HEFSL： high-efficient federated split learning framework for edge heterogeneity

doi:10.11772/j.issn.1001-9081.2025050601

Journal of Computer Applications ›› 2026, Vol. 46 ›› Issue (5): 1397-1407.DOI: 10.11772/j.issn.1001-9081.2025050601

• Artificial intelligence • Previous Articles

HEFSL： high-efficient federated split learning framework for edge heterogeneity

Hao YU¹^,²^,³, Jing FAN¹^,²^,³(), Enkang XI¹^,²^,³, Yadong JIN¹^,²^,³, Hua DONG¹^,²^,³, Yihang SUN¹^,²^,³

^1.College of Electrical and Information Technology，Yunnan Minzu University，Kunming Yunnan 650000，China
^2.Yunnan Key Laboratory of Unmanned Autonomous System（Yunnan Minzu University），Kunming Yunan，650500，China
^3.Key Laboratory of Information and Communication Security and Disaster Recovery in Universities of Yunnan Province （Yunnan Minzu University），Kunming Yunan 650500，China

Received:2025-05-30 Revised:2025-08-20 Accepted:2025-08-28 Online:2025-09-05 Published:2026-05-10
Contact: Jing FAN
About author:YU Hao， born in 2000， M. S. candidate. His research interests include federated learning， split learning， wireless edge intelligence.
XI Enkang， born in 2000， M. S. candidate. His research interests include federated learning， privacy security.
JIN Yadong， born in 1998， M. S. candidate. His research interests include federated learning， space-air-ground integrated network.
DONG Hua， born in 2001， M. S. candidate. His research interests include federated learning， computational efficiency optimization.
SUN Yihang， born in 2001， M. S. candidate. His research interests include federated learning， asynchronous communication.
Supported by:
2023 China University Industry-Academic-Research Innovation Fund — New Generation Information Technology Innovation Project(2023IT077);Scientific Research Foundation of Education Department of Yunnan Province(2025Y0670);Project of Wu Zhonghai Expert Workstation(202305AF150045)

边缘异构下的高效联邦分割学习框架HEFSL

俞浩¹^,²^,³, 范菁¹^,²^,³(), 郗恩康¹^,²^,³, 金亚东¹^,²^,³, 董华¹^,²^,³, 孙伊航¹^,²^,³

^1.云南民族大学电气信息工程学院，昆明 650000
^2.云南省无人自主系统重点实验室（云南民族大学），昆明 650500
^3.云南省高校信息与通信安全灾备重点实验室（云南民族大学），昆明 650500

通讯作者: 范菁
作者简介:俞浩（2000—），男，湖北咸宁人，硕士研究生，CCF会员，主要研究方向：联邦学习、分割学习、无线边缘智能
郗恩康（2000—），男，山东枣庄人，硕士研究生，主要研究方向：联邦学习、隐私安全
金亚东（1998—），男（彝族），云南曲靖人，硕士研究生，主要研究方向：联邦学习、空天地一体化网络
董华（2001—），男，山西运城人，硕士研究生，主要研究方向：联邦学习、计算效率优化
孙伊航（2001—），男（回族），河南许昌人，硕士研究生，主要研究方向：联邦学习、异步通信。
基金资助:
2023年中国高校产学研创新基金—新一代信息技术创新项目(2023IT077);云南省教育厅科学研究基金资助项目(2025Y0670);云南省吴中海专家工作站项目(202305AF150045)

1. .pdf(272KB)

Abstract

Abstract:

Federated Learning （FL） in edge-heterogeneous environments faces challenges such as significant disparities in terminal computing capabilities， inconsistent data distributions， and high communication overhead， which severely constrain its deployment and application in practical intelligent systems. To address these issues， a High-Efficiency Federated Split Learning （HEFSL） framework was proposed by integrating the advantages of FL and Split Learning （SL）. Through a triple mechanism of “model partitioning， client selection， and dual-layer aggregation”， HEFSL achieves joint optimization of system and statistical heterogeneity. In the HEFSL framework， an Adaptive Splitting Strategy （ASS） was first introduced to dynamically determine the model partition structure based on the computing capacity of each client， alleviating the straggler effect. Secondly， a Client Diversity-based Heuristic Selection （CDHS） mechanism was designed， using a low-complexity label-entropy-driven strategy to enhance data representativeness. Finally， an Asynchronous Dual-end Aggregation （ADA） scheme was developed to enable layered asynchronous updates between clients and edge servers， breaking the synchronous communication bottleneck and accelerating model convergence. The theoretical section provided a rigorous analysis and proof of the convergence and error bounds of the HEFSL framework. Experimental results on three datasets with label heterogeneity characteristics， FMNIST， CIFAR-10， and CIFAR-100， showed that HEFSL achieved the highest model accuracy， outperforming FedAvg， FedProx （Federated Proximal）， MOON （MOdel-cONtrastive learning）， Federated Split learning （SplitFed）， SplitMix （Split Mixing）， and FedCRS （Federated Cluster-based Round Splitting） by at least 4.3， 10.5， and 4.1 percentage points， respectively. Additionally， its convergence speed was improved by at least 78.6%， 89.8%， and 64.5%， respectively. HEFSL exhibits significant advantages in distributed collaborative intelligence for edge-heterogeneous scenarios， providing a practical pathway for efficient and scalable federated learning in resource-constrained environments with strong engineering adaptability and application prospects.

