  Federated learning allows for the training of a model using data on multiple
clients without the clients transmitting that raw data. However the standard
method is to transmit model parameters (or updates), which for modern neural
networks can be on the scale of millions of parameters, inflicting significant
computational costs on the clients. We propose a method for federated learning
where instead of transmitting a gradient update back to the server, we instead
transmit a small amount of synthetic `data'. We describe the procedure and show
some experimental results suggesting this procedure has potential, providing
more than an order of magnitude reduction in communication costs with minimal
model degradation.
