# Hierarchical Split Federated Learning: Convergence Analysis and System Optimization

arXiv: https://arxiv.org/abs/2412.07197 · HTML: https://mlsanity.com/paper/2412.07197/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 63 references that are in the map.
- First posted on arXiv 10 Dec 2024.

## Builds on (most cited first, 30 of 37)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning for Mobile Keyboard Prediction](https://mlsanity.com/paper/1811.03604/) (2018)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Adaptive Federated Learning in Resource Constrained Edge Computing Systems](https://mlsanity.com/paper/1804.05271/) (2018)
- [Split learning for health: Distributed deep learning without sharing raw patient data](https://mlsanity.com/paper/1812.00564/) (2018)
- [SplitFed: When Federated Learning Meets Split Learning](https://mlsanity.com/paper/2004.12088/) (2020)
- [Don't Use Large Mini-Batches, Use Local SGD](https://mlsanity.com/paper/1808.07217/) (2018)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [Energy Efficient Federated Learning Over Wireless Communication Networks](https://mlsanity.com/paper/1911.02417/) (2019)
- [On the Linear Speedup Analysis of Communication Efficient Momentum SGD for Distributed Non-Convex Optimization](https://mlsanity.com/paper/1905.03817/) (2019)
- [Efficient Parallel Split Learning over Resource-constrained Wireless Edge Networks](https://mlsanity.com/paper/2303.15991/) (2023)
- [On the convergence properties of a K-step averaging stochastic gradient descent algorithm for nonconvex optimization](https://mlsanity.com/paper/1708.01012/) (2017)
- [Joint Device Scheduling and Resource Allocation for Latency Constrained Wireless Federated Learning](https://mlsanity.com/paper/2007.07174/) (2020)
- [Pushing Large Language Models to the 6G Edge: Vision, Challenges, and Opportunities](https://mlsanity.com/paper/2309.16739/) (2023)
- [Split Learning over Wireless Networks: Parallel Design and Resource Management](https://mlsanity.com/paper/2204.08119/) (2022)
- [Split Learning in 6G Edge Networks](https://mlsanity.com/paper/2306.12194/) (2023)
- [Perturbed Iterate Analysis for Asynchronous Stochastic Optimization](https://mlsanity.com/paper/1507.06970/) (2015)
- [AdaptSFL: Adaptive Split Federated Learning in Resource-constrained Edge Networks](https://mlsanity.com/paper/2403.13101/) (2024)
- [SplitLoRA: A Split Parameter-Efficient Fine-Tuning Framework for Large Language Models](https://mlsanity.com/paper/2407.00952/) (2024)
- [Automated Federated Pipeline for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2404.06448/) (2024)
- [Hierarchical Federated Learning with Quantization: Convergence Analysis and System Design](https://mlsanity.com/paper/2103.14272/) (2021)
- [FedSN: A Federated Learning Framework over Heterogeneous LEO Satellite Networks](https://mlsanity.com/paper/2311.01483/) (2023)
- [Optimal Resource Allocation for U-Shaped Parallel Split Learning](https://mlsanity.com/paper/2308.08896/) (2023)
- [Convergence Analysis and System Design for Federated Learning over Wireless Networks](https://mlsanity.com/paper/2105.00872/) (2021)
- [FedAC: An Adaptive Clustered Federated Learning Framework for Heterogeneous Data](https://mlsanity.com/paper/2403.16460/) (2024)
- [A Bargaining Game for Personalized, Energy Efficient Split Learning over Wireless Networks](https://mlsanity.com/paper/2212.06107/) (2022)
- [SatFed: A Resource-Efficient LEO Satellite-Assisted Heterogeneous Federated Learning Framework](https://mlsanity.com/paper/2409.13503/) (2024)
- [Convergence Analysis of Split Federated Learning on Heterogeneous Data](https://mlsanity.com/paper/2402.15166/) (2024)
- [IFViT: Interpretable Fixed-Length Representation for Fingerprint Matching via Vision Transformer](https://mlsanity.com/paper/2404.08237/) (2024)

