Variable synaptic strengths controls the firing rate distribution in feedforward neural networks.

Heterogeneity of firing rate statistics is known to have severe consequences on neural coding. Recent experimental recordings in weakly electric fish indicate that the distribution-width of superficial pyramidal cell firing rates (trial- and time-averaged) in the electrosensory lateral line lobe (ELL) depends on the stimulus, and also that network inputs can mediate changes in the firing rate distribution across the population. We previously developed theoretical methods to understand how two attributes (synaptic and intrinsic heterogeneity) interact and alter the firing rate distribution in a population of integrate-and-fire neurons with random recurrent coupling. Inspired by our experimental data, we extend these theoretical results to a delayed feedforward spiking network that qualitatively capture the changes of firing rate heterogeneity observed in in-vivo recordings. We demonstrate how heterogeneous neural attributes alter firing rate heterogeneity, accounting for the effect with various sensory stimuli. The model predicts how the strength of the effective network connectivity is related to intrinsic heterogeneity in such delayed feedforward networks: the strength of the feedforward input is positively correlated with excitability (threshold value for spiking) when firing rate heterogeneity is low and is negatively correlated with excitability with high firing rate heterogeneity. We also show how our theory can be used to predict effective neural architecture. We demonstrate that neural attributes do not interact in a simple manner but rather in a complex stimulus-dependent fashion to control neural heterogeneity and discuss how it can ultimately shape population codes.