For the backward phase (figure 7) the neuron **j** in the output layer calculates the error between its
actual output value , known from the forward phase, and the expected nominal target value :

The error is propagated backwards to the previous hidden layer.

The neuron **i** in a hidden layer calculates an error that is propagated
backwards again to its previous layer. Therefor a column of the weight matrix is used.

To minimize the error the weights of the projective edges of neuron **i** and
the bias values in the receptive layer have to be changed.
The old values have to be increased by:

is the training rate and has an empirical value: .

The back-propagation algorithm optimizes the error by the method of gradient descent, where ist the length of each step.

Fri Jun 23 12:20:25 MET DST 1995