  We consider an infinite system of spiking neurons with a drift and both
excitatory and inhibitory connections. We study conditions for
non-explosiveness and the uniqueness of the invariant measure. In particular,
we examine conditions that allow this infinite interacting system to go beyond
the usual interactions of uniformly summable weights. As a result, we extend
the Galves-L\"ocherbach model beyond the restrictive uniform summability of the
model.
