The approximation power of neural networks

Neural Nets generate outputs according to a specific recipe, i.e., they form a certain family of (vector valued) functions, determined by a typically large number of parameters (the weights). Training a Neural Net means to adjust the parameters to produce a desired output, i.e., find a good approximation to a given output function from the family of functions produced by the Net.
In this course we will explore, in relation to classical approximation by polynomials and splines, how good an approximation can be so obtained.
The course will be completely self contained.

Schedule: (TBA)