QueryPrint: Measuring Behavioral Similarity with Counterfactual Futures

Representation learning transforms observations into features for prediction and control. For control, a useful notion of state similarity asks whether the same policies lead to similar futures. Existing behavioral and predictive methods learn state relationships from trajectories, which show one future of each state and rarely the futures of different states under the same policies. We introduce QueryPrint, which restores saved states in resettable environments, executes fixed query policies, and summarizes the resulting counterfactual futures into fingerprints. Distances between fingerprints define a query-relative behavioral target, which we test for action dependence, reliability, and non-degeneracy and use to supervise a compact encoder. Across 55 Atari games, this encoder captures the measured geometry in its native distances and generalizes to unseen states and query policies. In contrast, the 9 learned objectives and 12 frozen pretrained representations we evaluate show little of this geometry in their native distances. Heads trained on the same target recover much of it from frozen features and reach the encoder's level at matched capacity. The measured distance also predicts differences in lives lost under independently trained PPO agents, while a learned world model recovers the geometry only partially. Replayed futures provide a directly measured target for learning and evaluating behavioral geometry, and show that information recoverable from features need not appear in native distances.