Precise About the Wrong Law: Uncertainty Misses Pooled Sources

Foundation inference models estimate a dynamical law and its uncertainty from a set of trajectories in a single forward pass. This interface assumes that every trajectory comes from the same system, yet the input carries no record of where each trajectory came from. We show that when trajectories from different systems are pooled, the models’ native uncertainty does not reveal the violation. In the released model for Markov jump processes, a two-source context and a single-law context matched to its one-step transition statistics receive nearly identical uncertainty. The complete trajectories still tell the two apart: a likelihood-ratio witness that knows the candidate laws, but not the source labels, separates them almost perfectly. Decoders trained on the uncertainty output, by contrast, stay near chance on held-out tasks. We call this failure context aliasing: the trajectories expose source heterogeneity that native uncertainty fails to flag. As in classical misspecification, the model fits a pooled pseudo-law while losing fidelity to its sources, with little change in uncertainty. Routing the same trajectories by source cuts generator and first-passage-time error by more than half. A simple transition-count test provides an effective check for source heterogeneity. In controlled simulations, the model for ordinary differential equations shows the same decoupling of error and uncertainty. On recorded motion, the response varies across record groups. Uncertainty from these models is conditional on an experiment; it alone does not establish whether its trajectories should be pooled.