Parameter-Shared Blockwise Forecasting: Trading Sequential Compute for Storage
ORIGINAL / Compose the Horizon: Parameter-Shared Blockwise Forecasting under a Sequential-Compute Trade-off
This study proposes Recursive Functional Decomposition (RFD), which uses a compact parameter-shared operator to sequentially emit contiguous future blocks instead of forecasting the entire horizon in one pass, trading sequential computation for parameter storage; in a frozen long-context cross-protocol comparison, it records lower test error in most cells against ten baseline families.
01 ABSTRACT
Fact: RFD factorizes the long-horizon mapping into three parameter-shared block predictions that occupy disjoint future intervals and are concatenated, not added as trend, seasonal, or residual components; each emitted block joins the rolling context to condition the next application. In controlled three-seed experiments, removing forward feedback hurts all four datasets, while stopping gradients through it changes little, indicating the useful signal comes from the evolving forecast state itself. Author view: reapplying the shared operator helps consistently, but by less than widening it.
02 KEY FINDINGS
- RFD uses a parameter-shared operator to sequentially generate future blocks; the three blocks are concatenated, not added as components, and each output joins the rolling context.
- Controlled experiments show that removing forward feedback hurts all four datasets, but blocking its gradients has little effect, indicating the signal comes from the evolving forecast state.
- In a frozen long-context comparison, RFD records lower test error in 23 of 24 cells, but this is cross-protocol: RFD uses 512/720-step context while baselines use 96 steps.
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