GateCorrect: Recursive Self-Improvement for Frozen Time-Series Forecasters

Even after a time-series forecaster is frozen, its errors can contain patterns predictable from the input history. The unresolved problem is sequential: accepting one correction changes the residual that supplies supervision for the next, so a basis diagnosed for the earlier target may no longer describe the useful correction directions. GateCorrect formulates this process as recursive self-improvement (RSI): each round re-diagnoses the current residual, allocates a new correction unit, and admits it only when validation supports the update. A directional path uses a low-dimensional, predictability-screened output span for uncapped amplitudes; a bounded, level-aware path fits the remaining error while retaining window-level information. Across three forecasters and seven datasets, one unit reduces test MSE by 3.74% over 252 runs. In a separate 216-run matched comparison, RSI raises mean reduction from 2.18% with one unit to 2.81%; later units improve 32 of the 37 runs that accept them. GateCorrect therefore makes residual diagnosis and depth selection part of the learning method, rather than treating successive residual fitting as a fixed stack.