# Differentially Private Federated Learning with Laplacian Smoothing

arXiv: https://arxiv.org/abs/2005.00218 · HTML: https://mlsanity.com/paper/2005.00218/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2020.

## Built on by (most cited first, 8 of 8)

- [Do Gradient Inversion Attacks Make Federated Learning Unsafe?](https://mlsanity.com/paper/2202.06924/) (2022)
- [Federated Learning with Sparsified Model Perturbation: Improving Accuracy under Client-Level Differential Privacy](https://mlsanity.com/paper/2202.07178/) (2022)
- [Trustworthy Federated Learning: Privacy, Security, and Beyond](https://mlsanity.com/paper/2411.01583/) (2024)
- [DIFF2: Differential Private Optimization via Gradient Differences for Nonconvex Distributed Learning](https://mlsanity.com/paper/2302.03884/) (2023)
- [DP-FedPGN: Finding Global Flat Minima for Differentially Private Federated Learning via Penalizing Gradient Norm](https://mlsanity.com/paper/2510.27504/) (2025)
- [DP-FedAdamW: An Efficient Optimizer for Differentially Private Federated Large Models](https://mlsanity.com/paper/2602.19945/) (2026)
- [Adaptive Selection of LoRA Components in Privacy-Preserving Federated Learning](https://mlsanity.com/paper/2605.05769/) (2026)
- [Privacy-Preserving Heterogeneous Multi-LLM Federated Inference for Cognitive Diagnosis](https://mlsanity.com/paper/2609.02947/) (2026)

## Abstract (arXiv)

Federated learning aims to protect data privacy by collaboratively learning a model without sharing private data among users. However, an adversary may still be able to infer the private training data by attacking the released model. Differential privacy provides a statistical protection against such attacks at the price of significantly degrading the accuracy or utility of the trained models. In this paper, we investigate a utility enhancement scheme based on Laplacian smoothing for differentially private federated learning (DP-Fed-LS), where the parameter aggregation with injected Gaussian noise is improved in statistical precision without losing privacy budget. Our key observation is that the aggregated gradients in federated learning often enjoy a type of smoothness, i.e. sparsity in the graph Fourier basis with polynomial decays of Fourier coefficients as frequency grows, which can be exploited by the Laplacian smoothing efficiently. Under a prescribed differential privacy budget, convergence error bounds with tight rates are provided for DP-Fed-LS with uniform subsampling of heterogeneous Non-IID data, revealing possible utility improvement of Laplacian smoothing in effective dimensionality and variance reduction, among others. Experiments over MNIST, SVHN, and Shakespeare datasets show that the proposed method can improve model accuracy with DP-guarantee and membership privacy under both uniform and Poisson subsampling mechanisms.