Category: Neuroscience

Summary: Finding how much excitatory leakage between modules is needed to destabilize an otherwise balanced modular Dale-law neural network.

Neural circuits constrained by Dale's law separate excitatory and inhibitory cells by sign, and modular organization can create local balance that helps keep activity stable. This experiment asks when that protection fails once excitatory signals begin leaking too strongly between modules instead of staying mostly contained within them.

The model builds dense non-symmetric random matrices with strict-sign excitatory and inhibitory structure, then uses iterative deepening and bisection to locate the leak level where the leading eigenvalue crosses the stability boundary. Carrying the threshold bracket to larger system sizes turns the result into a finite-size stability map rather than a single simulation point.

That matters because modular circuit structure and random-matrix stability are often studied separately. Here the experiment isolates inter-module leak as the control knob and tests how much locally balanced modular structure can really protect a dense recurrent network.

Method: Dense non-symmetric eigensolve with iterative deepening and bisection on inter-module excitatory leak across system sizes N = 64 to 2048.

What is measured: Critical leak threshold, leading-eigenvalue stability boundary, system size reached, and threshold bracket width.