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

By Ben Krose, Patrick van der Smagt

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

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

Example text

For convenience, the subscripts are de ned modulo n. 10) ;C global inhibition ;DdXY ( k j+1 + k j;1) data term where jk = 1 if j = k and 0 otherwise. Finally, each neuron has an external bias input Cn. Discussion Although this application is interesting from a theoretical point of view, the applicability is limited. Whereas Hop eld and Tank state that, in a ten city tour, the network converges to a valid solution in 16 out of 20 trials while 50% of the solutions are optimal, other reports show less encouraging results.

The central idea behind this solution is that the errors for the units of the hidden layer are determined by back-propagating the errors of the units of the output layer. For this reason the method is often called the back-propagation learning rule. Back-propagation can also be considered as a generalisation of the delta rule for non-linear activation functions1 and multilayer networks. 1 Multi-layer feed-forward networks A feed-forward network has a layered structure. Each layer consists of units which receive their input from units from a layer directly below and send their output to units in a layer directly above the unit.

A lot of advanced algorithms based on back-propagation learning have some optimised method to adapt this learning rate, as will be discussed in the next section. Outright training failures generally arise from two sources: network paralysis and local minima. Network paralysis. As the network trains, the weights can be adjusted to very large values. The total input of a hidden unit or output unit can therefore reach very high (either positive or negative) values, and because of the sigmoid activation function the unit will have an activation very close to zero or very close to one.

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