By Kroese B., van der Smagt P.
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Extra info for An Introduction to Neural Networks
A pattern p is applied, E p is calculated, and the weights are adapted (p = 1, 2, . . , 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.
The network fits 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 ‘fit the noise’ of the learning samples instead of making a smooth approximation. 9. 9: Effect of the number of hidden units on the network performance. The dashed line gives the desired function, the circles denote the learning samples and the drawn line gives the approximation by the network.
42 CHAPTER 4. 6: Slow decrease with conjugate gradient in non-quadratic systems. The hills on the left are very steep, resulting in a large search vector ui . When the quadratic portion is entered the new search direction is constructed from the previous direction and the gradient, resulting in a spiraling minimisation. This problem can be overcome by detecting such spiraling minimisations and restarting the algorithm with u0 = −∇f . Some improvements on back-propagation have been presented based on an independent adaptive learning rate parameter for each weight.
An Introduction to Neural Networks by Kroese B., van der Smagt P.