When Does Input Adaptation Need a Selector? The Role of Routing-Capable Baselines

Input adaptation gives a frozen predictor several possible corrections. A learned selector can choose one for each example. Its value, however, depends on what a single candidate can already do. We study this dependence by adding routing candidates built from the same fitted maps. This enlargement preserves the pointwise oracle for fixed row-wise maps. It strengthens the best complete candidate and cannot increase selector headroom. An exact value decomposition locates the remaining losses in a learned tree. The controlled study makes the effect concrete. With 200 development examples, the original selector gains 9.6 accuracy points over the frozen predictor. A routed candidate gains 12.4 points using the same maps. Across 36 datasets, cross-fitted selectors add little to enlarged libraries with three frozen networks. Split learning and TabICLv2 retain positive increments, showing that the outcome depends on the learning setup. Natural-shift sensitivity checks separate adaptation gains from inactive input pathways. Finally, we distinguish testing an overall improvement from testing a selector upgrade. The resulting evaluation asks what selection adds after simple routing is already available to the baseline.