Dynamics of temporal learning rules.

The changes of synaptic strength are analyzed on two time scales: the fast local field dynamics, and the slow synaptic modification dynamics. The fast dynamics are determined by the synaptic strengths and background noise in the system. The slow dynamics are determined by the functional form of a temporal learning rule. Temporal learning rules are defined to be functions yielding state dependent changes in synaptic strengths depending on the timing of pre- and postsynaptic states in the network. The evolution of local field dynamics that result from various learning rules are analyzed for a stochastic, discrete time neural model with no relative refractory period that receives a series of delayed adaptive inputs. A fixed point is found in the learning dynamics, and conditions for two types of instabilities are analyzed. Four universality classes of dynamics are found that are independent of the details of the temporal learning rules. Examples are given of biological systems in which these temporal learning rules have been identified, and their functional consequences are discussed.