Nonlinear continuous functions are thus used. In practice, these functions can have various aspects according to the application. The usual case is a continuous function of sigmoid type which preserves the aspect of a function of threshold, while being continuous and monotonous. That is:

The choice of this function is justified by the simple expression of its derivative:

The weights of the layer of output are adjusted using the rule, since the errors can be calculated from the difference between the output values and the wanted values. On the other hand, for the hidden layers, no wished values are given, the error must be estimated from the following layer.