Perceptual separability is a foundational concept in cognitive psychology. A variety of research questions in perception - particularly those dealing with notions such as "independence," "invariance," "holism," and "configurality" - can be characterized as special cases of the problem of perceptual separability. Furthermore, many cognitive mechanisms are applied differently to perceptually separable dimensions than to non-separable dimensions. Despite the importance of dimensional separability, surprisingly little is known about its origins. Previous research suggests that categorization training can lead to learning of novel dimensions, but it is not known whether the separability of such dimensions also increases with training. Here, we report evidence that training in a categorization task increases perceptual separability of the category-relevant dimension according to a variety of tests from general recognition theory (GRT). In Experiment 1, participants who received pre-training in a categorization task showed reduced Garner interference effects and reduced violations of marginal invariance, compared to participants who did not receive such pre-training. Both of these tests are theoretically related to violations of perceptual separability. In Experiment 2, participants who received pre-training in a categorization task showed reduced violations of perceptual separability according to a model-based analysis of data using GRT. These results are at odds with the common assumption that separability and independence are fixed, hardwired characteristics of features and dimensions.