Is there literature on how big a net needs to be to learn an arbitrary classification problem where the input is a n-bit integer and the output is one of k categories? I'm interested in both a theoretical bound and the size needed in practice with current training and initialization techniques. To be specific, the neural net is allowed to see all possible inputs and their respective outputs, so I will not hide anything from the training set, as the function is not assumed to have any structure whatsoever.
How big does a Neural Net need to be to learn anything
neural network