# Green, Quantized Federated Learning over Wireless Networks: An Energy-Efficient Design

arXiv: https://arxiv.org/abs/2207.09387 · HTML: https://mlsanity.com/paper/2207.09387/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 53 references that are in the map.
- First posted on arXiv 19 Jul 2022.

## Builds on (most cited first, 29 of 29)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Green AI](https://mlsanity.com/paper/1907.10597/) (2019)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [Energy Efficient Federated Learning Over Wireless Communication Networks](https://mlsanity.com/paper/1911.02417/) (2019)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [SGD and Hogwild! Convergence Without the Bounded Gradients Assumption](https://mlsanity.com/paper/1802.03801/) (2018)
- [Cost-Effective Federated Learning Design](https://mlsanity.com/paper/2012.08336/) (2020)
- [Ternary Compression for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2003.03564/) (2020)
- [Design and Analysis of Uplink and Downlink Communications for Federated Learning](https://mlsanity.com/paper/2012.04057/) (2020)
- [Motivating Workers in Federated Learning: A Stackelberg Game Perspective](https://mlsanity.com/paper/1908.03092/) (2019)
- [Variance Reduced Stochastic Gradient Descent with Neighbors](https://mlsanity.com/paper/1506.03662/) (2015)
- [Energy-Efficient Resource Management for Federated Edge Learning with CPU-GPU Heterogeneous Computing](https://mlsanity.com/paper/2007.07122/) (2020)
- [Energy Efficient Federated Learning over Heterogeneous Mobile Devices via Joint Design of Weight Quantization and Wireless Transmission](https://mlsanity.com/paper/2012.11070/) (2020)
- [Minimum Energy Quantized Neural Networks](https://mlsanity.com/paper/1711.00215/) (2017)
- [The Impact of the Mini-batch Size on the Variance of Gradients in Stochastic Gradient Descent](https://mlsanity.com/paper/2004.13146/) (2020)
- [An Energy and Carbon Footprint Analysis of Distributed and Federated Learning](https://mlsanity.com/paper/2206.10380/) (2022)
- [Wireless Quantized Federated Learning: A Joint Computation and Communication Design](https://mlsanity.com/paper/2203.05878/) (2022)
- [Communication-Efficient Federated Learning with Binary Neural Networks](https://mlsanity.com/paper/2110.02226/) (2021)
- [On the Tradeoff between Energy, Precision, and Accuracy in Federated Quantized Neural Networks](https://mlsanity.com/paper/2111.07911/) (2021)
- [Multi-Objective Signal Processing Optimization: The Way to Balance Conflicting Metrics in 5G Systems](https://mlsanity.com/paper/1406.2871/) (2014)
- [Exploiting Local Convergence of Quasi-Newton Methods Globally: Adaptive Sample Size Approach](https://mlsanity.com/paper/2106.05445/) (2021)

## Built on by (most cited first, 15 of 15)

- [Green Edge AI: A Contemporary Survey](https://mlsanity.com/paper/2312.00333/) (2023)
- [Federated Learning Priorities Under the European Union Artificial Intelligence Act](https://mlsanity.com/paper/2402.05968/) (2024)
- [Federated Learning for 6G: Paradigms, Taxonomy, Recent Advances and Insights](https://mlsanity.com/paper/2312.04688/) (2023)
- [Energy-Efficient Channel Decoding for Wireless Federated Learning: Convergence Analysis and Adaptive Design](https://mlsanity.com/paper/2407.13703/) (2024)
- [Communication-Efficient Federated Learning by Quantized Variance Reduction for Heterogeneous Wireless Edge Networks](https://mlsanity.com/paper/2501.11267/) (2025)
- [SusFL: Energy-Aware Federated Learning-based Monitoring for Sustainable Smart Farms](https://mlsanity.com/paper/2402.10280/) (2024)
- [Online-Score-Aided Federated Learning for Resource-Constrained Wireless Clients with Continual Data Arrival](https://mlsanity.com/paper/2408.05886/) (2024)
- [Communication and Energy Efficient Federated Learning using Zero-Order Optimization Technique](https://mlsanity.com/paper/2409.16456/) (2024)
- [Deploying Large AI Models on Resource-Limited Devices with Split Federated Learning](https://mlsanity.com/paper/2504.09114/) (2025)
- [Pareto Actor-Critic for Communication and Computation Co-Optimization in Non-Cooperative Federated Learning Services](https://mlsanity.com/paper/2508.16037/) (2025)
- [Transformers for Green Semantic Communication: Less Energy, More Semantics](https://mlsanity.com/paper/2310.07592/) (2023)
- [MetaGreen: Meta-Learning Inspired Transformer Selection for Green Semantic Communication](https://mlsanity.com/paper/2406.16962/) (2024)
- [FairEnergy: Contribution-Based Fairness meets Energy Efficiency in Federated Learning](https://mlsanity.com/paper/2511.15454/) (2025)
- [Standardized Methods and Recommendations for Green Federated Learning](https://mlsanity.com/paper/2602.00343/) (2026)
- [GQ-FSL: Green Quantized Federated Split Learning Framework for Wireless Edge Networks](https://mlsanity.com/paper/2607.29659/) (2026)

## Abstract (arXiv)

In this paper, a green-quantized FL framework, which represents data with a finite precision level in both local training and uplink transmission, is proposed. Here, the finite precision level is captured through the use of quantized neural networks (QNNs) that quantize weights and activations in fixed-precision format. In the considered FL model, each device trains its QNN and transmits a quantized training result to the base station. Energy models for the local training and the transmission with quantization are rigorously derived. To minimize the energy consumption and the number of communication rounds simultaneously, a multi-objective optimization problem is formulated with respect to the number of local iterations, the number of selected devices, and the precision levels for both local training and transmission while ensuring convergence under a target accuracy constraint. To solve this problem, the convergence rate of the proposed FL system is analytically derived with respect to the system control variables. Then, the Pareto boundary of the problem is characterized to provide efficient solutions using the normal boundary inspection method. Design insights on balancing the tradeoff between the two objectives while achieving a target accuracy are drawn from using the Nash bargaining solution and analyzing the derived convergence rate. Simulation results show that the proposed FL framework can reduce energy consumption until convergence by up to 70% compared to a baseline FL algorithm that represents data with full precision without damaging the convergence rate.