# A New Dimensionality Reduction Method Based on Hensel's Compression for Privacy Protection in Federated Learning

arXiv: https://arxiv.org/abs/2205.02089 · HTML: https://mlsanity.com/paper/2205.02089/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 1 May 2022.

## Builds on (most cited first, 6 of 6)

- [Local Model Poisoning Attacks to Byzantine-Robust Federated Learning](https://mlsanity.com/paper/1911.11815/) (2019)
- [Federated Learning with Local Differential Privacy: Trade-offs between Privacy, Utility, and Communication](https://mlsanity.com/paper/2102.04737/) (2021)
- [GRNN: Generative Regression Neural Network -- A Data Leakage Attack for Federated Learning](https://mlsanity.com/paper/2105.00529/) (2021)
- [Privacy Amplification by Decentralization](https://mlsanity.com/paper/2012.05326/) (2020)
- [Three Variants of Differential Privacy: Lossless Conversion and Applications](https://mlsanity.com/paper/2008.06529/) (2020)
- [A Theoretical Perspective on Differentially Private Federated Multi-task Learning](https://mlsanity.com/paper/2011.07179/) (2020)

## Built on by (most cited first, 1 of 1)

- [AI-Driven Secure Data Sharing: A Trustworthy and Privacy-Preserving Approach](https://mlsanity.com/paper/2501.15363/) (2025)

## Abstract (arXiv)

Differential privacy (DP) is considered a de-facto standard for protecting users' privacy in data analysis, machine, and deep learning. Existing DP-based privacy-preserving training approaches consist of adding noise to the clients' gradients before sharing them with the server. However, implementing DP on the gradient is not efficient as the privacy leakage increases by increasing the synchronization training epochs due to the composition theorem. Recently researchers were able to recover images used in the training dataset using Generative Regression Neural Network (GRNN) even when the gradient was protected by DP. In this paper, we propose two layers of privacy protection approach to overcome the limitations of the existing DP-based approaches. The first layer reduces the dimension of the training dataset based on Hensel's Lemma. We are the first to use Hensel's Lemma for reducing the dimension (i.e., compress) of a dataset. The new dimensionality reduction method allows reducing the dimension of a dataset without losing information since Hensel's Lemma guarantees uniqueness. The second layer applies DP to the compressed dataset generated by the first layer. The proposed approach overcomes the problem of privacy leakage due to composition by applying DP only once before the training; clients train their local model on the privacy-preserving dataset generated by the second layer. Experimental results show that the proposed approach ensures strong privacy protection while achieving good accuracy. The new dimensionality reduction method achieves an accuracy of 97%, with only 25 % of the original data size.