The rule is a generalization of the perceptron learning algorithm, which tends to minimize the error. It uses continuous and monotonous functions of activation, which are thus bijective and derivable, and allow the direction in which it is necessary to apply the correction, to be assessed.

A gradient method can be used to minimize the error.

The output S of a neuron using a function of continuous activation is given by:

The expression of the gradient is given by the derivative of the function of activation, that is:

The correction carried out to each weight is proportional to the error and to the derivative of the function of activation. The gradient is used to minimize the total error, which for K samples is expressed by:

The correction of the weights using rule, for a output value S and a desired value D, is defined as follows:

All the samples are presented to the network, then the total error is calculated. The process is performed until the total error is higher than a fixed threshold.