We use the olfactory system and forebrain of (adult) zebrafish as a model to analyze how relevant information is extracted from sensory inputs, how information is stored in memory circuits, and how sensory inputs inform behavior. A series of recent findings provides evidence that inhibition has not only homeostatic functions in neuronal circuits but makes highly specific, instructive contributions to behaviorally relevant computations in different brain regions. These observations imply that the connectivity among excitatory and inhibitory neurons exhibits essential higher-order structure that cannot be determined without dense network reconstructions. To analyze such connectivity we developed an approach referred to as “dynamical connectomics” that combines 2-photon calcium imaging of neuronal population activity with EM-based dense neuronal circuit reconstruction. In the olfactory bulb, this approach identified specific connectivity among co-tuned cohorts of excitatory and inhibitory neurons that can account for the decorrelation and normalization (“whitening”) of odor representations in this brain region. These results provide a mechanistic explanation for a fundamental neural computation that strictly requires specific network connectivity.