# On the Tradeoff between Energy, Precision, and Accuracy in Federated Quantized Neural Networks

arXiv: https://arxiv.org/abs/2111.07911 · HTML: https://mlsanity.com/paper/2111.07911/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 17 references that are in the map.
- First posted on arXiv 15 Nov 2021.

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

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [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)
- [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)
- [Energy Efficient Federated Learning Over Wireless Communication Networks](https://mlsanity.com/paper/1911.02417/) (2019)
- [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)
- [Design and Analysis of Uplink and Downlink Communications for Federated Learning](https://mlsanity.com/paper/2012.04057/) (2020)
- [Energy-Efficient Resource Management for Federated Edge Learning with CPU-GPU Heterogeneous Computing](https://mlsanity.com/paper/2007.07122/) (2020)
- [Minimum Energy Quantized Neural Networks](https://mlsanity.com/paper/1711.00215/) (2017)
- [Communication-Efficient Federated Learning with Binary Neural Networks](https://mlsanity.com/paper/2110.02226/) (2021)
- [A Framework for Energy and Carbon Footprint Analysis of Distributed and Federated Edge Learning](https://mlsanity.com/paper/2103.10346/) (2021)

## Built on by (most cited first, 10 of 10)

- [A Systematic Review of Green AI](https://mlsanity.com/paper/2301.11047/) (2023)
- [A Synthesis of Green Architectural Tactics for ML-Enabled Systems](https://mlsanity.com/paper/2312.09610/) (2023)
- [Wireless Quantized Federated Learning: A Joint Computation and Communication Design](https://mlsanity.com/paper/2203.05878/) (2022)
- [Green, Quantized Federated Learning over Wireless Networks: An Energy-Efficient Design](https://mlsanity.com/paper/2207.09387/) (2022)
- [Over-the-Air Computation Based on Balanced Number Systems for Federated Edge Learning](https://mlsanity.com/paper/2210.07012/) (2022)
- [Federated Learning for 6G: Paradigms, Taxonomy, Recent Advances and Insights](https://mlsanity.com/paper/2312.04688/) (2023)
- [Choosing to Be Green: Advancing Green AI via Dynamic Model Selection](https://mlsanity.com/paper/2509.19996/) (2025)
- [SustainDiffusion: Optimising the Social and Environmental Sustainability of Stable Diffusion Models](https://mlsanity.com/paper/2507.15663/) (2025)
- [Energy-Efficient Quantized Federated Learning for Resource-constrained IoT devices](https://mlsanity.com/paper/2509.12814/) (2025)
- [Quantization in Federated Learning: Methods, Challenges and Future Directions](https://mlsanity.com/paper/2606.26822/) (2026)

## Abstract (arXiv)

Deploying federated learning (FL) over wireless networks with resource-constrained devices requires balancing between accuracy, energy efficiency, and precision. Prior art on FL often requires devices to train deep neural networks (DNNs) using a 32-bit precision level for data representation to improve accuracy. However, such algorithms are impractical for resource-constrained devices since DNNs could require execution of millions of operations. Thus, training DNNs with a high precision level incurs a high energy cost for FL. In this paper, a quantized FL framework, that represents data with a finite level of precision in both local training and uplink transmission, is proposed. Here, the finite level of precision 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 the quantization are rigorously derived. An energy minimization problem is formulated with respect to the level of precision while ensuring convergence. To solve the problem, we first analytically derive the FL convergence rate and use a line search method. Simulation results show that our FL framework can reduce energy consumption by up to 53% compared to a standard FL model. The results also shed light on the tradeoff between precision, energy, and accuracy in FL over wireless networks.