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

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A more elegant proof is given in (Minsky & Papert, 1969), but the point is that for complex transformations the number of required units in the hidden layer is exponential in N . 7 Conclusions In this chapter we presented single layer feedforward networks for classi cation tasks and for function approximation tasks. The representational power of single layer feedforward networks was discussed and two learning algorithms for nding the optimal weights were presented. The simple networks presented here have their advantages and disadvantages.

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.

B. , but with di erent lengths. , vectors x and w1 are nearest to each other, and their dot product xT w1 = jxjjw1 j cos is larger than the dot product of x and w2 . , however, the pattern and weight vectors are not normalised, and in this case w2 should be considered the `winner' when x is applied. However, the dot product xT w1 is still larger than xT w2 . Winner selection: Euclidean distance Previously it was assumed that both inputs x and weight vectors w were normalised. 1) gives a `biological plausible' solution.

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