  Recurrent Backpropagation and Equilibrium Propagation are supervised learning
algorithms for fixed point recurrent neural networks which differ in their
second phase. In the first phase, both algorithms converge to a fixed point
which corresponds to the configuration where the prediction is made. In the
second phase, Equilibrium Propagation relaxes to another nearby fixed point
corresponding to smaller prediction error, whereas Recurrent Backpropagation
uses a side network to compute error derivatives iteratively. In this work we
establish a close connection between these two algorithms. We show that, at
every moment in the second phase, the temporal derivatives of the neural
activities in Equilibrium Propagation are equal to the error derivatives
computed iteratively by Recurrent Backpropagation in the side network. This
work shows that it is not required to have a side network for the computation
of error derivatives, and supports the hypothesis that, in biological neural
networks, temporal derivatives of neural activities may code for error signals.
