Sensitivity and stability: A signal propagation sweet spot in a sheet of recurrent centre crossing neurons

In this paper we demonstrate that signal propagation across a laminar sheet of recurrent neurons is maximised when two conditions are met. First, neurons must be in the so-called centre crossing configuration. Second, the network’s topology and weights must be such that the network comprises strongly coupled nodes, yet lies within the weakly coupled regime. We develop tools from linear stability analysis with which to describe this regime in terms of the connectivity and weight strengths of a network. We use these results to examine the apparent tension between the sensitivity and instability of centre crossing networks.