Cross-Task Transfer in LLM Population Simulators: Identification and Failure Modes

Large language models (LLMs) are increasingly used to construct synthetic populations and behavioral digital twins that are calibrated to observed behavior and then deployed in new or counterfactual settings. We study when such calibration supports reliable cross-task transfer. We model the population as a finite mixture of LLM personas, estimate mixture weights from aggregate behavior on a source task, and transfer them to predict behavior on a target task. We identify two failure modes. First, source-task calibration may not identify the underlying persona mixture, although target behavior can still be identified under a simple cross-task condition. Second, finite-sample noise can mask population-level non-identification and create spurious transfer precision. Experiments across different LLMs illustrate both phenomena, showing that source-task fit alone is insufficient to validate downstream predictions.