An ongoing debate in phonology concerns the treatment of cumulative constraint interactions, or ‘gang effects’, and by extension the question of which phonological frameworks are suitable models of the grammar. This paper uses a series of artificial grammar learning experiments to examine the inferences that learners draw about cumulative constraint violations in phonotactics in the absence of a confounding natural-language lexicon. I find that learners consistently infer linear counting and ganging cumulativity across a range of phonotactic violations.