Endpoint Sensitivities Guide Limited-Query Shapley Regression

Shapley attribution needs every coalition of input groups, and for an implicit graph neural network each coalition costs an equilibrium solve. An affordable budget can fit a polynomial surrogate's pairwise interactions but not its three-way ones, so one three-way term must be chosen before the sampled values can fit its coefficient. We let the explained model make that choice. Its endpoint sensitivities, measured only at the empty and the full coalition, select the term at the cost of two linear solves, and we prove that the coalition values cannot make the choice themselves, since their own endpoint information reduces to a single number beyond pairwise structure. Across four graph-classification datasets and twenty independently trained models, sensitivity-informed cubic Shapley regression cuts low-budget attribution error by over 75% against second-order PolySHAP, and matched controls that choose the term differently all have higher error, 1.55 times ours when our choice is permuted across groups. More broadly, model derivatives can choose where to spend scarce representational capacity, while the costly evaluations that define the target decide how much of it to use.