When Are Joint Predictive Models Reusable?

Joint predictive models are reused after training under new compositions, observations, and questions. Familiar-task accuracy alone does not establish which later answers remain available. We ask what training records must reveal and what a retained state must preserve for such reuse. For known finite operators, we characterize the information required by future queries and evidence updates. Across 32 newly sampled worlds, records targeting a theoretically identified missing three-way interaction reduce conditional-query excess Brier score by 0.0206 relative to equal-budget irrelevant records. At the primary budget, direct fits of a sufficient target marginal with seven free parameters and the full 64-state law achieve nearly identical mean risks. In a separate dynamic intervention, removing past–current coupling preserves tested forward predictions but stops revision of the past; a five-coordinate state preserves revision for a fixed past event. Within the supplied mechanism class, local mechanisms learned from chain endpoints also predict unseen trees and use their outputs to revise later predictions with fixed parameters. Thus familiar-task accuracy can conceal different reuse abilities, while the information sufficient for a future use can be smaller than a full world law.