Given a deep net graph and the activation functions on the hidden vertices do we have a description of the function space spanned by it? (even if for some specific architectures and activation functions)
Or conversely : think of being given a function and an error tolerance (say in the sup norm) and a network architecture (with activation functions). Then is it known how to decide if edge weights can be assigned to the net to represent a function within the given error tolerance?
A few papers which I think addresses related questions are,