Straggler-Resilient Hierarchical Split Federated Learning via Smashed Data Generation

Large-scale edge intelligence requires collaborative training across resource-constrained and heterogeneous connected devices without uploading raw data. Split federated learning reduces the computation burden on devices by partitioning a model between clients and edge servers, while hierarchical deployment improves the scalability of distributed training. However, existing hierarchical split federated learning (HSFL) designs are still sensitive to stragglers and non-IID data, since delayed clients reduce training efficiency and their missing or stale smashed data may bias server-side updates. This paper proposes SAGE-HSFL, a smashed data generation-enabled semi-asynchronous hierarchical split federated learning framework. In SAGE-HSFL, each edge server maintains a labeled smashed-data pool, learns online distributions from the received cut layer representations, and generates supplementary smashed data to compensate for underrepresented or delayed client updates. This enables server-side training to proceed with reduced gradient dissimilarity while preserving the raw-data locality of split learning. We establish a convergence bound for general non-convex objectives and reveal how smashed data generation mitigates the impact of stragglers on update bias. Based on the staleness-dependent term in the convergence bound, we formulate an online joint optimization of client scheduling, cut layer selection, bandwidth allocation, and edge association, and solve it through Lyapunov-based decomposition and adaptive association. Experiments on FMNIST and CIFAR-10 show that SAGE-HSFL improves test accuracy and reduces gradient dissimilarity. SAGE yields 0.79%–2.06% accuracy gains over its disabled variant, while the complete framework achieves 2.42%–4.53% higher accuracy than representative external baselines. The complete framework further achieves up to 10.21% and 14.17% higher accuracy than external baselines under the same target time on FMNIST and CIFAR-10, respectively, and reaches the target accuracy 6.20 and 7.02 times faster than a basic HSFL ablation.