Interesting, thanks! On https://www.tensorflow.org/tutorials/seq2seq I found a link to https://arxiv.org/abs/1406.1078, which says
> $One RNN encodes a sequence of symbols into a fixed-length vector representation, and the other decodes the representation into another sequence of symbols.$
To me it sounds like they use an RNN to learn a hash function.
Thanks for the NTM link, I'll check it out.
How would you sort integers? using neural turing machines: https://arxiv.org/abs/1410.5401
NMTs and other memory network architectures have explicit memory as state (including stacks!), indeed any recurrent neural net has state.
Are NNs Turing complete? Yes! http://binds.cs.umass.edu/papers/1992_Siegelmann_COLT.pdf