A Mathematical Model for Feed � Forward Neural Networks

We present a general model for di erentiable feed forward neural networks Its general mathemat ical description includes the standard multi layer perceptron as well as its common derivatives These standard structures assume a strong relationship between the network links and the neuron weights Our generalization takes advantage of the suppression of this assumption Since our model is especially well adapted to gradient based learning algorithms we present a direct and a backward algorithm that can be used to di erentiate the output of the network Theoretical computation times are estimated for both algorithms We describe a direct application of this model a parallelization method that uses the expression of our general backward di erentiation to overlap the communication times