A large program of research has aimed to ground large-scale cultural phenomena in processes taking place within individual minds. For example, investigating whether individual agents equipped with the right social learning strategies can enable cumulative cultural evolution given long enough time horizons. However, this approach often omits the critical processes that mediate between individual agents and multi-generational societies. Here, we argue that interacting groups are a necessary and explanatory level of analysis, linking individual and collective intelligence through two characteristic feedback loops. In the first loop, more sophisticated individual-level social learning mechanisms based on Theory of Mind facilitate group-level complementarity, allowing distributed knowledge to be compositionally recombined in groups; these group-level innovations, in turn, ease the cognitive load on individuals. In the second loop, societal-level processes of cumulative culture provide groups with new cognitive technologies, including shared language and conceptual abstractions, which set in motion new group-level processes to further coordinate, recombine, and innovate. Taken together, these cycles establish group-level interaction as a of intelligence, catalyzing both individual cognition and cumulative culture.