Coarse-Grained Dynamics of Multi-Agent Collective AutoResearch

Multi-agent collective AutoResearch generates research findings through shared knowledge and collaborative exploration. As the number of agents increases, collective behavior arising from complex interactions becomes increasingly important, making system-level performance and scalability difficult to predict and motivating an effective dynamical description. We model the effective dynamics of collective behavior from a statistical physics perspective using coarse-graining methods and formalize a multi-agent collective AutoResearch system as a stochastic growth process in which agents are coupled through a growing knowledge hypergraph. We describe each agent by the phase-type distribution of its action duration and outcome, specify local hypergraph interaction rules, and average over the agents to obtain the coarse-grained dynamics. This formulation can model and predict collective behavior using measurements on single agents, mapping different research agents onto their phase-type distributions and different frameworks onto interaction rules and correction terms. We evaluate the model's predictive ability in formal theorem-proving tasks: from the phase-type distribution of a single agent, it predicts how the completion time of many agents sharing a record changes with their number, in close agreement with experiments. This provides a dynamical framework for understanding and predicting the scalability of collective AutoResearch systems.