Renormalized Cellular Intelligence: When Does Model Reduction Preserve Collective Capability?
Xuening Wu, Yanlan Kang, Qianya Xu, Haode Yang, Shan Yu, Shenqin Yin
As multi-agent systems grow in size and complexity, understanding which features of their interactions support collective capability becomes increasingly difficult. Can a simpler description preserve both task performance and the measured contribution of interactions between agents? Preserving collective dynamics alone is insufficient: reduction can alter decision-relevant information or give a non-communicating baseline access to pooled observations, distorting the measured advantage of interaction. We introduce Renormalized Cellular Intelligence (RCI), a framework for specifying and auditing capability preservation across scales. RCI treats the task, interacting dynamics, matched baseline, decision interfaces, and resource budget as a joint object of reduction. It specifies dynamical closure, decision compatibility, and preservation of the intended baseline comparison, and bounds the resulting error in relative capability gain. An exact analytical construction demonstrates task-score preservation, while a counterexample shows how closed reduced dynamics can erase the measured interaction gain. Using cellular systems as models of locally interacting agents, we evaluate three reduction candidates on five frozen learned models without retraining. The final candidate reduces the evolving state from eight to five dimensions per cell (37.5%). Within-run uncertainty bounds support relative gain above a prespecified threshold for the fixed model collection, yet the candidate fails the closure and decision-preservation requirements for a complete RCI certificate. RCI provides explicit criteria for distinguishing positive interaction gains from
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