# Leveraging Channel Noise for Sampling and Privacy via Quantized Federated Langevin Monte Carlo

arXiv: https://arxiv.org/abs/2202.13932 · HTML: https://mlsanity.com/paper/2202.13932/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 17 of 17)

- [Edge Intelligence: Paving the Last Mile of Artificial Intelligence with Edge Computing](https://mlsanity.com/paper/1905.10083/) (2019)
- [Understanding Gradient Clipping in Private SGD: A Geometric Perspective](https://mlsanity.com/paper/2006.15429/) (2020)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [The Bayesian Learning Rule](https://mlsanity.com/paper/2107.04562/) (2021)
- [Towards an Intelligent Edge: Wireless Communication Meets Machine Learning](https://mlsanity.com/paper/1809.00343/) (2018)
- [Wireless Network Intelligence at the Edge](https://mlsanity.com/paper/1812.02858/) (2018)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo](https://mlsanity.com/paper/1502.07645/) (2015)
- [Privacy For Free: Wireless Federated Learning Via Uncoded Transmission With Adaptive Power Control](https://mlsanity.com/paper/2006.05459/) (2020)
- [Wireless Federated Learning with Local Differential Privacy](https://mlsanity.com/paper/2002.05151/) (2020)
- [Optimized Power Control Design for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2106.09316/) (2021)
- [Stochastic-Sign SGD for Federated Learning with Theoretical Guarantees](https://mlsanity.com/paper/2002.10940/) (2020)
- [Machine Learning in the Air](https://mlsanity.com/paper/1904.12385/) (2019)
- [Over-the-Air Computation Systems: Optimization, Analysis and Scaling Laws](https://mlsanity.com/paper/1909.00329/) (2019)
- [Patterns of Scalable Bayesian Inference](https://mlsanity.com/paper/1602.05221/) (2016)
- [Differentially Private AirComp Federated Learning with Power Adaptation Harnessing Receiver Noise](https://mlsanity.com/paper/2004.06337/) (2020)
- [Wireless Federated Langevin Monte Carlo: Repurposing Channel Noise for Bayesian Sampling and Privacy](https://mlsanity.com/paper/2108.07644/) (2021)

## Built on by (most cited first, 3 of 3)

- [Joint Privacy Enhancement and Quantization in Federated Learning](https://mlsanity.com/paper/2208.10888/) (2022)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Federated Averaging Langevin Dynamics: Toward a unified theory and new algorithms](https://mlsanity.com/paper/2211.00100/) (2022)

## Abstract (arXiv)

For engineering applications of artificial intelligence, Bayesian learning holds significant advantages over standard frequentist learning, including the capacity to quantify uncertainty. Langevin Monte Carlo (LMC) is an efficient gradient-based approximate Bayesian learning strategy that aims at producing samples drawn from the posterior distribution of the model parameters. Prior work focused on a distributed implementation of LMC over a multi-access wireless channel via analog modulation. In contrast, this paper proposes quantized federated LMC (FLMC), which integrates one-bit stochastic quantization of the local gradients with channel-driven sampling. Channel-driven sampling leverages channel noise for the purpose of contributing to Monte Carlo sampling, while also serving the role of privacy mechanism. Analog and digital implementations of wireless LMC are compared as a function of differential privacy (DP) requirements, revealing the advantages of the latter at sufficiently high signal-to-noise ratio.