In a neural integrator, the variability and topographical organization of neuronal firing-rate persistence can provide information about the circuit's functional architecture. We used optical recording to measure the time constant of decay of persistent firing (persistence time) across a population of neurons comprising the larval zebrafish oculomotor velocity-to-position neural integrator. We found extensive persistence time variation (tenfold; coefficients of variation = 0.58-1.20) across cells in individual larvae. We also found that the similarity in firing between two neurons decreased as the distance between them increased and that a gradient in persistence time was mapped along the rostrocaudal and dorsoventral axes. This topography is consistent with the emergence of persistence time heterogeneity from a circuit architecture in which nearby neurons are more strongly interconnected than distant ones. Integrator circuit models characterized by multiple dimensions of slow firing-rate dynamics can account for our results.