Key words: Federated Learning (FL), Split Learning (SL), distributed optimization, resource constrained, heterogeneity

摘要：

边缘异构环境下的联邦学习（FL）面临终端算力差异大、数据分布不一致及通信开销高等挑战，严重制约了它在实际智能系统中的部署与应用。因此，提出一种高效联邦分割学习（HEFSL）框架，融合FL与分割学习（SL）的优势，通过“模型切分-客户端选择-双层聚合”的三重机制，实现系统异构性与统计异构性的协同优化。HEFSL框架中，首先引入自适应分割策略（ASS），依据客户端计算能力动态确定模型切分结构，缓解“落后者”效应；其次设计基于多样性的启发式客户端选择（CDHS）机制，基于标签熵驱动的低复杂度策略提升数据代表性；最后构建异步双端聚合（ADA）方案，在客户端与边缘服务器间实现分层异步更新，突破同步通信瓶颈，加快模型收敛。理论部分对HEFSL框架的收敛性与误差上界进行了严格分析与证明。在3个具有标签异构特征的数据集FMNIST、CIFAR-10与CIFAR-100上的实验结果表明，HEFSL的模型精度表现最优，相较于FedAvg、FedProx（Federated Proximal）、MOON（MOdel-cONtrastive learning）、联邦分割学习（SplitFed）、SplitMix（Split Mixing）与FedCRS（Federated Cluster-based Round Splitting）分别至少提高了4.3、10.5与4.1个百分点；同时，在收敛速度上分别至少提升78.6%、89.8%与64.5%。HEFSL在面向边缘异构场景的分布式协同智能中优势明显，可为资源受限环境下高效、可扩展的联邦学习提供一种可行路径，具备良好的工程适应性与应用前景。

关键词: 联邦学习, 分割学习, 分布式优化, 资源受限, 异构性

CLC Number:

TP399

Hao YU, Jing FAN, Enkang XI, Yadong JIN, Hua DONG, Yihang SUN. HEFSL： high-efficient federated split learning framework for edge heterogeneity[J]. Journal of Computer Applications, 2026, 46(5): 1397-1407.

俞浩, 范菁, 郗恩康, 金亚东, 董华, 孙伊航. 边缘异构下的高效联邦分割学习框架HEFSL[J]. 《计算机应用》唯一官方网站, 2026, 46(5): 1397-1407.

Figures/Tables 11

Fig. 1 General processes of federated learning and split learning

Fig. 2 General process of federated split learning

Fig. 3 Schematic diagram of HEFSL framework

Tab. 1 Main symbols in this paper

符号	描述	符号	描述	符号	描述
$K$	客户端数量	$v k$	客户端k的标签分布向量	$w s'$	所有边缘服务器子模型聚合后的模型
$f k$	客户端k的计算能力	$P$	全局客户端参与率	$τ 1$	客户端子模型聚合周期
$L$	完整的神经网络层数	$ζ$	启发式阶段随机客户端选择比例	$τ 2$	边缘服务器子模型聚合周期
$ψ k$	客户端k的负载系数	$K m t, r e m$	第t轮次边缘簇m待选择客户端集合	$f (w T)$	第T轮次全局损失
$s k$	客户端k的模型切割点	$K m t, s e l$	第t轮边缘簇m已选择客户端集合	$a k$	客户端k的权重
$M$	边缘服务器可用数量	$w k$	客户端k的局部子模型	$e$	边缘服务器子模型冗余传播次数
$C m$	第m个边缘簇	$w c m$	边缘簇m客户端聚合后客户端子模型
$K m t$	第t轮边缘簇m客户端集合	$w s m$	边缘簇m的边缘服务器子模型

