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The gradient descent algorithm is generally very slow because it requires small learning rates for stable learning. The momentum variation is usually faster than simple gradient descent, because it allows higher learning rates while maintaining stability, but it is still too slow for many practical applications. These two methods are normally used only when incremental training is desired. You would normally use Levenberg-Marquardt training for small and medium size networks, if you have enough memory available. If memory is a problem, then there are a variety of other fast algorithms available. For large networks you will probably want to use trainscg or trainrp.

Multilayered networks are capable of performing just about any linear or nonlinear computation, and can approximate any reasonable function arbitrarily well. Such networks overcome the problems associated with the perceptron and linear networks. However, while the network being trained might theoretically be capable of performing correctly, backpropagation and its variations might not always find a solution

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