SHIFT: Progressive Feedback for Time Series Forecasting

A point forecast is a compromise: when several futures are consistent with the observed history, the conditional mean matches none of them. This compromise is unnecessary in staged deployment, where a long-horizon forecast is released block by block and each released block is measured before the next one is due— early observations discriminate between futures, and the forecaster should change its mind rather than merely its output. We present SHIFT, which maintains a bank of complete future hypotheses together with a belief over them. A historyconditioned generator writes hypotheses as low-rank residual fields around a base forecast; as blocks are revealed, a causal filter updates the belief through a discounted log-linear rule that combines a likelihood energy with a learned, calibrated evidence term, while a recurrent assimilator rewrites the not-yet-released portion of every hypothesis in response to sample-specific innovations. Supervising such a filter is the central difficulty: the correct belief is only unambiguous in hindsight. SHIFT therefore trains the causal student against a hindsight teacher— a posterior computed with the full target—distilling privileged information into every intermediate belief, and augments this with coverage, diversity, balance, and entropy-contraction objectives that shape the bank and the filter.