Abstract--Federated split learning (FedSL) has emerged as a promising paradigm for enabling collaborative intelligence in industrial Internet of Things (IoT) systems, particularly in smart factories where data privacy, communication efficiency, and device heterogeneity are critical concerns. In this article, we present a comprehensive study of FedSL frameworks tailored for resource-constrained robots in industrial scenarios. We compare synchronous, asynchronous, hierarchical, and heterogeneous FedSL frameworks in terms of workflow, scalability, adaptability, and limitations under dynamic industrial conditions. Furthermore, we systematically categorize token fusion strategies into three paradigms: input-level (pre-fusion), intermediate-level (intra-fusion), and output-level (post-fusion), and summarize their respective strengths in industrial applications. We also provide adaptive optimization techniques to enhance the efficiency and feasibility of FedSL implementation, including model compression, split layer selection, computing frequency allocation, and wireless resource management. Finally, we outline open issues and research directions of FedSL in future smart manufacturing systems. The rapid evolution of the industrial Internet of Things (IoT) has catalyzed a paradigm shift toward intelligent, autonomous, and interconnected manufacturing systems [1]. At the heart of this transformation are networked robots that perform complex tasks such as quality inspection, predictive maintenance, and multi-device collaboration across dynamic production environments. These robots are increasingly equipped with multimodal sensors and onboard computing units, enabling them to perceive, reason, and act in real time [2].

Split federated learning (SFL) is a recent distributed approach for collaborative model training among multiple clients. In SFL, a global model is typically split into two parts, where clients train one part in a parallel federated manner, and a main server trains the other. Despite the recent research on SFL algorithm development, the convergence analysis of SFL is missing in the literature, and this paper aims to fill this gap. The analysis of SFL can be more challenging than that of federated learning (FL), due to the potential dual-paced updates at the clients and the main server. We provide convergence analysis of SFL for strongly convex and general convex objectives on heterogeneous data.

Split Federated Learning (SFL) offers a promising approach for distributed model training in edge computing, combining the strengths of split learning in reducing computational demands on edge devices and enhancing data privacy, with the role of federated aggregation to ensure model convergence and synchronization across users. However, synchronization issues caused by user heterogeneity have hindered the development of the framework. To optimize synchronization efficiency among users and improve overall system performance, we propose a collaborative SFL framework (CSFL). Based on the model's partitioning capabilities, we design a mechanism called the collaborative relay optimization mechanism (CROM), where the assistance provided by high-efficiency users is seen as a relay process, with the portion of the model they compute acting as the relay point. Wireless communication between users facilitates real-time collaboration, allowing high-efficiency users to assist bottleneck users in handling part of the model's computation, thereby alleviating the computational load on bottleneck users. Simulation results show that our proposed CSFL framework reduces synchronization delays and improves overall system throughput while maintaining similar performance and convergence rate to the SFL framework. This demonstrates that the collaboration not only reduces synchronization waiting time but also accelerates model convergence.

Foundation models (FMs) such as GPT-4 exhibit exceptional generative capabilities across diverse downstream tasks through fine-tuning. Split Federated Learning (SFL) facilitates privacy-preserving FM fine-tuning on resource-constrained local devices by offloading partial FM computations to edge servers, enabling device-edge synergistic fine-tuning. Practical edge networks often host multiple SFL tenants to support diversified downstream tasks. However, existing research primarily focuses on single-tenant SFL scenarios, and lacks tailored incentive mechanisms for multi-tenant settings, which are essential to effectively coordinate self-interested local devices for participation in various downstream tasks, ensuring that each SFL tenant's distinct FM fine-tuning requirements (e.g., FM types, performance targets, and fine-tuning deadlines) are met. To address this gap, we propose a novel Price-Incentive Mechanism (PRINCE) that guides multiple SFL tenants to offer strategic price incentives, which solicit high-quality device participation for efficient FM fine-tuning. Specifically, we first develop a bias-resilient global SFL model aggregation scheme to eliminate model biases caused by independent device participation. We then derive a rigorous SFL convergence bound to evaluate the contributions of heterogeneous devices to FM performance improvements, guiding the incentive strategies of SFL tenants. Furthermore, we model inter-tenant device competition as a congestion game for Stackelberg equilibrium (SE) analysis, deriving each SFL tenant's optimal incentive strategy. Extensive simulations involving four representative SFL tenant types (ViT, BERT, Whisper, and LLaMA) across diverse data modalities (text, images, and audio) demonstrate that PRINCE accelerates FM fine-tuning by up to 3.07x compared to state-of-the-art approaches, while consistently meeting fine-tuning performance targets.

To alleviate the training burden in federated learning while enhancing convergence speed, Split Federated Learning (SFL) has emerged as a promising approach by combining the advantages of federated and split learning. However, recent studies have largely overlooked competitive situations. In this framework, the SFL model owner can choose the cut layer to balance the training load between the server and clients, ensuring the necessary level of privacy for the clients. Additionally, the SFL model owner sets incentives to encourage client participation in the SFL process. The optimization strategies employed by the SFL model owner influence clients' decisions regarding the amount of data they contribute, taking into account the shared incentives over clients and anticipated energy consumption during SFL. To address this framework, we model the problem using a hierarchical decision-making approach, formulated as a single-leader multi-follower Stackelberg game. We demonstrate the existence and uniqueness of the Nash equilibrium among clients and analyze the Stackelberg equilibrium by examining the leader's game. Furthermore, we discuss privacy concerns related to differential privacy and the criteria for selecting the minimum required cut layer. Our findings show that the Stackelberg equilibrium solution maximizes the utility for both the clients and the SFL model owner.

