This paper addresses two main challenges facing systems neuroscience today: understanding the nature and function of a) cortical feedback between sensory areas and b) correlated variability. Starting from the old idea of perception as probabilistic inference, we show how to use knowledge of the psychophysical task to make easily testable predictions for the impact that feedback signals have on early sensory representations. Applying our framework to the well-studied two-alternative forced choice task paradigm, we can explain multiple empirical findings that have been hard to account for by the traditional feedforward model of sensory processing, including the task-dependence of neural response correlations, and the diverging time courses of choice probabilities and psychophysical kernels. Our model makes a number of new predictions and, importantly, characterizes a component of correlated variability that represents task-related information rather than performance-degrading noise. It also demonstrates a normative way to integrate sensory and cognitive components into physiologically testable mathematical models of perceptual decision-making.
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