Distributions of covariances as a window into the operational regime of neuronal networks

TL;DR

This paper develops a mean-field theory linking the distribution of neuronal covariances to the network's operational regime, revealing divergence at critical coupling and suggesting brain networks operate near this critical point.

Contribution

It introduces a finite-size mean-field approach that connects connection statistics with covariance distributions, explaining their divergence at criticality in neuronal networks.

Findings

Covariance distribution width diverges at a critical coupling.

Networks transition from regular to chaotic dynamics at this critical point.

Brain recordings suggest operation near this critical regime.

Abstract

Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static (quenched) disorder of the connectivity in recurrent random networks was so far elusive. We here derive a finite-size mean-field theory that reduces a disordered to a highly symmetric network with fluctuating auxiliary fields. The exposed analytical relation between the statistics of connections and the statistics of pairwise covariances shows that both, average and dispersion of the latter, diverge at a critical coupling. At this point, a network of nonlinear units transits from regular to chaotic dynamics. Applying these results to recordings from the mammalian brain suggests its operation close to this edge of criticality.