# Unified Privacy Guarantees for Decentralized Learning via Matrix Factorization

arXiv: https://arxiv.org/abs/2510.17480 · HTML: https://mlsanity.com/paper/2510.17480/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 45 references that are in the map.
- First posted on arXiv 20 Oct 2025.

## Builds on (most cited first, 26 of 26)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Practical and Private (Deep) Learning without Sampling or Shuffling](https://mlsanity.com/paper/2103.00039/) (2021)
- [Asynchronous Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1710.06952/) (2017)
- [Decentralized Federated Learning: A Survey and Perspective](https://mlsanity.com/paper/2306.01603/) (2023)
- [Improved Differential Privacy for SGD via Optimal Private Linear Operators on Adaptive Streams](https://mlsanity.com/paper/2202.08312/) (2022)
- [Personalized and Private Peer-to-Peer Machine Learning](https://mlsanity.com/paper/1705.08435/) (2017)
- [(Amplified) Banded Matrix Factorization: A unified approach to private training](https://mlsanity.com/paper/2306.08153/) (2023)
- [Multi-Epoch Matrix Factorization Mechanisms for Private Machine Learning](https://mlsanity.com/paper/2211.06530/) (2022)
- [Privacy Amplification by Decentralization](https://mlsanity.com/paper/2012.05326/) (2020)
- [Muffliato: Peer-to-Peer Privacy Amplification for Decentralized Optimization and Averaging](https://mlsanity.com/paper/2206.05091/) (2022)
- [Differentially Private Distributed Optimization](https://mlsanity.com/paper/1401.2596/) (2014)
- [On the (In)security of Peer-to-Peer Decentralized Machine Learning](https://mlsanity.com/paper/2205.08443/) (2022)
- [Correlated Noise Provably Beats Independent Noise for Differentially Private Learning](https://mlsanity.com/paper/2310.06771/) (2023)
- [An Accurate, Scalable and Verifiable Protocol for Federated Differentially Private Averaging](https://mlsanity.com/paper/2006.07218/) (2020)
- [Gradient Descent with Linearly Correlated Noise: Theory and Applications to Differential Privacy](https://mlsanity.com/paper/2302.01463/) (2023)
- [The Privacy Power of Correlated Noise in Decentralized Learning](https://mlsanity.com/paper/2405.01031/) (2024)
- [Banded Square Root Matrix Factorization for Differentially Private Model Training](https://mlsanity.com/paper/2405.13763/) (2024)
- [Differentially Private Decentralized Learning with Random Walks](https://mlsanity.com/paper/2402.07471/) (2024)
- [Privacy Attacks in Decentralized Learning](https://mlsanity.com/paper/2402.10001/) (2024)
- [Low-Cost Privacy-Preserving Decentralized Learning](https://mlsanity.com/paper/2403.11795/) (2024)
- [Information-Theoretic Privacy in Distributed Average Consensus](https://mlsanity.com/paper/1809.01794/) (2018)
- [Differential Privacy Analysis of Decentralized Gossip Averaging under Varying Threat Models](https://mlsanity.com/paper/2505.19969/) (2025)
- [Fedivertex: a Graph Dataset based on Decentralized Social Networks for Trustworthy Machine Learning](https://mlsanity.com/paper/2505.20882/) (2025)

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

- [Learning Rate Scheduling with Matrix Factorization for Private Training](https://mlsanity.com/paper/2511.17994/) (2025)
- [Fully Decentralized Certified Unlearning](https://mlsanity.com/paper/2512.08443/) (2025)

## Abstract (arXiv)

Decentralized Learning (DL) enables users to collaboratively train models without sharing raw data by iteratively averaging local updates with neighbors in a network graph. This setting is increasingly popular for its scalability and its ability to keep data local under user control. Strong privacy guarantees in DL are typically achieved through Differential Privacy (DP), with results showing that DL can even amplify privacy by disseminating noise across peer-to-peer communications. Yet in practice, the observed privacy-utility trade-off often appears worse than in centralized training, which may be due to limitations in current DP accounting methods for DL. In this paper, we show that recent advances in centralized DP accounting based on Matrix Factorization (MF) for analyzing temporal noise correlations can also be leveraged in DL. By generalizing existing MF results, we show how to cast both standard DL algorithms and common trust models into a unified formulation. This yields tighter privacy accounting for existing DP-DL algorithms and provides a principled way to develop new ones. To demonstrate the approach, we introduce MAFALDA-SGD, a gossip-based DL algorithm with user-level correlated noise that outperforms existing methods on synthetic and real-world graphs.