# HOSL: Hybrid-Order Split Learning for Memory-Constrained Edge Training

arXiv: https://arxiv.org/abs/2601.10940 · HTML: https://mlsanity.com/paper/2601.10940/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 31 references that are in the map.
- First posted on arXiv 16 Jan 2026.

## Builds on (most cited first, 23 of 23)

- [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)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Split learning for health: Distributed deep learning without sharing raw patient data](https://mlsanity.com/paper/1812.00564/) (2018)
- [WiC: the Word-in-Context Dataset for Evaluating Context-Sensitive Meaning Representations](https://mlsanity.com/paper/1808.09121/) (2018)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [SplitFed: When Federated Learning Meets Split Learning](https://mlsanity.com/paper/2004.12088/) (2020)
- [Efficient Parallel Split Learning over Resource-constrained Wireless Edge Networks](https://mlsanity.com/paper/2303.15991/) (2023)
- [Split Learning for collaborative deep learning in healthcare](https://mlsanity.com/paper/1912.12115/) (2019)
- [SplitLoRA: A Split Parameter-Efficient Fine-Tuning Framework for Large Language Models](https://mlsanity.com/paper/2407.00952/) (2024)
- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [Federated Full-Parameter Tuning of Billion-Sized Language Models with Communication Cost under 18 Kilobytes](https://mlsanity.com/paper/2312.06353/) (2023)
- [Sparse MeZO: Less Parameters for Better Performance in Zeroth-Order LLM Fine-Tuning](https://mlsanity.com/paper/2402.15751/) (2024)
- [HSplitLoRA: A Heterogeneous Split Parameter-Efficient Fine-Tuning Framework for Large Language Models](https://mlsanity.com/paper/2505.02795/) (2025)
- [A Review of Winograd Schema Challenge Datasets and Approaches](https://mlsanity.com/paper/2004.13831/) (2020)
- [Achieving Dimension-Free Communication in Federated Learning via Zeroth-Order Optimization](https://mlsanity.com/paper/2405.15861/) (2024)
- [Towards Straggler-Resilient Split Federated Learning: An Unbalanced Update Approach](https://mlsanity.com/paper/2510.21155/) (2025)
- [VFLAIR-LLM: A Comprehensive Framework and Benchmark for Split Learning of LLMs](https://mlsanity.com/paper/2508.03097/) (2025)

## Built on by (most cited first, 3 of 3)

- [HO-SFL: Hybrid-Order Split Federated Learning with Backprop-Free Clients and Dimension-Free Aggregation](https://mlsanity.com/paper/2603.14773/) (2026)
- [Decoupled Split Learning via Auxiliary Loss](https://mlsanity.com/paper/2601.19261/) (2026)
- [HO-FL: Hybrid-Order Federated Learning for Heterogeneous Edge Devices](https://mlsanity.com/paper/2609.39074/) (2026)

## Abstract (arXiv)

Split learning (SL) enables collaborative training of large language models (LLMs) between resource-constrained edge devices and compute-rich servers by partitioning model computation across the network boundary. However, existing SL systems predominantly rely on first-order (FO) optimization, which requires clients to store intermediate quantities such as activations for backpropagation. This results in substantial memory overhead, largely negating benefits of model partitioning. In contrast, zeroth-order (ZO) optimization eliminates backpropagation and significantly reduces memory usage, but often suffers from slow convergence and degraded performance. In this work, we propose HOSL, a novel Hybrid-Order Split Learning framework that addresses this fundamental trade-off between memory efficiency and optimization effectiveness by strategically integrating ZO optimization on the client side with FO optimization on the server side. By employing memory-efficient ZO gradient estimation at the client, HOSL eliminates backpropagation and activation storage, reducing client memory consumption. Meanwhile, server-side FO optimization ensures fast convergence and competitive performance. Theoretically, we show that HOSL achieves an O(√dc/TQ) rate, which depends on client-side model dimension dc rather than the full model dimension d, demonstrating that convergence improves as more computation is offloaded to the server. Extensive experiments on OPT models (125M and 1.3B parameters) across 6 tasks demonstrate that HOSL reduces client GPU memory by up to 3.7× compared to the FO method while achieving accuracy within 0.20%-4.23% of this baseline. Furthermore, HOSL outperforms the ZO baseline by up to 15.55%, validating the effectiveness of our hybrid strategy for memory-efficient training on edge devices.