How do neurons encode information about sensory inputs and motor
outputs?  In many cases, the averaged spiking rates of populations
of similarly "tuned" neurons carry these signals.  This has inspired
mean-field models of these populations, which commonly assume that
the individual neurons spike independently or have fixed values of
correlations.  We use linear response calculations and an intuitive
statistical model to show that neither of these cases is to be
expected.

Instead, correlations vary sharply with firing rates and hence with
the signals themselves.  This has strong consequences for the neural
code.  We illustrate these via closed-form calculations of Fisher
information, which quantifies the accuracy of encoding.

This is joint work with Jaime de la Rocha, Brent Doiron, Kreso
Josic, and Alex Reyes.