leakage. Applying differential privacy (DP) to federated LoRA encounters a dilemma: adding noise to both adapters amplifies synthetic noise on the model, while fixing one adapter impairs the learnability of fine-tuning. In this paper, we propose FedASK (Differentially Private Federated Low Rank Adaptation with Double Sketching) , a novel federated LoRA framework to enable effective updating of both low-rank adapters with robust differential privacy. Inspired by randomized SVD, our key idea is a two-stage sketching pipeline. This pipeline first aggregates carefully sketched, privacy-preserving local updates, and then reconstructs the global matrices on the server to facilitate effective updating of both adapters. We theoretically prove FedASK's differential privacy guarantee and its exact aggregation property. Comprehensive experiments demonstrate that FedASK consistently outperforms baseline methods across a variety of privacy settings and data distributions.