A power law describes the magnitude of adaptation in neural populations of primary visual cortex

How do neural populations adapt to the time-varying statistics of sensory input? We used two-photon imaging to measure the activity of neurons in mouse primary visual cortex adapted to different sensory environments, each defined by a distinct probability distribution over a stimulus set. We find that two properties of adaptation capture how the population response to a given stimulus, viewed as a vector, changes across environments. First, the ratio between the response magnitudes is a power law of the ratio between the stimulus probabilities. Second, the response direction to a stimulus is largely invariant. These rules could be used to predict how cortical populations adapt to novel, sensory environments. Finally, we show how the power law enables the cortex to preferentially signal unexpected stimuli and to adjust the metabolic cost of its sensory representation to the entropy of the environment.