Category: Neuroscience

Summary: Finding how strongly inhibitory targets must cluster before a balanced Dale-law network becomes unstable.

Balanced excitatory-inhibitory networks can remain stable even when individual connections are strong, but patterns in who inhibits whom may still matter. This experiment asks how much target-side clustering of inhibitory connections is needed before that balance breaks down.

The script builds dense non-symmetric matrices that respect Dale's law and then bisects an inhibitory-clustering parameter while increasing network size through iterative deepening. The threshold marks the point where structured inhibitory motifs produce an unstable spectral outlier.

This is useful because motif effects are often discussed qualitatively, while random-matrix stability is usually analyzed with weaker structural assumptions. The experiment turns inhibitory clustering into a direct finite-size instability threshold.

Method: Dense non-symmetric eigensolve with iterative deepening and bisection on inhibitory target clustering in Dale-law networks.

What is measured: Critical inhibitory-clustering threshold, instability onset, leading spectral outlier behavior, and bracket width.