A long tradition of studies in psycholinguistics has examined the formation and generalization of ad hoc conventions in reference games, showing how newly acquired conventions for a given target transfer to new referential contexts. However, another axis of generalization remains understudied: how do conventions formed for one target transfer to completely distinct targets, when specific lexical choices are unlikely to repeat? This paper presents two dyadic studies (N = 240) that address this axis of generalization, focusing on the role of nameability -- the a priori likelihood that two individuals will share the same label. We leverage the recently-released KiloGram dataset, a collection of abstract tangram images that is orders of magnitude larger than previously available, exhibiting high diversity of properties like nameability. Our first study asks how nameability shapes convention formation, while the second asks how new conventions generalize to entirely new targets of reference. Our results raise new questions about how ad hoc conventions extend beyond target-specific re-use of specific lexical choices.

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