# Q-LocalAdam: Memory-Efficient Client-Side Adaptive Optimization for Edge Federated Learning

arXiv: https://arxiv.org/abs/2605.17552 · HTML: https://mlsanity.com/paper/2605.17552/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 30 references that are in the map.
- First posted on arXiv 17 May 2026.

## Builds on (most cited first, 20 of 20)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Federated Learning on Non-IID Data Silos: An Experimental Study](https://mlsanity.com/paper/2102.02079/) (2021)
- [FedMD: Heterogenous Federated Learning via Model Distillation](https://mlsanity.com/paper/1910.03581/) (2019)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [Split learning for health: Distributed deep learning without sharing raw patient data](https://mlsanity.com/paper/1812.00564/) (2018)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [SplitFed: When Federated Learning Meets Split Learning](https://mlsanity.com/paper/2004.12088/) (2020)
- [FedKD: Communication Efficient Federated Learning via Knowledge Distillation](https://mlsanity.com/paper/2108.13323/) (2021)
- [Qsparse-local-SGD: Distributed SGD with Quantization, Sparsification, and Local Computations](https://mlsanity.com/paper/1906.02367/) (2019)
- [FedBE: Making Bayesian Model Ensemble Applicable to Federated Learning](https://mlsanity.com/paper/2009.01974/) (2020)
- [FedPara: Low-Rank Hadamard Product for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2108.06098/) (2021)
- [Local Learning Matters: Rethinking Data Heterogeneity in Federated Learning](https://mlsanity.com/paper/2111.14213/) (2021)
- [Multi-Task Federated Learning for Personalised Deep Neural Networks in Edge Computing](https://mlsanity.com/paper/2007.09236/) (2020)
- [Artificial Intelligence and Statistics](https://mlsanity.com/paper/1712.03779/) (2017)
- [FedSelect: Personalized Federated Learning with Customized Selection of Parameters for Fine-Tuning](https://mlsanity.com/paper/2404.02478/) (2024)
- [Communication-Efficient Federated Learning via Quantized Compressed Sensing](https://mlsanity.com/paper/2111.15071/) (2021)
- [FedHQ: Hybrid Runtime Quantization for Federated Learning](https://mlsanity.com/paper/2505.11982/) (2025)

## Abstract (arXiv)

Federated learning on edge devices must cope with non-IID client data and tight memory budgets. Adaptive optimizers like Adam stabilize training under data heterogeneity but require storing full-precision momentum and variance states, often tripling client memory overhead. This limits deployable model sizes and concurrent federated jobs on resource-constrained devices. We empirically observe that momentum and variance in federated Adam exhibit fundamentally different statistical properties: momentum values are symmetric and bounded, while variance spans eight orders of magnitude with log-normal structure. Motivated by this asymmetry, we propose Q-LocalAdam, which applies distribution-aware 8-bit quantization block-wise linear encoding for momentum and log-space encoding for variance while keeping model parameters in full precision. Across CIFAR-10 and CIFAR-100 under varying data heterogeneity (α ∈ 0.1, 0.5, 1.0, IID), Q-LocalAdam achieves 3.37× optimizer memory reduction with no accuracy loss under moderate heterogeneity and significant improvements under extreme heterogeneity (e.g., +5.74pp on CIFAR-100, α=0.1). Multi-seed validation confirms statistical significance (p<0.01). In contrast, naive uniform quantization degrades to random performance, demonstrating that distribution-aware design is essential. Q-LocalAdam enables larger models and more concurrent workloads on memory-constrained edge devices without modifying the federated protocol.