The quest for determining the degree of learning difficulty associated with different types of categories has been instrumental in our understanding of human categorization behavior and, more broadly, human generalization. For instance, we now know that the topological nature of the dimensions (e.g., whether these are integral or separable) that define the family of categories generated with three binary dimensions yield two different learning difficulty orderings. In our study, for the first time, we replicated one such classic ordering involving integral dimensions and explored the impact that the choice of dimensional values, along with the nature of the stimulus presentation, had on learning difficulty during the learning phase of our four experiments. Two standard orderings were observed in our investigation which were consistent with the hypothesis that multilevel discrimination plays a key role in concept learning. We accounted for our empirical results by making this role explicit at three levels, the feature, object, and category structure levels, using a dual discrimination invariance model (DDIM) derived from the core invariance law of generalized invariance structure theory (GIST). The model involves a "discrimination switch" via what is referred to in GIST as the "tau discrimination threshold" where two distinct extreme degrees of discrimination yield two fundamental learning difficulty orderings able to account for results from our experiments without free parameters. We then show how the DDIM is not only a more accurate and general predictor than the best alternatives but also provides a plausible and tenable cognitive mechanism for understanding these behaviors.