How the activity of sensory neurons supports perceptual decisions remains one of the central questions of systems neuroscience. Two primary frameworks guide the field’s thinking on this question. One framework, guided by ideas of information maximization, redundancy reduction, and efficient coding, focuses on the decision-related information represented by neural responses and how it is extracted from sensory populations. In another framework, based on the Bayesian brain hypothesis, sensory responses represent posterior beliefs about the outside world, which then guide decision-making. Interestingly, these complementary perspectives make seemingly contradictory predictions for how the structure of neural covariability should change over the course of learning a perceptual decision-making task. Here, we present new empirical and theoretical results that address this paradox. Training two monkeys on two different orientation discrimination tasks each, while recording from area V4 using Utah arrays, we find that noise correlations become more information-limiting both over the course of weeks (learning) and – after learning, but not before – over the course of a single trial (inference). These findings confirm critical predictions of the hierarchical inference framework and are compatible with empirical studies that have found task-specific noise correlations at the end of learning. Importantly, they directly contradict the dominant interpretation of changes in noise correlations due to learning and attention: mediating the relationship between learning and attention with behavior by how much they reduce, or limit, information. We show that during hierarchical inference an increase in information-limiting correlations does not reflect lower feedforward input information, but instead a redistribution of task-related population information to individual neurons. We confirm this theoretical prediction in our data by showing that the increased redundancy does not reflect a decrease in information in the population, but instead an increase in the information carried by each individual neuron.