Same Error, Different Consequences: Information Interfaces between Deterministic Completion and Stochastic Time-Series Generation

Deterministic completion is often used as an intermediate step before stochastic generation for irregular time series, and its quality is typically assessed by pointwise reconstruction errors such as MAE or RMSE. However, two completions with the same reconstruction error need not be equally useful as conditions for a downstream generator. This raises a basic question: is completion accuracy sufficient to characterize downstream conditioning utility? We study this question through the information interface between deterministic completion and stochastic generation. To separate how much a completion is wrong from how it is wrong, we construct controlled interventions that match aggregate missing-region RMSE while changing the temporal organization of completion errors. We then measure how these interventions alter the relative utility of transmitting the full completion versus a coarse temporal representation to the generator. Across four time-series datasets and two downstream generator architectures, we find that aggregate completion RMSE alone is insufficient to predict downstream behavior. Reorganizing learned completion errors with RMS matching can substantially change generation quality and the relative preference between full and coarse interfaces. Importantly, the direction of this effect is not universal: sensor datasets and a prospectively preregistered financial-domain test exhibit different, and in some cases opposite, interface shifts. These results show that completion accuracy and downstream conditioning utility are distinct quantities, and suggest that the information interface between deterministic completion and stochastic generation should be treated as a modeling problem in its own right rather than as a passive handoff of the completed sequence.