Split Federated Learning (SFL) is a distributed machine learning paradigm that combines federated learning and split learning. In SFL, a neural network is partitioned at a cut layer, with the initial layers deployed on clients and remaining layers on a training server. There are two main variants of SFL: SFL-V1 where the training server maintains separate server-side models for each client, and SFL-V2 where the training server maintains a single shared model for all clients. While existing studies have focused on algorithm development for SFL, a comprehensive quantitative analysis of how the cut layer selection affects model performance remains unexplored. This paper addresses this gap by providing numerical and theoretical analysis of SFL performance and convergence relative to cut layer selection. We find that SFL-V1 is relatively invariant to the choice of cut layer, which is consistent with our theoretical results. Numerical experiments on four datasets and two neural networks show that the cut layer selection significantly affects the performance of SFL-V2. Moreover, SFL-V2 with an appropriate cut layer selection outperforms FedAvg on heterogeneous data.

Split Learning (SL) is a promising collaborative machine learning approach, enabling resource-constrained devices to train models without sharing raw data, while reducing computational load and preserving privacy simultaneously. However, current SL algorithms face limitations in training efficiency and suffer from prolonged latency, particularly in sequential settings, where the slowest device can bottleneck the entire process due to heterogeneous resources and frequent data exchanges between clients and servers. To address these challenges, we propose the Heterogeneous Split Federated Learning (HSFL) framework, which allows resource-constrained clients to train their personalized client-side models in parallel, utilizing different cut layers. Aiming to mitigate the impact of heterogeneous environments and accelerate the training process, we formulate a latency minimization problem that optimizes computational and transmission resources jointly. Additionally, we design a resource allocation algorithm that combines the Sample Average Approximation (SAA), Genetic Algorithm (GA), Lagrangian relaxation and Branch and Bound (B\&B) methods to efficiently solve this problem. Simulation results demonstrate that HSFL outperforms other frameworks in terms of both convergence rate and model accuracy on heterogeneous devices with non-iid data, while the optimization algorithm is better than other baseline methods in reducing latency.

Extreme resource constraints make large-scale machine learning (ML) with distributed clients challenging in wireless networks. On the one hand, large-scale ML requires massive information exchange between clients and server(s). On the other hand, these clients have limited battery and computation powers that are often dedicated to operational computations. Split federated learning (SFL) is emerging as a potential solution to mitigate these challenges, by splitting the ML model into client-side and server-side model blocks, where only the client-side block is trained on the client device. However, practical applications require personalized models that are suitable for the client's personal task. Motivated by this, we propose a personalized hierarchical split federated learning (PHSFL) algorithm that is specially designed to achieve better personalization performance. More specially, owing to the fact that regardless of the severity of the statistical data distributions across the clients, many of the features have similar attributes, we only train the body part of the federated learning (FL) model while keeping the (randomly initialized) classifier frozen during the training phase. We first perform extensive theoretical analysis to understand the impact of model splitting and hierarchical model aggregations on the global model. Once the global model is trained, we fine-tune each client classifier to obtain the personalized models. Our empirical findings suggest that while the globally trained model with the untrained classifier performs quite similarly to other existing solutions, the fine-tuned models show significantly improved personalized performance.

Vehicular edge intelligence (VEI) is a promising paradigm for enabling future intelligent transportation systems by accommodating artificial intelligence (AI) at the vehicular edge computing (VEC) system. Federated learning (FL) stands as one of the fundamental technologies facilitating collaborative model training locally and aggregation, while safeguarding the privacy of vehicle data in VEI. However, traditional FL faces challenges in adapting to vehicle heterogeneity, training large models on resource-constrained vehicles, and remaining susceptible to model weight privacy leakage. Meanwhile, split learning (SL) is proposed as a promising collaborative learning framework which can mitigate the risk of model wights leakage, and release the training workload on vehicles. SL sequentially trains a model between a vehicle and an edge cloud (EC) by dividing the entire model into a vehicle-side model and an EC-side model at a given cut layer. In this work, we combine the advantages of SL and FL to develop an Adaptive Split Federated Learning scheme for Vehicular Edge Computing (ASFV). The ASFV scheme adaptively splits the model and parallelizes the training process, taking into account mobile vehicle selection and resource allocation. Our extensive simulations, conducted on non-independent and identically distributed data, demonstrate that the proposed ASFV solution significantly reduces training latency compared to existing benchmarks, while adapting to network dynamics and vehicles' mobility.

Split Federated Learning (SFL) is a distributed machine learning framework which strategically divides the learning process between a server and clients and collaboratively trains a shared model by aggregating local models updated based on data from distributed clients. However, data heterogeneity and partial client participation result in label distribution skew, which severely degrades the learning performance. To address this issue, we propose SFL with Concatenated Activations and Logit Adjustments (SCALA). Specifically, the activations from the client-side models are concatenated as the input of the server-side model so as to centrally adjust label distribution across different clients, and logit adjustments of loss functions on both server-side and client-side models are performed to deal with the label distribution variation across different subsets of participating clients. Theoretical analysis and experimental results verify the superiority of the proposed SCALA on public datasets.