Models of balanced autoassociative memory networks predict that specific inhibition is critical to store information in connectivity. To explore these predictions, we characterized and manipulated different subtypes of fast-spiking interneurons in the posterior telencephalic area Dp (pDp) of adult zebrafish, the homolog of the piriform cortex. Modeling of recurrent networks with assemblies showed that a precise balance of excitation and inhibition is important to prevent not only excessive firing rates ("runaway activity") but also the stochastic occurrence of high pattern correlations ("runaway correlations"). Consistent with model predictions, runaway correlations emerged in pDp when synaptic balance was perturbed by optogenetic manipulations of feedback inhibition but not feedforward inhibition. Runaway correlations were driven by sparse subsets of strongly active neurons rather than by a general broadening of tuning curves. These results are consistent with balanced neuronal assemblies in pDp and reveal novel computational functions of inhibitory microcircuits in an autoassociative network.