Moritz Helias, Institute of Neuroscience and Medicine, Research Centre Jülich | Distributed correlations indicate optimal sequence memory

Abstract

The brain processes time-varying input, but is it not known if its dynamical state is optimal for this task. Indeed, recurrent and randomly coupled networks of rate neurons display a rich internal dynamics near the transition to chaos, which has been associated with optimal information processing capabilities. In particular, the dynamics becomes arbitrarily slow at the onset of chaos similar to ‘critical slowing down’. The interplay between time-dependent input signals, network dynamics, and the resulting consequences for information processing are, however, yet poorly understood.

We here present a completely solvable model that allows us to investigate the effect of time-varying input on the transition to chaos. We analytically obtain the phase diagram spanned by the coupling strength and the input amplitude: External drive shifts the transition to chaos to significantly larger coupling strengths than predicted by linear stability analysis. The intermediate regime is absent in time-discrete networks and only exists in their more realistic time-continuous counterparts. This novel dynamical regime combines locally expansive dynamics with asymptotic stability. We investigate sequential memory and analytically show that memory capacity is optimal within the novel regime. Because it is unclear if cortex operates in such a computationally beneficial regime, we develop a finite-size mean-field theory which relates the statistics of measured covariances to the statistics of connections, in particular the spectral radius of the connectivity matrix. The theory shows that the large dispersion of spike count covariances across pairs of neurons, observed in massively parallel recordings, is an indicator that cortex indeed operates close to the breakdown of linear stability