  We show that the local Spike Timing-Dependent Plasticity (STDP) rule has the
effect of regulating the trans-synaptic weights of loops of any length within a
simulated network of neurons. We show that depending on STDP's polarity,
functional loops are formed or eliminated in networks driven to normal spiking
conditions by random, partially correlated inputs, where functional loops
comprise weights that exceed a non-zero threshold. We further prove that STDP
is a form of loop-regulating plasticity for the case of a linear network
comprising random weights drawn from certain distributions. Thus a notable
local synaptic learning rule makes a specific prediction about synapses in the
brain in which standard STDP is present: that under normal spiking conditions,
they should participate in predominantly feed-forward connections at all
scales. Our model implies that any deviations from this prediction would
require a substantial modification to the hypothesized role for standard STDP.
Given its widespread occurrence in the brain, we predict that STDP could also
regulate long range synaptic loops among individual neurons across all brain
scales, up to, and including, the scale of global brain network topology.
