# Fractional-Order Federated Learning

arXiv: https://arxiv.org/abs/2602.15380 · HTML: https://mlsanity.com/paper/2602.15380/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 17 Feb 2026.

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

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [EMNIST: an extension of MNIST to handwritten letters](https://mlsanity.com/paper/1702.05373/) (2017)
- [MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysis](https://mlsanity.com/paper/2010.14925/) (2020)
- [Convolutional neural networks with fractional order gradient method](https://mlsanity.com/paper/1905.05336/) (2019)
- [Sparsified Secure Aggregation for Privacy-Preserving Federated Learning](https://mlsanity.com/paper/2112.12872/) (2021)
- [Decentralized and Robust Privacy-Preserving Model Using Blockchain-Enabled Federated Deep Learning in Intelligent Enterprises](https://mlsanity.com/paper/2502.17485/) (2025)
- [Federated Learning with Domain Shift Eraser](https://mlsanity.com/paper/2503.13063/) (2025)
- [A Lightweight and Secure Deep Learning Model for Privacy-Preserving Federated Learning in Intelligent Enterprises](https://mlsanity.com/paper/2503.02017/) (2025)

## Abstract (arXiv)

Federated learning (FL) allows remote clients to train a global model collaboratively while protecting client privacy. Despite its privacy-preserving benefits, FL has significant drawbacks, including slow convergence, high communication cost, and non-independent-and-identically-distributed (non-IID) data. In this work, we present a novel FedAvg variation called Fractional-Order Federated Averaging (FOFedAvg), which incorporates Fractional-Order Stochastic Gradient Descent (FOSGD) to capture long-range relationships and deeper historical information. By introducing memory-aware fractional-order updates, FOFedAvg improves communication efficiency and accelerates convergence while mitigating instability caused by heterogeneous, non-IID client data. We compare FOFedAvg against a broad set of established federated optimization algorithms on benchmark datasets including MNIST, FEMNIST, CIFAR-10, CIFAR-100, EMNIST, the Cleveland heart disease dataset, Sent140, PneumoniaMNIST, and Edge-IIoTset. Across a range of non-IID partitioning schemes, FOFedAvg is competitive with, and often outperforms, these baselines in terms of test performance and convergence speed. On the theoretical side, we prove that FOFedAvg converges to a stationary point under standard smoothness and bounded-variance assumptions for fractional order 0<α≤ 1. Together, these results show that fractional-order, memory-aware updates can substantially improve the robustness and effectiveness of federated learning, offering a practical path toward distributed training on heterogeneous data.