  Identifying, formalizing and combining biological mechanisms which implement
known brain functions, such as prediction, is a main aspect of current research
in theoretical neuroscience. In this letter, the mechanisms of Spike Timing
Dependent Plasticity (STDP) and homeostatic plasticity, combined in an original
mathematical formalism, are shown to shape recurrent neural networks into
predictors. Following a rigorous mathematical treatment, we prove that they
implement the online gradient descent of a distance between the network
activity and its stimuli. The convergence to an equilibrium, where the network
can spontaneously reproduce or predict its stimuli, does not suffer from
bifurcation issues usually encountered in learning in recurrent neural
networks.
