Statistical learning is a powerful mechanism that allows us torapidly extract structure from the environment. However,nuances of what structure is extracted—for example, whetherreliable groups are stored without knowledge of theirconstituent item order—are not well understood, leaving uswith open questions about how this mechanism supportsbehaviour. Here, we extend prior work on the representation ofstatistical structure by asking what specific aspects of structurematter for memory judgments. We consider three candidatesfor memory representation: transitional probability, order-independent group information, and position tags. Participantswatched a stream of shape triplets and then completed arecognition memory test designed to isolate contributions oftransitional probability, group, and position. We demonstratethat although memory for transitions alone would be sufficientfor knowledge of triplets, participants showed evidence ofrepresenting both transitional probability and group. Our datahighlight statistical learning as a mechanism enablinggeneralization across experiences.