Claims of AI emergence should be grounded in information decomposition

When a language model develops capabilities not traceable to its individual components, when a multi-agent AI system outperforms any agent alone, or when a human–AI pair succeeds where either fails in isolation, AI researchers describe it as ``synergy''. However, these are usually informal assessments not supported by a theoretical framework, making these claims impossible to compare or even meaningfully dispute. This position paper argues that information decomposition can serve as a unifying formal framework to operationalize this intuition. Information decomposition provides a way to distinguish qualitatively different \emph{types} of information, including unique information available on individual components, redundant information shared across components, and synergistic information accessible only from all parts together. We present how this decomposition can be naturally used to study ensembles of attention heads, autonomous agents, or a human and an AI. We demonstrate the utility of this lens across different scales and substrates, show how it unifies existing knowledge across fields, and leads to cross-level conjectures that none of these fields would generate independently.