Download An Introduction to Neural Networks (8th Edition) by Ben Krose, Patrick van der Smagt PDF

By Ben Krose, Patrick van der Smagt

This manuscript makes an attempt to supply the reader with an perception in synthetic neural networks.

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Additional resources for An Introduction to Neural Networks (8th Edition)

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THE GENERALISED DELTA RULE 35 To compute kp we apply the chain rule to write this partial derivative as the product of two factors, one factor re ecting the change in error as a function of the output of the unit and one re ecting the change in the output as a function of changes in the input. 9) Let us compute the second factor. 10) which is simply the derivative of the squashing function F for the kth unit, evaluated at the net input spk to that unit. 9), we consider two cases. First, assume that unit k is an output unit k = o of the network.

9) Let us compute the second factor. 10) which is simply the derivative of the squashing function F for the kth unit, evaluated at the net input spk to that unit. 9), we consider two cases. First, assume that unit k is an output unit k = o of the network. 11) o o @yp o which is the same result as we obtained with the standard delta rule. 12) for any output unit o. Secondly, if k is not an output unit but a hidden unit k = h, we do not readily know the contribution of the unit to the output error of the network.

True gradient descent requires that in nitesimal steps are taken. The constant of proportionality is the learning rate . For practical purposes we choose a learning rate that is as large as possible without leading to oscillation. 22) where t indexes the presentation number and is a constant which determines the e ect of the previous weight change. 2. When no momentum term is used, it takes a long time before the minimum has been reached with a low learning rate, whereas for high learning rates the minimum is never reached because of the oscillations.

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