The ability to associate sensory stimuli (e.g., apples and cookies) with abstract knowledge (e.g., “healthy” versus “unhealthy”) is critical for survival. How are these associations implemented in the brain? And what governs how neural activity changes during abstract knowledge acquisition? To investigate these questions, we consider a circuit model that learns to map sensory stimuli into abstract categories via gradient-descent plasticity. We focus on typical neuroscience tasks (simple, and context-dependent categorization), and use simulations and mathematical analysis to uncover how neural activity evolves during learning. We find that activity of single neurons becomes, over learning, selective to abstract variables: these include variables that are explicitly reinforced, such as category, and variables that represent task rules and are indirectly cued, such as context. Such behaviour is universal, and independent of model details; this is in agreement with experiments, where the emergence of selectivity has been consistently reported across studies. On the other hand, how the population as a whole responds to categories and contexts does depend on details - and thus carries valuable information on the circuitry that implements the task. For instance, over learning, category and context correlations (i.e., correlations among population activity in response to different categories and contexts) can become either positive or negative. Also, the population can exhibit either symmetric or asymmetric responses: the number of neurons that most strongly respond to a given category can be similar or very different across categories. Negative and positive correlations, as well as symmetric and asymmetric responses, have been observed in experiments; our model provides a single explanation for these seemingly contradictory studies. We determined how, in the model, correlations and symmetry depend on circuit (gain and sparsity of activity, relative learning rates) and task (number of stimuli, context-dependence) parameters; these dependencies make experimentally testable predictions about the underlying circuitry.