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I know that the delta rule is a gradient decent learning rule. But, what are the differences between these two delta rules? Thanks in advance.

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If I'm not mistaken the generalised delta rule refers to the backpropagation algorithm, which is basically an extension of the delta rule to deal with hidden layers.

Have a look at the paper "Learning internal representations by error propagation" by Rumelhart, Hinton, and Williams for details.

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