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So what's up with that differentiable stack? Is that similar to what the Facebook people were doing on learning addition?

Here's the differentiable stack/queue/deque paper: http://arxiv.org/abs/1506.02516

It is indeed similar to some work from FAIR, where one of the tasks was binary addition: http://arxiv.org/abs/1503.01007

Yes, similar.

There is a lot of work around this going on at the moment. Google's neural Turing machine is a similar idea.