APS: Bias-Controlled Adaptive Prototype Simulation for Population-Scale LLM Agents

LLM-agent simulation offers a flexible computational tool for studying population response trajectories that depend on scenario events, memory, demographics, and evolving social context. However, full multi-round simulation scales linearly with both population size and horizon, requiring every agent to query the LLM at every round. We propose \textbf{Adaptive Prototype Simulation (APS)}, a framework that treats scaling as a recurrent LLM-oracle allocation problem rather than a static sampling, propagation, or surrogate-modeling problem. APS preserves the specified LLM as the online transition oracle while querying adaptive core prototypes, selected singleton-tail agents, and shadow-audit agents. Prototype responses induce local response surfaces for nearby agents, reducing online LLM calls without replacing the underlying transition model. To control approximation bias, shadow-audit residual correction estimates propagation residuals for aggregate correction and future budget allocation, while tail-protected singleton routing directly queries selected isolated, heterogeneous, or high-curvature regions that are vulnerable to smoothing. We analyze APS as an estimator of the LLM-induced population transition and decompose its error into prototype-coverage error, shadow-audit residual-correction error, local-propagation bias, and temporal context mismatch. Under the reported protocols, APS gives lower reference-aligned distributional discrepancy than scale-oriented and same-budget baselines while reducing online LLM calls, with ablations and compact robustness checks diagnosing the main bias-control mechanisms. In a 10M-agent, multi-round public-opinion simulation, APS achieves a $381.1\times$ reduction over full simulation, with reference-aligned final-round JSD 0.094 against the corresponding full-LLM reference.