Practicing simple visual tasks leads to a dramatic improvement in performing them. This learning is specific to the stimuli used for training. We show here that the degree of specificity depends on the difficulty of the training conditions. We find that the pattern of specificities maps onto the pattern of receptive field selectivities along the visual pathway. With easy conditions, learning generalizes across orientation and retinal position, matching the spatial generalization of higher visual areas. As task difficulty increases, learning becomes more specific with respect to both orientation and position, matching the fine spatial retinotopy exhibited by lower areas. Consequently, we enjoy the benefits of learning generalization when possible, and of fine grain but specific training when necessary. The dynamics of learning show a corresponding feature. Improvement begins with easy cases (when the subject is allowed long processing times) and only subsequently proceeds to harder cases. This learning cascade implies that easy conditions guide the learning of hard ones. Taken together, the specificity and dynamics suggest that learning proceeds as a countercurrent along the cortical hierarchy. Improvement begins at higher generalizing levels, which, in turn, direct harder-condition learning to the subdomain of their lower-level inputs. As predicted by this reverse hierarchy model, learning can be effective using only difficult trials, but on condition that learning onset has previously been enabled. A single prolonged presentation suffices to initiate learning. We call this single-encounter enabling effect 'eureka'.