Is it possible to run a neural network in reverse?

Question

If we have a neural network such as the multilayer perceptron back propagation neural network that uses sigmodial logistic activation functions is it possible to feed the networ

Answer 1

As there is an infinite number of possibilities to distribute the result to the feeding neurons this is only possible for each layer where the number of receiving neurons equals the number of the feeding neurons. There it is a simple linear equation which boils down to a Matrix multiplication/inversion problem, that can easily be solved.

If the number of neurons where the number of the receiving neurons (n) is smaller than the number of the feeding neurons (m), you have as solution space a manifold with m - n dimensions.