Contrast gain control is a reparameterization of a population response curve

Neurons in primary visual cortex (area V1) adapt in different degrees to the average contrast of the environment, suggesting that the representation of visual stimuli may interact with the state of cortical gain control in complex ways. To investigate this possibility, we measured and analyzed the responses of neural populations to visual stimuli as a function of contrast in different environments, each characterized by a unique distribution of contrast. Our findings reveal that, for a given stimulus, the population response can be described by a vector function $\text{r}\left(g_{e}c\right)$ , where the gain $g_e$ is a decreasing function of the mean contrast of the environment. Thus, gain control can be viewed as a reparameterization of a population response curve, which is invariant across environments. Different stimuli are mapped to distinct curves, all originating from a common origin, corresponding to a zero-contrast response. Altogether, our findings provide a straightforward, geometric interpretation of contrast gain control at the population level and show that changes in gain are well coordinated among members of a neural population.