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By Shahab D. Mohaghegh (Ed.), Saud M. Al-Fattah (Ed.), Andrei S. Popa (Ed.)

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A-I4) Eq. A-I4 gives the weight change in a link between Layer j and an output layer. 1/ usually is called the learning rate and takes any value between 0 and 1. The higher the learning rate, the higher the weight changes. 2) during early stages oflearning and that it be increased as the net begins to converge. , links between Layers i and j). AWij is defined as AWij = -1/(8EI8wij)' ............................ (A-IS) The output, OPj' from a node in the middle (hidden) Layer j because of Pattern P is defined as The derivation that follows is similar to that for the case when the link is connected to the output layer.

Saturation is the stage when the net stops learning because of very small sigmoidal function derivatives. Very small or zero derivatives occur when the argument of the sigmoidal function is large (Fig. 6). Note that the derivative curve on the logarithmic scale is shifted to the right or up by a value equal to the absolute value of the largest negative number on the axis on which the shift is done. This is necessary to scale all data points from 0 to 1. The output layer nodes are assigned the values 1 (firing) or 0 (silent), depending on whether the node represents the model.

5. Calculate the error at the output layer. If the node error is larger than the maximum error, set the maximum error equal to the node error. Repeat for all nodes in a feed-forward manner. 6. Use the backpropagation procedure described in Appendix A to calculate the amount of weight change required in each link be- 240 cause of the current pattern. Do not apply any changes to the links yet. 7. Repeat Steps 3 through 6 until the net has been presented with all the patterns in the training set. During this process, accumulate the weight changes in each link caused by the different patterns.

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