The Gain Control is used to ensure that the resonating signal is greater than the gain value before a PE can act on it. In the same general category as the ART networks are the Boltzmann machines. The result is that the relative entropy of the system gradually decreases as the weights are decreased. Boltzmann machines are reportedly good at constraint-satisfaction tasks involving a large number of weak constraints. It is similar to the standard backprop model, except that it allows backward connectivity, and connectivity direct from the input layer to the output PE's.
Any PE can be an input node, output node, or both.
If a node is not an input or output node, it is a hidden node. The NN is trained through the standard backpropagation rule. Recurrent backprop NN's are better at learning with noisy or missing data. Like the normal backprop model, recurrent backprop relies on a steepest descent method of gradient descent, and both are easily trapped in local a local minimum. Fundamentals of Artificial Neural Networks, Cambridge, MA, MIT Press.