Regulation of homeostatic hyperparameters for critical hovering

Identify practical principles or mechanisms to regulate the hyperparameters of the homeostatic synaptic adaptation—namely the baseline A, the depression strength U_W, and the recovery time τ in W_{ij}[t+1] = W_{ij}[t] + (1/τ)(A − W_{ij}[t]) − U_W W_{ij} S_i[t] S_j[t]—so that the average coupling W* robustly converges to and hovers near the synchronization critical point W_c under realistic constraints and perturbations.

Background

The proposed anti-Hebbian plasticity drives the network toward the edge of synchronization, with W* depending on the hyperparameters A, U_W, and τ. The paper characterizes how W* scales with these parameters and demonstrates robustness over wide ranges.

Despite this characterization, a concrete strategy for regulating these hyperparameters in realistic or biological settings to ensure stable near-critical operation remains unspecified and is explicitly posed as an open question.