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

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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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Extra info for An Introduction to Neural Networks (8th Edition)

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A pattern p is applied, E p is calculated, and the weights are adapted (p = 1 2 : : : P ). There exists empirical indication that this results in faster convergence. Care has to be taken, however, with the order in which the patterns are taught. For example, when using the same sequence over and over again the network may become focused on the rst few patterns. This problem can be overcome by using a permuted training method. 4 An example A feed-forward network can be used to approximate a function from examples.

There are no connections within a layer. The Ni inputs are fed into the rst layer of Nh 1 hidden units. The input units are merely `fan-out' units no processing takes place in these units. The activation of a hidden unit is a function Fi of the weighted inputs plus a bias, as given in in eq. 4). 1). 6) it has been shown (Hornik, Stinchcombe, & White, 1989 Funahashi, 1989 Cybenko, 1989 Hartman, Keeler, & Kowalski, 1990) that only one layer of hidden units su ces to approximate any function with nitely many discontinuities to arbitrary precision, provided the activation functions of the hidden units are non-linear (the universal approximation theorem).

After all, when one is considering a recurrent network, it is possible to continue propagating activation values ad in nitum, or until a stable point (attractor) is reached. , the activation values in the network are repeatedly updated until a stable point is reached after which the weights are adapted, but there are also recurrent networks where the learning rule is used after each propagation (where an activation value is transversed over each weight only once), while external inputs are included in each propagation.

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