IsoKoop: The Cycle Comes From Outside the Window

In long-horizon multivariate forecasting, a look-back window shorter than the cycle it must forecast does not fix that cycle's length: two cycles of different length can agree on the whole window, so the length is absent from it, not hard to fit. Per-window normalisation turns that observation into an exact interface, one that binds published models too: moved in front of its normaliser, FreqCycle's cycle table costs that model up to 210.6% under a gain. A forecaster that standardises each window by its own mean and scale is scale-equivariant for every inner network, and a profile supplied from outside the window keeps that guarantee when subtracted in raw units only if it is a constant level, but at any shape once it enters in the normalised coordinates or is rescaled by the window's scale. The ratio of the dataset cycle to the look-back, fixed by the protocol, says what the window cannot hold, and IsoKoop supplies it. Against eight forecasters retrained in one pipeline on thirteen public benchmarks, four horizons and three seeds, IsoKoop attains the best mean rank in MSE and MAE (2.34 against 3.77 and 2.14 against 3.65) and the lowest MSE in 34 of the 52 settings (2.24 against 3.99 and 38 of 56 with our TrafficC panel). On the 883-variate network it uses a fourteenth of EMAformer's parameters, the runner-up in mean rank. IsoKoop's supply is a rank-R prototype read at the sample index, zero-initialised so that its profile, though not its period, is learned, and an optional level anchor. In our ablations, and in the baselines with no new run, the supply helps most where the cycle exceeds the look-back, on panels that here are also the sensor networks, so ratio and panel type are not separated; on the real shifts we tested, these readings lower the error only on Solar at H=96, less where the scale moved most, and raise it on PEMS04 and PEMS08. The same lens audits the benchmarks: on Exchange no model beats persistence, many variates change scale from training to test, and nine drifting sensors decide Traffic's ranking.