A biological gradient descent for prediction through a combination of STDP and homeostatic plasticity.

Identifying, formalizing, and combining biological mechanisms that implement known brain functions, such as prediction, is a main aspect of research in theoretical neuroscience. In this letter, the mechanisms of spike-timing-dependent plasticity 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.