The Living Thing / Notebooks :

Differentiable learning of automata

Learning stack machines, random access machines, nested hierarchical parsing machines, Turing machines and whatever other automata-with-memory that you wish, from data. In other words, teaching computers to program themselves, via a deep learning formalism.

The border between these and recurrent neural networks is porous.

Google branded: Differentiable neural computers

Christopher Olah's Characteristically pedagogic intro

Adrian Colyer's introduction to neural Turing machines.

Andrej Karpathy's memory machine list has some good starting point.