Open Mined (http://openmined.org/) are looking at this from the other angle - sharing the encrypted neural network with their users so that they can train it without sharing their data at all - the encrypted gradients are computed by the user and collated and decrypted by the company that wants to train the neural network.

(Not affiliated in any way, but went to a really interesting talk on this a few weeks ago as part of the London Machine Learning meetup group - https://www.meetup.com/London-Machine-Learning-Meetup/events...)