  The representation of the natural-density, heterogeneous connectivity of
neuronal network models at relevant spatial scales remains a challenge for
Computational Neuroscience and Neuromorphic Computing. In particular, the
memory demands imposed by the vast number of synapses in brain-scale network
simulations constitutes a major obstacle. Limiting the number resolution of
synaptic weights appears to be a natural strategy to reduce memory and compute
load. In this study, we investigate the effects of a limited synaptic-weight
resolution on the dynamics of recurrent spiking neuronal networks resembling
local cortical circuits, and develop strategies for minimizing deviations from
the dynamics of networks with high-resolution synaptic weights. We mimic the
effect of a limited synaptic weight resolution by replacing normally
distributed synaptic weights by weights drawn from a discrete distribution, and
compare the resulting statistics characterizing firing rates, spike-train
irregularity, and correlation coefficients with the reference solution. We show
that a naive discretization of synaptic weights generally leads to a distortion
of the spike-train statistics. Only if the weights are discretized such that
the mean and the variance of the total synaptic input currents are preserved,
the firing statistics remains unaffected for the types of networks considered
in this study. For networks with sufficiently heterogeneous in-degrees, the
firing statistics can be preserved even if all synaptic weights are replaced by
the mean of the weight distribution. We conclude that even for simple networks
with non-plastic neurons and synapses, a discretization of synaptic weights can
lead to substantial deviations in the firing statistics, unless the
discretization is performed with care and guided by a rigorous validation
process.
