# Numerically approximate the maximum of an element of a vector after a series of matrix multiplications.

Where S is a sigmoidal function, A_i is a matrix, and x is an input vector, and S is applied element-wise to its matrix argument, a specific type of artificial neural network can be described as

S(A_2 (S(A_1 (S(A_0 x)))))

Out for an arbitrary number of A terms. The A matrices are not necessarily square, but of course their dimensions match up so the output of one matrix vector multiplication and be the input of the next.

Sometimes, it is desirable to know which input vector maximizes a specific element of the output vector. How can I find an x which approximately maximizes a particular element in the output vector?

• i suppose you can omit the leading S(.) Aug 13, 2014 at 17:38
• This is dual of fitting the first layer of a multilayer perceptron. There's no easy method for this. Good luck! Aug 16, 2014 at 18:20