Reasoning behind using Deep Learning on non-local data
It appear that I forgot one point of the ANN, at least forgot one of its effects : the activation function.

It is true that for linear activation, multi-layer can be reduce to a single-one, but with a non-linear function, 


  a two-layer neural network can be proven to be a universal function approximator.


Sources

However, it is true that I dont understand now why to use more than two hidden layers...