Systemic Tau as a homeostatic trigger for structural self-repair in event-driven networks

Abstract

Systemic Tau, the mean pairwise Kendall rank correlation of module activity on a common event index, is used as the signal for a structural repair of an event-driven exclusive-or network. Because that mean is signed, an increase in one pair and a decrease in another can cancel. The operative alarm is therefore the mean absolute change in rank correlation on the edges present at the end of calibration. The signed mean is retained as a control, and its definition is unchanged. In a feed-forward network of seven modules and six excitatory edges, deletion of three edges is followed for 1,500 trials across 30 seeds reserved before the run. The matrix alarm restores six edges in every seed. Its paired advantage over a random target, a random time and no repair is 0.276, 0.216 and 0.264, and each 95% interval lies above +0.05. Against an alarm that uses the label error, the difference is −0.019, inside a margin of 0.05 and entirely below zero. A polarity reversal that leaves the wiring intact does not separate the event-driven conditions. A long short-term memory network, damaged by a mask on its weights rather than by deletion of edges, relearns the task because training continues. This record contains the English article and a Spanish summary. The reference implementation and the trial-level records are archived separately under the MIT license at https://doi.org/10.5281/zenodo.23001551. The code is developed at https://github.com/johelpadilla/tri-structural-repair. No funding is declared. The article text is distributed under the Creative Commons Attribution 4.0 International license.