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

Perception is often characterized computationally as an inference process in which uncertain or ambiguous sensory inputs are combined with prior expectations. Although behavioral studies have shown that observers can change their prior expectations in the context of a task, robust neural signatures of task-specific priors have been elusive. Here, we analytically derive such signatures under the general assumption that the responses of sensory neurons encode posterior beliefs that combine sensory inputs with task-specific expectations. Specifically, we derive predictions for the task-dependence of correlated neural variability and decision-related signals in sensory neurons. The qualitative aspects of our results are parameter-free and specific to the statistics of each task. The predictions for correlated variability also differ from predictions of classic feedforward models of sensory processing and are therefore a strong test of theories of hierarchical Bayesian inference in the brain. Importantly, we find that Bayesian learning predicts an increase in so-called “differential correlations” as the observer’s internal model learns the stimulus distribution, and the observer’s behavioral performance improves. This stands in contrast to classic feedforward encoding/decoding models of sensory processing, since such correlations are fundamentally information-limiting. We find support for our predictions in data from existing neurophysiological studies across a variety of tasks and brain areas. Finally, we show in simulation how measurements of sensory neural responses can reveal information about a subject’s internal beliefs about the task. Taken together, our results reinterpret task-dependent sources of neural covariability as signatures of Bayesian inference and provide new insights into their cause and their function.Author summary: Perceptual decision-making has classically been studied in the context of feedforward encoding/ decoding models. Here, we derive predictions for the responses of sensory neurons under the assumption that the brain performs hierarchical Bayesian inference, including feedback signals that communicate task-specific prior expectations. Interestingly, those predictions stand in contrast to some of the conclusions drawn in the classic framework. In particular, we find that Bayesian learning predicts the increase of a type of correlated variability called “differential correlations” over the course of learning. Differential correlations limit information, and hence are seen as harmful in feedforward models. Since our results are also specific to the statistics of a given task, and since they hold under a wide class of theories about how Bayesian probabilities may be represented by neural responses, they constitute a strong test of the Bayesian Brain hypothesis. Our results can explain the task-dependence of correlated variability in prior studies and suggest a reason why these kinds of correlations are surprisingly common in empirical data. Interpreted in a probabilistic framework, correlated variability provides a window into an observer’s task-related beliefs.