  Neural networks are a convenient way to automatically fit functions that are
too complex to be described by hand. The downside of this approach is that it
leads to build a black-box without understanding what happened inside. Finding
the preimage would help to better understand how and why such neural networks
had given such outputs. Because most of the neural networks are noninjective
function, it is often impossible to compute it entirely only by a numerical
way. The point of this study is to give a method to compute the exact preimage
of any Feed-Forward Neural Network with linear or piecewise linear activation
functions for hidden layers. In contrast to other methods, this one is not
returning a unique solution for a unique output but returns analytically the
entire and exact preimage.
