# HO-FL: Hybrid-Order Federated Learning for Heterogeneous Edge Devices

arXiv: https://arxiv.org/abs/2609.39074 · HTML: https://mlsanity.com/paper/2609.39074/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 25 references that are in the map.
- First posted on arXiv 30 Sep 2026.

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

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Federated Learning on Non-IID Data Silos: An Experimental Study](https://mlsanity.com/paper/2102.02079/) (2021)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [Federated Hyperparameter Tuning: Challenges, Baselines, and Connections to Weight-Sharing](https://mlsanity.com/paper/2106.04502/) (2021)
- [On the Unreasonable Effectiveness of Federated Averaging with Heterogeneous Data](https://mlsanity.com/paper/2206.04723/) (2022)
- [A Survey on Federated Fine-tuning of Large Language Models](https://mlsanity.com/paper/2503.12016/) (2025)
- [Achieving Dimension-Free Communication in Federated Learning via Zeroth-Order Optimization](https://mlsanity.com/paper/2405.15861/) (2024)
- [Converge Faster, Talk Less: Hessian-Informed Federated Zeroth-Order Optimization](https://mlsanity.com/paper/2506.02370/) (2025)
- [HOSL: Hybrid-Order Split Learning for Memory-Constrained Edge Training](https://mlsanity.com/paper/2601.10940/) (2026)
- [Lean Clients, Full Accuracy: Hybrid Zeroth- and First-Order Split Federated Learning](https://mlsanity.com/paper/2601.09076/) (2026)
- [HO-SFL: Hybrid-Order Split Federated Learning with Backprop-Free Clients and Dimension-Free Aggregation](https://mlsanity.com/paper/2603.14773/) (2026)

## Abstract (arXiv)

Federated learning (FL) on memory-constrained edge devices faces a dilemma: first-order (FO) optimization (i.e., backpropagation) demands substantial memory, whereas zeroth-order (ZO) optimization suffers from severe convergence slowdown. To resolve this dilemma, we introduce HO-FL, a hybrid-order FL framework that trains a model's bottom segment with ZO optimization and its top segment with FO optimization. Each device can flexibly select its order boundary according to its memory budget while participating in the training of the same global model. Moreover, our convergence analysis reveals a new, fundamental trade-off: clients with larger FO-trained segments can provide more accurate updates, but favoring them can underrepresent other clients' data. We connect this trade-off to the bias and variance of actual multi-step local updates, yielding a sampling optimization problem and a practical dimension-aware approximation with direct model averaging. Experiments on language tasks examine task performance, client memory, and sampling under data heterogeneity. The results show that hybrid-order local training can retain much of the full-FO performance with substantially lower client memory requirements. Our code is available at https://github.com/HKU-WILL-Lab/HO-FL.