  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.
