Federated learning facilitates learning across clients without transferring local data on these clients to a central server. Despite the success of the federated learning method, it remains to improve further w.r.t communicating the most critical information to update a model under limited communication conditions, which can benefit this learning scheme into a wide range of application scenarios. In this work, we propose a nonlinear quantization for compressed stochastic gradient descent, which can be easily utilized in federated learning. Based on the proposed quantization, our system significantly reduces the communication cost by up to three orders of magnitude, while maintaining convergence and accuracy of the training process to a large extent. Extensive experiments are conducted on image classification and brain tumor semantic segmentation using the MNIST, CIFAR-10 and BraTS datasets where we show state-of-the-art effectiveness and impressive communication efficiency.
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