Same Forecast, Different Capacity: Acquisition Paths in Time-Series Forecasting

How much structure does a forecasting model need to retain its prediction accuracy? The answer depends on how the smaller model is obtained. We study capacity as the first structural budget that reaches a fixed accuracy target, comparing models learned at that budget with restrictions of a learned full model. Across six public forecasting model families, the two routes can require substantially different capacities. More surprisingly, the complete forecasting function need not change for its restricted capacity to change: transferring functionally invisible components between trained linear representations changes the required budget in both directions, consistently across three seeds on four external model–task pairs. We identify two distinct sources of path dependence. A restriction can expose components that cancel in the full function; even when this source is eliminated, retained and discarded features remain coupled through the training covariance, producing different restricted and refitted solutions. Exact linear controls separate these sources from incomplete optimization. An exact risk response connects function-preserving interventions to capacity thresholds. Residual alignment explains why closer approximation of the full model need not improve task accuracy. Capacity is therefore an operational property of a forecasting task and its acquisition path, not a consequence of the full predictor alone.