Category: Neuroscience

Summary: Finding how much inhibitory gain heterogeneity destabilizes an otherwise stable dense Dale-law network.

Neural networks constrained by Dale's law separate excitatory and inhibitory cells by sign, but real inhibitory neurons can still differ substantially in strength from one another. This experiment asks when variation in inhibitory gain becomes large enough to tip an otherwise stable dense network into instability.

The model generates dense non-Hermitian matrices with fixed excitatory-inhibitory sign structure and then bisects a gain-dispersion parameter across increasing sizes. Alongside the stability boundary, it probes whether the first unstable mode becomes concentrated on the most strongly amplified inhibitory subpopulation.

That distinction matters because instability may emerge from structured heterogeneity rather than from changes in mean coupling alone. The output is therefore a finite-size threshold map for a biologically plausible source of variability that standard homogeneous analyses smooth away.

Method: Dense non-Hermitian eigensolve with iterative deepening and bisection on inhibitory gain dispersion.

What is measured: Critical gain-dispersion threshold, leading-eigenvalue stability boundary, localization of the unstable mode, and bracket width.