  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.
