  This paper aims to integrate two synergetic technologies, federated learning
(FL) and width-adjustable slimmable neural network (SNN) architectures. FL
preserves data privacy by exchanging the locally trained models of mobile
devices. By adopting SNNs as local models, FL can flexibly cope with the
time-varying energy capacities of mobile devices. Combining FL and SNNs is
however non-trivial, particularly under wireless connections with time-varying
channel conditions. Furthermore, existing multi-width SNN training algorithms
are sensitive to the data distributions across devices, so are ill-suited to
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 that are decoded as many as possible for a given communication
throughput. Leveraging ST, SlimFL aligns the forward propagation of different
width configurations, while avoiding the inter-width interference during
backpropagation. We formally prove the convergence of SlimFL. The result
reveals that SlimFL is not only communication-efficient but also can counteract
non-IID data distributions and poor channel conditions, which is also
corroborated by simulations.
