# Multi-Hop Privacy Propagation for Differentially Private Federated Learning in Social Networks

arXiv: https://arxiv.org/abs/2508.07676 · HTML: https://mlsanity.com/paper/2508.07676/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 11 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [LDP-Fed: Federated Learning with Local Differential Privacy](https://mlsanity.com/paper/2006.03637/) (2020)
- [Source Inference Attacks in Federated Learning](https://mlsanity.com/paper/2109.05659/) (2021)
- [Central Server Free Federated Learning over Single-sided Trust Social Networks](https://mlsanity.com/paper/1910.04956/) (2019)
- [Joint Auction-Coalition Formation Framework for Communication-Efficient Federated Learning in UAV-Enabled Internet of Vehicles](https://mlsanity.com/paper/2007.06378/) (2020)
- [Task-Agnostic Privacy-Preserving Representation Learning for Federated Learning Against Attribute Inference Attacks](https://mlsanity.com/paper/2312.06989/) (2023)
- [Robust Federated Learning Mitigates Client-side Training Data Distribution Inference Attacks](https://mlsanity.com/paper/2403.03149/) (2024)
- [A New Federated Learning Framework Against Gradient Inversion Attacks](https://mlsanity.com/paper/2412.07187/) (2024)
- [Trade Privacy for Utility: A Learning-Based Privacy Pricing Game in Federated Learning](https://mlsanity.com/paper/2301.08474/) (2023)

## Abstract (arXiv)

Federated learning (FL) enables collaborative model training across decentralized clients without sharing local data, thereby enhancing privacy and facilitating collaboration among clients connected via social networks. However, these social connections introduce privacy externalities: a client's privacy loss depends not only on its privacy protection strategy but also on the privacy decisions of others, propagated through the network via multi-hop interactions. In this work, we propose a socially-aware privacy-preserving FL mechanism that systematically quantifies indirect privacy leakage through a multi-hop propagation model. We formulate the server-client interaction as a two-stage Stackelberg game, where the server, as the leader, optimizes incentive policies, and clients, as followers, strategically select their privacy budgets, which determine their privacy-preserving levels by controlling the magnitude of added noise. To mitigate information asymmetry in networked privacy estimation, we introduce a mean-field estimator to approximate the average external privacy risk. We theoretically prove the existence and convergence of the fixed point of the mean-field estimator and derive closed-form expressions for the Stackelberg Nash Equilibrium. Despite being designed from a client-centric incentive perspective, our mechanism achieves approximately-optimal social welfare, as revealed by Price of Anarchy (PoA) analysis. Experiments on diverse datasets demonstrate that our approach significantly improves client utilities and reduces server costs while maintaining model performance, outperforming both Social-Agnostic (SA) baselines and methods that account for social externalities.