By Kroese B., van der Smagt P.

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7 Conclusions In this chapter we presented single layer feedforward networks for classification tasks and for function approximation tasks. The representational power of single layer feedforward networks was discussed and two learning algorithms for finding the optimal weights were presented. The simple networks presented here have their advantages and disadvantages. The disadvantage is the limited representational power: only linear classifiers can be constructed or, in case of function approximation, only linear functions can be represented.

The theory of the dynamics of recurrent networks extends beyond the scope of a one-semester course on neural networks. Yet the basics of these networks will be discussed. 2, which can be used for the representation of binary patterns; subsequently we touch upon Boltzmann machines, therewith introducing stochasticity in neural computation. 1 The generalised delta-rule in recurrent networks The back-propagation learning rule, introduced in chapter 4, can be easily used for training patterns in recurrent networks.

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 θk are constant. 5) is always negative when yk changes according to eqs. 2). 1 Often, these networks are described using the symbols used by Hopfield: 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 θk . 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.

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An Introduction to Neural Networks by Kroese B., van der Smagt P.

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