Category: Neuroscience

Summary: Estimating the stability boundary for dense Dale-law neural networks with heavy-tailed synaptic magnitudes.

Random neural-network models are often studied either with Dale sign constraints or with heavy-tailed synaptic weights, but rarely with both at once in a dense finite-size setting. This experiment asks how the critical gain for instability shifts when a sign-constrained excitatory-inhibitory network also has heavy-tailed synaptic magnitudes.

The model generates dense non-symmetric matrices whose entries respect Dale's law while drawing magnitudes from a heavy-tailed distribution. Iterative deepening then tracks the stability boundary across increasing sizes, locating the critical coupling scale where the spectrum crosses into instability.

The interest is in whether heavy tails change the familiar balance between excitation and inhibition in a systematic way. If they do, standard Gaussian intuition about recurrent-network stability may be incomplete for strongly heterogeneous circuits.

Method: Dense non-symmetric eigensolve with iterative deepening to estimate the critical gain in heavy-tailed Dale-law matrices.

What is measured: Critical gain threshold, leading spectral stability indicator, system size reached, and threshold bracket width.