Task-induced neural covariability as a signature of approximate Bayesian learning and inference

Perception can be characterized as an inference process in which beliefs are formed about the world given sensory observations. The sensory neurons implementing these computations, however, are classically characterized with firing rates, tuning curves, and correlated noise. To connect these two levels of description, we derive expressions for how inferences themselves vary across trials, and how this predicts task-dependent patterns of correlated variability in the responses of sensory neurons. Importantly, our results require minimal assumptions about the nature of the inferred variables or how their distributions are encoded in neural activity. We show that our predictions are in agreement with existing measurements across a range of tasks and brain areas. Our results reinterpret task-dependent sources of neural covariability as signatures of Bayesian inference and provide new insights into their cause and their function. HighlightsO_LIGeneral connection between neural covariability and approximate Bayesian inference based on variability in the encoded posterior density. C_LIO_LIOptimal learning of a discrimination task predicts top-down components of noise correlations and choice probabilities in agreement with existing data. C_LIO_LIDifferential correlations are predicted to grow over the course of perceptual learning. C_LIO_LINeural covariability can be used to reverse-engineer the subjects internal model. C_LI