  The magnitude of correlations between stimulus-driven responses of pairs of
neurons can itself be stimulus-dependent. We examine how this dependence
impacts the information carried by neural populations about the stimuli that
drive them. Stimulus-dependent changes in correlations can both carry
information directly and modulate the information separately carried by the
firing rates and variances. We use Fisher information to quantify these effects
and show that, although stimulus dependent correlations often carry little
information directly, their modulatory effects on the overall information can
be large. In particular, if the stimulus-dependence is such that correlations
increase with stimulus-induced firing rates, this can significantly enhance the
information of the population when the structure of correlations is determined
solely by the stimulus. However, in the presence of additional strong spatial
decay of correlations, such stimulus-dependence may have a negative impact.
Opposite relationships hold when correlations decrease with firing rates.
