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

By Kroese B., van der Smagt P.

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P ). There exists empirical indication that this results in faster convergence. Care has to be taken, however, with the order in which the patterns are taught. For example, when using the same sequence over and over again the network may become focused on the first few patterns. This problem can be overcome by using a permuted training method. 4 An example A feed-forward network can be used to approximate a function from examples. Suppose we have a system (for example a chemical process or a financial market) of which we want to know 38 CHAPTER 4.

This stochastic activation function is not to be confused with neurons having a sigmoid deterministic activation function. 12) where Pα is the probability of being in the α th global state, and Eα is the energy of that state. Note that at thermal equilibrium the units still change state, but the probability of finding the network in any global state remains constant. At low temperatures there is a strong bias in favour of states with low energy, but the time required to reach equilibrium may be long.

2) with a sigmoid activation function between 0 and 1. The activation value y Xj = 1 indicates that city X occupies the j th place in the tour. An energy function describing this problem can be set up as follows. 8) where A, B, and C are constants. 8) are zero if and only if there is a maximum of one active neuron in each row and column, respectively. The last term is zero if and only if there are exactly n active neurons. 9) X Y =X j is added to the energy, where dXY is the distance between cities X and Y and D is a constant.