Convex AI Compositionality and the Governance of AI System Populations

AI governance increasingly requires providers and public authorities to reason about multiple AI instantiations, alternative versions, and deployment configurations of multiple AI systems. Yet current regulation remains predominantly single-system-centric, acknowledging such multiplicity only sparsely without treating collections of related AI systems as governance objects. This creates an AI population governance problem: determining which instantiations can be meaningfully considered together and how their changing configurations can be represented and monitored. The first requirement has recently been addressed through trustworthiness-based accounts of AI identity. We address the second by introducing convex AI compositionality: a formal representation of the configurations generated by finite AI system populations that uses convex spaces. The core idea is that convex compositions of the operational states that a population of AI system instantiations may occupy over time are compatible with lifecycle reachability across the population and can preserve the formal identity relations between these systems. Well-known statistical and geometric constructions, such as weighted state distributions and convex hulls, become AI governance tools for distinguishing operational states, population weights, heterogeneity, and AI configuration change across different governance modes while remaining compatible, under stated conditions, with lifecycle reachability and AI identity. We illustrate our AI population governance framework through distributed healthcare deployments and controlled deployment of recruitment AI variants.