Tight bounds on the size of neural networks for classification problems

This paper relies on the entropy of a data-set (i.e., number-of-bits) to prove tight bounds on the size of neural networks solving a classification problem. First, based on a sequence of geometrical steps, the authors constructively compute an upper bound of O(mn) on the number-of-bits for a given data-set - here m is the number of examples and n is the number of dimensions (i.e., R{sup n}). This result is used further in a nonconstructive way to bound the size of neural networks which correctly classify that data-set