Category: Neuroscience

Summary: Finding the critical gain for stability when strict excitatory-inhibitory sign structure is combined with heavy-tailed synaptic magnitudes in dense random neural networks.

Random neural-network theory has studied both Dale-law sign constraints and heavy-tailed synaptic weights, but the combination of the two is less well mapped at finite size. This experiment asks where the stability boundary lies when a dense non-symmetric Dale-law network is driven by heavy-tailed synaptic magnitudes rather than Gaussian-like disorder.

The code uses GPU-accelerated iterative deepening and repeated spectral estimates to bisect the critical gain across increasing network sizes. It tracks the fraction of stable disorder realizations, the mean maximal real part of the spectrum, and a localization score for the leading unstable mode.

That framing matters because heavy tails can shift not only when instability appears, but also how concentrated the destabilizing mode becomes. The output is therefore both a stability-threshold map and a structural diagnostic of the instability that emerges.

Method: GPU spectral threshold search with iterative deepening and bisection on gain sigma in heavy-tailed, non-symmetric Dale-law neural ensembles.

What is measured: Critical gain threshold, stable-fraction estimate, leading real-part growth, localization score, inhibitory fraction, heavy-tail parameter, and bracket width.