## Built on by (most cited first, 30 of 38)

- [HSplitLoRA: A Heterogeneous Split Parameter-Efficient Fine-Tuning Framework for Large Language Models](https://mlsanity.com/paper/2505.02795/) (2025)
- [LEO-Split: A Semi-Supervised Split Learning Framework over LEO Satellite Networks](https://mlsanity.com/paper/2501.01293/) (2025)
- [HASFL: Heterogeneity-aware Split Federated Learning over Edge Computing Systems](https://mlsanity.com/paper/2506.08426/) (2025)
- [Multimodal Multi-Agent Empowered Legal Judgment Prediction](https://mlsanity.com/paper/2601.12815/) (2026)
- [CP-Guard: Malicious Agent Detection and Defense in Collaborative Bird's Eye View Perception](https://mlsanity.com/paper/2412.12000/) (2024)
- [HFedMoE: Resource-aware Heterogeneous Federated Learning with Mixture-of-Experts](https://mlsanity.com/paper/2601.00583/) (2026)
- [PRISM: Privacy-Aware Routing for Adaptive Cloud-Edge LLM Inference via Semantic Sketch Collaboration](https://mlsanity.com/paper/2511.22788/) (2025)
- [State-Aware Perturbation Optimization for Robust Deep Reinforcement Learning](https://mlsanity.com/paper/2503.20613/) (2025)
- [LLM-Driven Stationarity-Aware Expert Demonstrations for Multi-Agent Reinforcement Learning in Mobile Systems](https://mlsanity.com/paper/2511.19368/) (2025)
- [Robust Deep Reinforcement Learning in Robotics via Adaptive Gradient-Masked Adversarial Attacks](https://mlsanity.com/paper/2503.20844/) (2025)
- [Rethinking Membership Inference Attacks Against Transfer Learning](https://mlsanity.com/paper/2501.11577/) (2025)
- [SL-ACC: A Communication-Efficient Split Learning Framework with Adaptive Channel-wise Compression](https://mlsanity.com/paper/2508.12984/) (2025)
- [LEED: A Highly Efficient and Scalable LLM-Empowered Expert Demonstrations Framework for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2509.14680/) (2025)
- [Conflict-Aware Client Selection for Multi-Server Federated Learning](https://mlsanity.com/paper/2602.02458/) (2026)
- [Defensive Adversarial CAPTCHA: A Semantics-Driven Framework for Natural Adversarial Example Generation](https://mlsanity.com/paper/2506.10685/) (2025)
- [Task-Aware Parameter-Efficient Fine-Tuning of Large Pre-Trained Models at the Edge](https://mlsanity.com/paper/2504.03718/) (2025)
- [SFL-LEO: Asynchronous Split-Federated Learning Design for LEO Satellite-Ground Network Framework](https://mlsanity.com/paper/2504.13479/) (2025)
- [Lean Clients, Full Accuracy: Hybrid Zeroth- and First-Order Split Federated Learning](https://mlsanity.com/paper/2601.09076/) (2026)
- [Secure Resource Allocation via Constrained Deep Reinforcement Learning](https://mlsanity.com/paper/2501.11557/) (2025)
- [SHeRL-FL: When Representation Learning Meets Split Learning in Hierarchical Federated Learning](https://mlsanity.com/paper/2508.08339/) (2025)
- [ASFL: An Adaptive Model Splitting and Resource Allocation Framework for Split Federated Learning](https://mlsanity.com/paper/2603.04437/) (2026)
- [SL-FAC: A Communication-Efficient Split Learning Framework with Frequency-Aware Compression](https://mlsanity.com/paper/2604.07316/) (2026)
- [Physically-Induced Atmospheric Adversarial Perturbations: Enhancing Transferability and Robustness in Remote Sensing Image Classification](https://mlsanity.com/paper/2604.14643/) (2026)
- [DP-TRAE: A Dual-Phase Merging Transferable Reversible Adversarial Example for Image Privacy Protection](https://mlsanity.com/paper/2505.06860/) (2025)
- [Federated Split Learning for Resource-Constrained Robots in Industrial IoT: Framework Comparison, Optimization Strategies, and Future Directions](https://mlsanity.com/paper/2510.05713/) (2025)
- [Accelerating Wireless Distributed Learning via Hybrid Split and Federated Learning Optimization](https://mlsanity.com/paper/2511.19851/) (2025)
- [Parallax: Runtime Parallelization for Operator Fallbacks in Heterogeneous Edge Systems](https://mlsanity.com/paper/2512.11532/) (2025)
- [Device Association and Resource Allocation for Hierarchical Split Federated Learning in Space-Air-Ground Integrated Network](https://mlsanity.com/paper/2601.13817/) (2026)
- [Makespan Minimization in Split Learning: From Theory to Practice](https://mlsanity.com/paper/2602.06693/) (2026)
- [Split Federated Learning Architectures for High-Accuracy and Low-Delay Model Training](https://mlsanity.com/paper/2603.08687/) (2026)

## Abstract (arXiv)

As AI models expand in size, it has become increasingly challenging to deploy federated learning (FL) on resource-constrained edge devices. To tackle this issue, split federated learning (SFL) has emerged as an FL framework with reduced workload on edge devices via model splitting; it has received extensive attention from the research community in recent years. Nevertheless, most prior works on SFL focus only on a two-tier architecture without harnessing multi-tier cloudedge computing resources. In this paper, we intend to analyze and optimize the learning performance of SFL under multi-tier systems. Specifically, we propose the hierarchical SFL (HSFL) framework and derive its convergence bound. Based on the theoretical results, we formulate a joint optimization problem for model splitting (MS) and model aggregation (MA). To solve this rather hard problem, we then decompose it into MS and MA subproblems that can be solved via an iterative descending algorithm. Simulation results demonstrate that the tailored algorithm can effectively optimize MS and MA for SFL within virtually any multi-tier system.