Identifying the regime in which the cortical microcircuit operates is a prerequisite to determine the mechanisms that mediate its response to stimulus. Classic modeling work has started to characterize this regime through the study of perturbations, but an encompassing perspective that links the full ensemble of the network's response to appropriate descriptors of the cortical operating regime is still lacking. Here we develop a class of mathematically tractable models that exactly describe the

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... modulation of the distribution of cell-type-specific calcium-imaging activity with the contrast of a visual stimulus. The model's fit recovers signatures of the connectivity structure found in mouse visual cortex. Analysis of this structure subsequently reveal parameter-independent relations between the responses of different cell types to perturbations and each interneuron's role in circuit-stabilization. Leveraging recent theoretical approaches, we derive explicit expressions for the distribution of responses to partial perturbations which reveal a novel, counter-intuitive effect in the sign of response functions.