Neural Identification of Controlled Dynamical Systems and Recurrent Networks - Neural Networks: Methodology and Applications - page 277

Fig. 4.18. Teacher-forced learning of a recurrent network

• Or approximate the gradient of previous states with respect to the cur-

rent weights by the values of those gradients with respect to the previous
weights: that is called real-time recurrent learning (RTRL).

More details are provided in the next section.

4.6.1 Teacher-Forced Learning

In the teacher-forced learning method, all the inputs of the canonical form of
the network are known during the training process. The name of the algorithm
is inspired from the teacher's behavior: the teacher corrects the student's
behavior at each step instead of first observing the behavior for a while and
correcting it afterwards. The engineer just takes into account the fact that
experimental data are available to set the model at any time-step. Then the
network learning process amounts to a nonlinear regression of the network
on its input (NARX) as shown in Chap. 2. That learning process is depicted
graphically in Fig. 4.18.
An input-state trajectory (set of N input-state pairs) is used as the data-
base for the training process. The intermediate states (time k ) are used both
as outputs to assess the evolution of the current network computing evolution
from time k 1totime k and as inputs to feed the network and compute

evolution from time k to time k + 1. Of course to apply this simple method,
one has to know the full input of the process at each time-step. It cannot be
implemented in the general case.

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4.6.2 Unfolding of the Canonical Form and Backpropagation
Through Time (BPTT)

In this method, the recurrent characteristics of the network are considered by
building a feedforward network whose outputs are identical to the sequence
of outputs of the recurrent network. As mentioned in Chap. 2, that network
is obtained by copying the feedforward part of the canonical form N times if