Systematically map eigenspectrum configurations beyond unit-rank mean connectivity

Systematically map the configurations of outlying eigenvalues and associated eigenmodes that arise when the mean connectivity has rank greater than one and the number of neuronal populations exceeds two in recurrent networks with chain motifs, thereby characterizing how relaxing the unit-rank assumption and increasing population complexity alter the eigenspectrum.

Background

The analysis in this work focuses on two-population networks with unit-rank mean connectivity, yielding a single mean-induced eigenmode and one additional chain-motif-induced mode. Relaxing these constraints—by increasing the number of populations or the rank of the mean connectivity—introduces additional non-trivial eigenmodes and potentially multiple outliers. A comprehensive taxonomy of these eigenspectrum configurations is needed to generalize the theory to richer cortical circuits with multiple inhibitory subtypes and more complex population structures.