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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Proof First, note that the energy expressed in eq. 4) is bounded from below, since the yk are bounded from below and the wjk and k are constant. 5) is always negative when yk changes according to eqs. 2). 1 Often, these networks are described using the symbols used by Hop eld: Vk for activation of unit k, Tjk for the connection weight between units j and k, and Uk for the external input of unit k. We decided to stick to the more general symbols yk , wjk , and k . 52 CHAPTER 5. RECURRENT NETWORKS The advantage of a +1=;1 model over a 1=0 model then is symmetry of the states of the network.

2 The e ect of the number of hidden units The same function as in the previous subsection is used, but now the number of hidden units is varied. 9B for 20 hidden units. 9B is called overtraining. The network ts exactly with the learning samples, but because of the large number of hidden units the function which is actually represented by the network is far more wild than the original one. Particularly in case of learning samples which contain a certain amount of noise (which all real-world data have), the network will ` t the noise' of the learning samples instead of making a smooth approximation.

This simple example demonstrates that adding hidden units increases the class of problems that are soluble by feed-forward, perceptronlike networks. However, by this generalisation of the basic architecture we have also incurred a serious loss: we no longer have a learning rule to determine the optimal weights! 6 Multi-layer perceptrons can do everything In the previous section we showed that by adding an extra hidden unit, the XOR problem can be solved. For binary units, one can prove that this architecture is able to perform any transformation given the correct connections and weights.

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