Recurrent Backpropagation is used for fixed-point learning. NeuroSolutions is one of the few software products having this ability.
As with static backpropagation, fixed-point learning maps a static input with a static output. The difference is that the mapping is not instantaneous. When data is fed to the input of the network, the network cycles the data through the recurrent connections until it reaches a fixed output. Training a network using fixed-point learning can be more difficult than with static backpropagation, but the added power of these networks can result in much smaller and more efficient implementations.
In recurrent backpropagation, activations are fed forward until a fixed value is achieved. After this relaxation period, the error is computed and propagated backwards. The error activations must be stable before the weights can be updated, so relaxation of the error is also needed.