Federated learning (FL) is a key enabler for efficient communication and computing, leveraging devices' distributed computing capabilities. However, applying FL in practice is challenging due to the local devices' heterogeneous energy, wireless channel conditions, and non-independently and identically distributed (non-IID) data distributions. To cope with these issues, this paper proposes a novel learning framework by integrating FL and width-adjustable slimmable neural networks (SNN). Integrating FL with SNNs is challenging due to time-varying channel conditions and data distributions. In addition, existing multi-width SNN training algorithms are sensitive to the data distributions across devices, which makes SNN ill-suited for FL. Motivated by this, we propose a communication and energy-efficient SNN-based FL (named SlimFL) that jointly utilizes superposition coding (SC) for global model aggregation and superposition training (ST) for updating local models. By applying SC, SlimFL exchanges the superposition of multiple-width configurations decoded as many times as possible for a given communication throughput. Leveraging ST, SlimFL aligns the forward propagation of different width configurations while avoiding inter-width interference during backpropagation. We formally prove the convergence of SlimFL. The result reveals that SlimFL is not only communication-efficient but also deals with non-IID data distributions and poor channel conditions, which is also corroborated by data-intensive simulations.

Mobile devices are indispensable sources of big data. Federated learning (FL) has a great potential in exploiting these private data by exchanging locally trained models instead of their raw data. However, mobile devices are often energy limited and wirelessly connected, and FL cannot cope flexibly with their heterogeneous and time-varying energy capacity and communication throughput, limiting the adoption. Motivated by these issues, we propose a novel energy and communication efficient FL framework, coined SlimFL. To resolve the heterogeneous energy capacity problem, each device in SlimFL runs a width-adjustable slimmable neural network (SNN). To address the heterogeneous communication throughput problem, each full-width (1.0x) SNN model and its half-width ($0.5$x) model are superposition-coded before transmission, and successively decoded after reception as the 0.5x or $1.0$x model depending on the channel quality. Simulation results show that SlimFL can simultaneously train both $0.5$x and $1.0$x models with reasonable accuracy and convergence speed, compared to its vanilla FL counterpart separately training the two models using $2$x more communication resources. Surprisingly, SlimFL achieves even higher accuracy with lower energy footprints than vanilla FL for poor channels and non-IID data distributions, under which vanilla FL converges slowly.