How strong are correlations in strongly recurrent neuronal networks?

TL;DR

This paper develops a theory explaining how strong, spatially modulated correlations in neural activity emerge in strongly recurrent networks, especially when an effective feedforward structure is present, reconciling strong correlations with irregular activity.

Contribution

The paper introduces a general theoretical framework linking network architecture, particularly effective feedforward structures, to the emergence and scaling of correlations in recurrent neural networks.

Findings

Strong correlations arise with effective feedforward structures.

Correlations scale with network size and connectivity degree.

Networks without feedforward structure exhibit weak, size-independent correlations.

Abstract

Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of the correlations in recurrent networks is not fully understood. Here, we develop a general theory for the emergence of correlated neuronal activity from the dynamics in strongly recurrent networks consisting of several populations of binary neurons. We apply this theory to the case in which the connectivity depends on the anatomical or functional distance between the neurons. We establish the architectural conditions under which the system settles into a dynamical state where correlations are strong, highly robust and spatially modulated. We show that such strong correlations arise if the network exhibits an effective feedforward structure. We establish how this feedforward structure determines the way correlations scale with the network size and the degree of the connectivity. In networks lacking an effective feedforward structure correlations are extremely small and only weakly depend on the number of connections per neuron. Our work shows how strong correlations can be consistent with highly irregular activity in recurrent networks, two key features of neuronal dynamics in the central nervous system.