Title: Supernet Training for Federated Image Classification Under System Heterogeneity. Abstract: Efficient deployment of deep neural networks across many devices and resource constraints, particularly on edge devices, is one of the most challenging problems in the presence of data-privacy preservation issues. Conventional approaches have evolved to either improve a single global model while keeping each local heterogeneous training data decentralized (i.e. data heterogeneity; Federated Learning (FL)) or to train an overarching network that supports diverse architectural settings to address heterogeneous systems equipped with different computational capabilities (i.e. system heterogeneity; Neural Architecture Search). However, few studies have considered both directions simultaneously. This paper proposes the federation of supernet training (FedSup) framework to consider both scenarios simultaneously, i.e., where clients send and receive a supernet that contains all possible architectures sampled from itself. The approach is inspired by observing that averaging parameters during model aggregation for FL is similar to weight-sharing in supernet training. Thus, the proposed FedSup framework combines a weight-sharing approach widely used for training single shot models with FL averaging (FedAvg). Furthermore, we develop an efficient algorithm (E-FedSup) by sending the sub-model to clients on the broadcast stage to reduce communication costs and training overhead, including several strategies to enhance supernet training in the FL environment. We verify the proposed approach with extensive empirical evaluations. The resulting framework also ensures data and model heterogeneity robustness on several standard benchmarks.