# Privacy Preserving Gossip Learning

arXiv: https://arxiv.org/abs/2609.14778 · HTML: https://mlsanity.com/paper/2609.14778/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 13 Sep 2026.

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

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Exploiting Unintended Feature Leakage in Collaborative Learning](https://mlsanity.com/paper/1805.04049/) (2018)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Evaluating Gradient Inversion Attacks and Defenses in Federated Learning](https://mlsanity.com/paper/2112.00059/) (2021)
- [Differentially Private Sharpness-Aware Training](https://mlsanity.com/paper/2306.05651/) (2023)
- [Control in the spaces of ensembles of points](https://mlsanity.com/paper/1907.00905/) (2019)
- [Control Theoretic Approach to Fine-Tuning and Transfer Learning](https://mlsanity.com/paper/2404.11013/) (2024)
- [Geometric Foundations of Tuning without Forgetting in Neural ODEs](https://mlsanity.com/paper/2509.03474/) (2025)
- [Error Bounds for the Method of Simultaneous Projections with Infinitely Many Subspaces](https://mlsanity.com/paper/2007.10664/) (2020)
- [Vector-Valued Gossip over w-Holonomic Networks](https://mlsanity.com/paper/2311.04455/) (2023)
- [Constructing Stochastic Matrices for Weighted Averaging in Gossip Networks](https://mlsanity.com/paper/2502.19821/) (2025)
- [Control Disturbance Rejection in Neural ODEs](https://mlsanity.com/paper/2509.18034/) (2025)

## Abstract (arXiv)

We propose a decentralized privacy-preserving learning algorithm in which each agent holds a single private sample and a shared model. Samples are learned sequentially, and each update must preserve the endpoint mappings at previously learned samples while protecting private data. This gives each agent three roles: (i) a learner that updates the model parameters, (ii) a teacher whose sample is learned at the current iteration, and (iii) a protected agent whose sample has already been learned. We build on Tuning without Forgetting (TwF) method to preserve previously learned mappings and show that TwF provides an indistinguishability guarantee for the learner whenever the set of protected agents contains another sample with the same label. For the teacher, we formulate a minimax optimal control problem that models the differential privacy noise as a worst-case disturbance to prevent performance loss while maintaining the same level of privacy for the gradient. For the protected agents, we compute the projections locally and aggregate them using a private push-sum gossip protocol. We prove geometric convergence of the decentralized gossip algorithm and of the distributed projection for TwF.