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Cross-correlations in the activity in neural networks are commonly used tocharacterize their dynamical states and their anatomical and functionalorganizations. Yet, how these latter network features affect the spatiotemporalstructure of the correlations in recurrent networks is not fully understood.Here, we develop a general theory for the emergence of correlated neuronalactivity from the dynamics in strongly recurrent networks consisting of severalpopulations of binary neurons. We apply this theory to the case in which theconnectivity depends on the anatomical or functional distance between theneurons. We establish the architectural conditions under which the systemsettles into a dynamical state where correlations are strong, highly robust andspatially modulated. We show that such strong correlations arise if the networkexhibits an effective feedforward structure. We establish how this feedforwardstructure determines the way correlations scale with the network size and thedegree of the connectivity. In networks lacking an effective feedforwardstructure correlations are extremely small and only weakly depend on the numberof connections per neuron. Our work shows how strong correlations can beconsistent with highly irregular activity in recurrent networks, two keyfeatures of neuronal dynamics in the central nervous system.

How strong are correlations in strongly recurrent neuronal networks?