GQ-FSL: Green Quantized Federated Split Learning

Deploying state-of-the-art deep neural networks (DNNs) at the wireless edge is severely bottlenecked by the strict energy and resource constraints of mobile devices. While federated split learning (FSL) mitigates on-device computation by offloading workloads to an edge server, this may introduce systemic overheads, while the continuous exchange of cut-layer data, and submodels still incurs significant energy consumption (EC). To address this, we propose a green quantized FSL (GQ-FSL) framework that incorporates stochastic quantization for both local collaborative training and wireless transmissions. Notably, GQ-FSL supports asymmetric precision levels for the client- and server-side submodels, effectively decoupling device energy constraints from global convergence degradation. To quantify these tradeoffs, we develop parameterized energy models for the split architecture and derive a theoretical convergence bound under statistically heterogeneous data. Building on that, we formulate a joint optimization problem to configure the DNN split point and precision levels, minimizing the total system EC while satisfying a strict target accuracy constraint. Ultimately, we demonstrate that GQ-FSL enables large-scale DNN deployment on resource-constrained devices, achieving superior energy efficiency compared to quantized federated learning and full-precision FSL.