Tab. 1 Main symbols in this paper

符号	描述	符号	描述	符号	描述
$K$	客户端数量	$v k$	客户端k的标签分布向量	$w s'$	所有边缘服务器子模型聚合后的模型
$f k$	客户端k的计算能力	$P$	全局客户端参与率	$τ 1$	客户端子模型聚合周期
$L$	完整的神经网络层数	$ζ$	启发式阶段随机客户端选择比例	$τ 2$	边缘服务器子模型聚合周期
$ψ k$	客户端k的负载系数	$K m t, r e m$	第t轮次边缘簇m待选择客户端集合	$f (w T)$	第T轮次全局损失
$s k$	客户端k的模型切割点	$K m t, s e l$	第t轮边缘簇m已选择客户端集合	$a k$	客户端k的权重
$M$	边缘服务器可用数量	$w k$	客户端k的局部子模型	$e$	边缘服务器子模型冗余传播次数
$C m$	第m个边缘簇	$w c m$	边缘簇m客户端聚合后客户端子模型
$K m t$	第t轮边缘簇m客户端集合	$w s m$	边缘簇m的边缘服务器子模型

Tab. 2 Datasets and configurations used in experiments

数据集	模型	学习率	衰减率	客户端类别数
FMNIST	2 conv +2 fc	0.10	0.980	2
CIFAR-10	VGG-16	0.03	0.997	2
CIFAR-100	VGG-19	0.03	0.998	20

Tab. 3 Accuracy comparison of various methods on different datasets

方法	FMNIST	CIFAR-10	CIFAR-100
FedAvg	71.4	41.7	29.6
FedProx	73.6	51.6	38.8
MOON	74.8	54.1	42.3
SplitFed	74.1	67.8	28.3
SplitMix	70.8	54.3	32.7
FedCRS	83.8	72.3	41.1
HEFSL	88.1	82.8	46.4

Fig. 4 Trend comparison of accuracies of various methods with training round count

Tab. 4 Minimum communication rounds required to reach precision threshold

方法	达到精度阈值的最低轮次
方法	FMNIST	CIFAR-10	CIFAR-100
FedAvg	72	≥500	983
FedProx	35	371	358
MOON	98	363	387
SplitFed	33	137	967
SplitMix	81	319	492
FedCRS	14	158	533
HEFSL	3	14	127

Tab. 5 Running time comparison to reach target precision

方法	FMNIST	CIFAR-10	CIFAR-100
SplitFed	68.97	252.32	1 801.52
SplitMix	156.29	591.43	916.61
FedCRS	29.36	292.53	992.93
HEFSL	7.27	25.76	236.60

Tab. 6 Precisions under different aggregation frequencies τ1 and τ2 on FMNIST dataset

$τ 1$	$τ 2$
$τ 1$	1	2	3	4	5	6	7	8
1	0.881 2	0.878 7	0.865 4	0.860 5	0.857 1	0.850 7	0.846 3	0.843 4
2	0.886 2	0.881 2	0.868 5	0.864 0	0.861 1	0.846 6	0.844 9	0.840 3
3	0.892 5	0.878 7	0.871 3	0.863 7	0.849 3	0.858 8	0.849 6	0.842 7
4	0.893 9	0.879 3	0.873 1	0.865 0	0.850 0	0.843 5	0.843 2	0.834 3
5	0.889 9	0.881 9	0.868 6	0.863 6	0.861 2	0.842 0	0.843 3	0.838 1
6	0.890 4	0.884 6	0.872 5	0.862 5	0.861 9	0.853 2	0.848 4	0.844 1
7	0.889 9	0.879 1	0.866 5	0.864 9	0.848 3	0.850 5	0.844 5	0.842 4
8	0.892 2	0.878 1	0.873 2	0.867 3	0.858 0	0.840 5	0.852 0	0.838 7

Tab. 6 Precisions under different aggregation frequencies τ1 and τ2 on FMNIST dataset

$τ 1$	$τ 2$
$τ 1$	1	2	3	4	5	6	7	8
1	0.881 2	0.878 7	0.865 4	0.860 5	0.857 1	0.850 7	0.846 3	0.843 4
2	0.886 2	0.881 2	0.868 5	0.864 0	0.861 1	0.846 6	0.844 9	0.840 3
3	0.892 5	0.878 7	0.871 3	0.863 7	0.849 3	0.858 8	0.849 6	0.842 7
4	0.893 9	0.879 3	0.873 1	0.865 0	0.850 0	0.843 5	0.843 2	0.834 3
5	0.889 9	0.881 9	0.868 6	0.863 6	0.861 2	0.842 0	0.843 3	0.838 1
6	0.890 4	0.884 6	0.872 5	0.862 5	0.861 9	0.853 2	0.848 4	0.844 1
7	0.889 9	0.879 1	0.866 5	0.864 9	0.848 3	0.850 5	0.844 5	0.842 4
8	0.892 2	0.878 1	0.873 2	0.867 3	0.858 0	0.840 5	0.852 0	0.838 7

Fig. 5 Precision variation under different random selection ratios ζ on FMNIST dataset

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HEFSL： high-efficient federated split learning framework for edge heterogeneity

边缘异构下的高效联邦分割学习框架HEFSL

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