I am trying to de-knot a point of confusion in my mind regarding turing-completeness and the universal approximation theorem. The context here is deep neural nets: So, consider two types of networks: a recurrent neural net, (RNN), and a feedforward net, say a pure convolutional neural net (CNN). I understand that the RNN is turing complete. I also know that a CNN is a universal approximator, but is NOT turing complete. What I am trying to understand is the link between universal approximation, and turing-completeness: Is there a link? Why is a CNN a universal approximator but NOT turing complete? Does a machine being turing-complete automatically make it a universal approximator? Trying to uncouple the two concepts. Thanks! 
Confused between turing-completeness and universal approximation - are they related?
turing machines;approximation;neural networks;recursion;turing completeness