The transformational theory of similarity suggests people are sensitive to the number of transformation operations needed to make two compared representations match. Although this theory has been quite influential, little is known about how transformations are learned and to what extent learned transformations affect similarity judgments. This paper presents two experiments addressing these questions, in which people learned categories defined by an arbitrary transformation. In Experiment 1, when the transformations were directly visible, people had no trouble learning and applied their knowledge to both similarity and categorization judgments involving previously unseen items. In Experiment 2, the task required transformations to be inferred rather than observed. People were still able to learn the categories, but in this more difficult case ratings were less strongly affected by training. Overall, this work suggests that newly learned transformations can impact similarity judgments but the salience of the transformation has a large impact on transfer.