  Human culture relies on collective innovation: our ability to continuously
explore how existing elements in our environment can be combined to create new
ones. Language is hypothesized to play a key role in human culture, driving
individual cognitive capacities and shaping communication. Yet the majority of
models of collective innovation assign no cognitive capacities or language
abilities to agents. Here, we contribute a computational study of collective
innovation where agents are Large Language Models (LLMs) that play Little
Alchemy 2, a creative video game originally developed for humans that, as we
argue, captures useful aspects of innovation landscapes not present in previous
test-beds. We, first, study an LLM in isolation and discover that it exhibits
both useful skills and crucial limitations. We, then, study groups of LLMs that
share information related to their behaviour and focus on the effect of social
connectivity on collective performance. In agreement with previous human and
computational studies, we observe that groups with dynamic connectivity
out-compete fully-connected groups. Our work reveals opportunities and
challenges for future studies of collective innovation that are becoming
increasingly relevant as Generative Artificial Intelligence algorithms and
humans innovate alongside each other.
