Identifying Intelligent Processes via Online Sequential Testing

Active sequential hypothesis testing studies how to identify an unknown hypothesis with a given set of sensing actions. We study this in the setting of identifying large language models (LLMs), \textit{i.e.}, if a user is conversing with an LLM drawn from a known set of models, how can they identify which one is in use? Here, the available sensing actions (evaluations) are themselves a design choice: an evaluator must first decide which environments and prompt families to construct, and only then decide how to use them sequentially. We formalize these two levels as an outer probe-design problem and an inner identification problem. Simply put, the outer stage selects a set of probes to be sent to the entire set of models, creating a kind of fingerprint dataset. This is followed by the inner stage, which sequentially sends a budget-minimizing set of those probes to identify the model in use. For the outer problem, we show that selecting which evaluations to construct at minimum cost, so that every pair of candidates is distinguished, is exactly a weighted set cover problem. Since the response distributions of the candidate models are not known exactly but only through calibration samples, we give a one-shot procedure that estimates the cover instance from these samples. For the inner problem, we bound the number of evaluations needed to identify the unknown model in terms of how well the available evaluations distinguish each pair of candidates.