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Convergence Analysis of Split Federated Learning on Heterogeneous Data
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Provides the first convergence analysis of split federated learning (SFL-V1 and SFL-V2) on heterogeneous data, with O(1/T) rates for strongly convex and O(1/cuberoot(T)) for general convex objectives, extended to non-convex and partial participation.
Problem
Convergence guarantees for split federated learning are missing; SFL's dual-paced server/client updates and client drift under heterogeneous data and partial participation make existing FL and SL analyses inapplicable.
Approach
Decomposes the global optimality gap into separate client-side and server-side gaps (Proposition on convergence decomposition), enabling analysis of dual-paced aggregation (SFL-V1) and sequential server updates (SFL-V2) under heterogeneous and partially participating clients.
Key results
- Theory: SFL-V1 and SFL-V2 achieve O(1/T) for strongly convex and O(1/cuberoot(T)) for general convex objectives on heterogeneous data, matching FL and SL orders for strongly convex.
- Experiments on CIFAR-10/100 with ResNet-18 show SFL-V2 outperforms FL and SL when data is highly heterogeneous (beta=0.1) and the number of clients is large (N up to 100).
- Partial participation worsens bounds by a G^2/q_n term; lower participation gives less stable convergence and lower accuracy in experiments.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| increase cut layer L_c so clients maintain a larger portion of the global model (ablation) | SFL-V1 and SFL-V2 · CIFAR-10 and CIFAR-100 | accuracy | Helped |
| increase data heterogeneity by decreasing Dirichlet parameter β (ablation) | SFL-V1 and SFL-V2 · CIFAR-10 and CIFAR-100 | accuracy | Hurt |
| decrease client participation probability q (ablation) | SFL · CIFAR-10 and CIFAR-100 | accuracy | Hurt |
| replace FL with SFL under mild data heterogeneity (β=0.5) | FL · CIFAR-10 and CIFAR-100, β=0.5 | accuracy | No clear effect |
| replace SFL or FL with SL under mild data heterogeneity (β=0.5) | SFL and FL · CIFAR-10 and CIFAR-100, β=0.5 | accuracy | Hurt |
| replace FL or SL with SFL-V2 under high data heterogeneity (β=0.1) | FL and SL · CIFAR-10 and CIFAR-100, β=0.1 | accuracy | Helped |
| increase cohort size when using SFL-V2 rather than FL or SL under high heterogeneity (ablation) | SFL-V2 · CIFAR-10 and CIFAR-100, β=0.1 | accuracy | Helped |
| replace SFL-V1 with SFL-V2 (ablation) | SFL · CIFAR-10 and CIFAR-100 | accuracy | Mixed |
Surprising findings
- SFL-V2 outperforms FL and SL under highly heterogeneous data with many clients, despite theory only matching FL's order.
- Performance increases with cut layer position (clients hold more of the model), which the authors link to smaller client gradient variance.
Limitations
- Theoretical bounds match FL order and do not explain SFL's empirical advantage over FL under high heterogeneity; tighter bounds needed.
- Analysis relies on standard assumptions (smoothness, bounded gradients and heterogeneity) and constant learning rates.
- Cut-layer effect on convergence is not theoretically analyzed.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 FEMNIST
Benchmarks: CIFAR-10 CIFAR-100 FEMNIST
Metrics: test accuracy convergence of global loss
Baselines: FedAvg split learning (SL) SFL-V1 SFL-V2
Builds on: FedAvg split learning SFL (Thapa et al.)
Closest papers by meaning
- FSL-SAGE: Accelerating Federated Split Learning via Smashed Activation Gradient Estimation (ICML 2025 · similarity 0.90)
- FedQS: Optimizing Gradient and Model Aggregation for Semi-Asynchronous Federated Learning (NeurIPS 2025 · similarity 0.90)
- Towards Straggler-Resilient Split Federated Learning: An Unbalanced Update Approach (NeurIPS 2025 · similarity 0.90)
- SemiDFL: A Semi-Supervised Paradigm for Decentralized Federated Learning (AAAI 2025 · similarity 0.89)
- GAS: Generative Activation-Aided Asynchronous Split Federated Learning (AAAI 2025 · similarity 0.89)
- Exact and Linear Convergence for Federated Learning under Arbitrary Client Participation is Attainable (NeurIPS 2025 · similarity 0.89)
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