Covariate Copies Count as Evidence in Time-Series Foundation Models

Covariate-aware time-series foundation models forecast a target from the related series supplied with it, and which series they receive depends on how a pipeline was built: the same sensor exported twice, a temperature in two units, one weather station joined in for several zones. We ask whether these models count such representations as evidence. In synthetic worlds with a closed-form Bayes reference, we supply one source as m channels and measure by finite differences how strongly the forecast follows it relative to a second source, its implied log evidence ratio. Eight exact copies raise this ratio by 0.81, 0.68 and 2.28 nats in Chronos-2, t0-beta and TiRex-2, where the Bayes reference does not move: 0.33, 0.28 and 1.00 of the response to eight independent measurements. Measurements that share part of their error are over-counted as well, and in variate attention an exact copy is exactly a log-multiplicity weight on its key. The count reaches beyond synthetic data. On 18 fev-bench tasks, supplying every dynamic covariate eight times raises the error of three of four models with resolved intervals, and in a public energy dataset whose own zone mapping duplicates a weather station, inputs that repeat a zone’s weather series change the day-ahead forecasts of all three models. Declaring the source removes the dependence without training: keeping one channel per declared alias, and adding to the keys of measurements that share an error the log of their effective number over their count, makes forecasts exactly invariant to copies. In a comparison fixed before its results and run on fresh worlds, this source bias has a smaller worst-case error on such measurements than reducing them to their effective number, in all three models, and it keeps the full response to independent measurements that averaging reduces. Copies sometimes help accuracy, and declaring a source gives that help up. For these models, how a covariate table is built is part of the model specification.