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ISBN-10: 0120121247

ISBN-13: 9780120121243

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Extra resources for Advances in Computers, Vol. 24

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1 Structure of Neural Networks 39 Fig. 1 A simple (artificial) neural network This matrix is to be read from the top to the right: the columns correspond to the neurons, from which the connections emanate, the rows to the neurons to which the connections lead. , graph with weighted edges) are called the network structure. According to the network structure, we distinguish two fundamental types of neural networks: if the graph that describes the network structure of a neural network is acyclic—that is, if it does not contain loops1 and no directed cycles—the network is called a feed forward network.

Un }, and m output neurons, that is, Uout = {v1 , . . , vm }, is a set of training patterns l = (i (l) , o (l) ), each consisting of an input vector (l) (l) (l) (l) i (l) = (extu1 , . . , extun ) and an output vector o (l) = (ov1 , . . , ovm ). If we are given a fixed learning task, we desire to train a neural network in such a way that it produces for all training patterns l ∈ Lfixed the outputs contained in the output vector o (l) if the external inputs of the corresponding input vector i (l) are fed into the network.

Therefore, we can define an error function e(w1 , . . , wn , θ), which states how well, for given weights and threshold, the computed function coincides with the desired one. Our objective is, of course, to determine the weights and the threshold in such a way that the error vanishes, that is, that the error function becomes 0. To achieve this, we try to reduce the value of the error function in every step. We illustrate this procedure with the help of a very simply example, namely a threshold logic unit with only one input.

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Advances in Computers, Vol. 24

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