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

Sample text

Adding hidden units will always lead to a reduction of the E learning . However, adding hidden units will rst lead to a reduction of the E test , but then lead to an increase of E test . This e ect is called the peaking e ect. 10. 10: The average learning error rate and the average test error rate as a function of the number of hidden units. 9 Applications Back-propagation has been applied to a wide variety of research applications. Sejnowski and Rosenberg (1987) (Sejnowski & Rosenberg, 1986) produced a spectacular success with NETtalk, a system that converts printed English text into highly intelligible speech.

A good way to beat this trade-o is to start at a high temperature and gradually reduce it. At high temperatures, the network will ignore small energy di erences and will rapidly approach equilibrium. In doing so, it will perform a search of the coarse overall structure of the space of global states, and will nd a good minimum at that coarse level. As the temperature is lowered, it will begin to respond to smaller energy di erences and will nd one of the better minima within the coarse-scale minimum it discovered at high temperature.

This can be seen as a feed-forward network with a single input unit for x a single output unit for f (x) and hidden units with an activation function F = sin(s ). The factor a0 corresponds with the bias of the output unit, the factors cn correspond with the weighs from hidden to output unit the phase factor n corresponds with the bias term of the hidden units and the factor n corresponds with the weights between the input and hidden layer. The basic di erence between the Fourier approach and the back-propagation approach is that the in the Fourier approach the `weights' between the input and the hidden units (these are the factors n) are xed integer numbers which are analytically determined, whereas in the back-propagation approach these weights can take any value and are typically learning using a learning heuristic.

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