# Graph-Homomorphic Perturbations for Private Decentralized Learning

arXiv: https://arxiv.org/abs/2010.12288 · HTML: https://mlsanity.com/paper/2010.12288/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2020.

## Built on by (most cited first, 6 of 6)

- [A Graph Federated Architecture with Privacy Preserving Learning](https://mlsanity.com/paper/2104.13215/) (2021)
- [Networked Signal and Information Processing](https://mlsanity.com/paper/2210.13767/) (2022)
- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [Enforcing Privacy in Distributed Learning with Performance Guarantees](https://mlsanity.com/paper/2301.06412/) (2023)
- [Privatized Graph Federated Learning](https://mlsanity.com/paper/2203.07105/) (2022)
- [Local Graph-homomorphic Processing for Privatized Distributed Systems](https://mlsanity.com/paper/2210.15414/) (2022)

## Abstract (arXiv)

Decentralized algorithms for stochastic optimization and learning rely on the diffusion of information as a result of repeated local exchanges of intermediate estimates. Such structures are particularly appealing in situations where agents may be hesitant to share raw data due to privacy concerns. Nevertheless, in the absence of additional privacy-preserving mechanisms, the exchange of local estimates, which are generated based on private data can allow for the inference of the data itself. The most common mechanism for guaranteeing privacy is the addition of perturbations to local estimates before broadcasting. These perturbations are generally chosen independently at every agent, resulting in a significant performance loss. We propose an alternative scheme, which constructs perturbations according to a particular nullspace condition, allowing them to be invisible (to first order in the step-size) to the network centroid, while preserving privacy guarantees. The analysis allows for general nonconvex loss functions, and is hence applicable to a large number of machine learning and signal processing problems, including deep learning.