## Real Time Recurrent Network

The real-time recurrent network (RTRN) is characterized as containing hidden neurons and allowing arbitrary dynamics with a fully connected network structure. The RTRN is especially capable of dealing with time-varying input or output through its own temporal operation and has been applied to speech recognition.

The RTRN has M external inputs, N concatenated nodes, and K outputs. Figure 5 shows the schematic diagram of RTRN. An external input vector of size M is applied to the network at a discrete time t. Let y(t) denote the corresponding vector of size N of individual neuron outputs produced one step later at time t. The input vector and the one-step delayed output vector are concatenated to form vectors of size (M + N). In total, an N by (M + N) recurrent weight matrix is formed.

The net internal activity of neuron j at time t is as follows:

where v(t) is x(t) ifj denotes the external input, and y(t — 1) if j denotes the neuron for outputs. The term wj{t) indicates the weight between the input and the hidden layers. At the next time step (t + 1), the output of neuron j is computed by passing v(t) through the nonlinearity (e.g., logistic function), resulting in the following:

The real-time recurrent learning handles weight feedback in the real-time process and allows faster convergence in recurrent learning. The detailed algorithm could be referred to Williams and Zisper.

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