## Recurrent Networks Back Propagation

A recurrent neural network (also called a feedback network) allows self-loops and backward connections between all neurons in the network. The back-propagation algorithm can be altered to a recurrent neural network by adding feedback connections, and the algorithm for training the recurrent network is called recurrent back-propagation (RBP). F.J. Pineda and L. B. Almeida proposed RBP methods in 1987, independently.

The general learning procedure for an RBP includes the following steps:

• Step 1. Initialize the weights to small random values.

• Step 2. Calculate the activations of all neurons for node j:

where a(.) is the activation function, wj is the weight from i to j, xj is input to neuron i, if there is one, otherwise 0, and t is a time constant. The fixed point can be calculated by setting dyj/dt = 0. The output yj (t) is found from the recursive formula:

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