Equilibrium properties of temporally asymmetric Hebbian plasticity

A theory of temporally asymmetric Hebb rules, which depress or potentiate s ynapses depending upon whether the postsynaptic cell fires before or after the presynaptic one, is presented. Using the Fokker-Planck formalism, we sh ow that the equilibrium synaptic distribution induced by such rules is high ly sensitive to the manner in which bounds on the allowed range of synaptic values are imposed. In a biologically plausible multiplicative model, the synapses in asynchronous networks reach a distribution that is invariant to the firing rates of either the presynaptic or postsynaptic cells. When the se cells are temporally correlated, the synaptic strength varies smoothly w ith the degree and phase of their synchrony.