Capacity and VC-dimension of multilayer network with higher order input transformation

The paper investigates a multilayer perceptron built of linear threshold units superposed on a higher order transformation of input, a type of structure considered for optical implementation. Theoretical estimates of its separating capacity, VC-dimension and probability of implementation of a random dichotomy are given. It is shown that the capacity is limited by the number of neurons in the first hidden layer and that for a sufficiently large network it can be lower than the VC-dimension.<
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