  A theory of temporally asymmetric Hebb (TAH) rules which depress or
potentiate synapses depending upon whether the postsynaptic cell fires before
or after the presynaptic one is presented. Using the Fokker-Planck formalism,
we show that the equilibrium synaptic distribution induced by such rules is
highly sensitive to the manner in which bounds on the allowed range of synaptic
values are imposed. In a biologically plausible multiplicative model, we find
that the synapses in asynchronous networks reach a distribution that is
invariant to the firing rates of either the pre- or post-synaptic cells. When
these cells are temporally correlated, the synaptic strength varies smoothly
with the degree and phase of synchrony between the cells.
