When Can Neural Routing Policies Discard Redundant Inputs?

Fixing an executed route prefix in capacitated vehicle routing leaves a residual optimization problem, yet neural solvers can continue to use inputs that no longer determine its feasible continuations or costs. When can such task-redundant inputs be removed while preserving routing quality? We connect residual-task formulation to computational interventions and controlled retraining. We select POMO and ReLD for their contrasting mechanisms of information reuse: cross-token normalization and cached readouts from a normalization-free encoder. In both, local masking leaves served-customer influence in shared statistics or retained embeddings. Closing the identified paths removes this influence but worsens fixed-weight route quality, separating task sufficiency from the dependencies of a trained representation. Complementary retraining experiments on progress inputs show that, under mixed-size training, deleting dedicated step inputs maintains quality comparable to normalized retention, while normalized progress better supports transfer from a single small training size. These findings motivate a state-aware graph-pointer that retains observed context, represents unfinished customers beyond current feasibility, and uses normalized progress. Arrivals and demand realizations update this same observation interface, allowing the solver to transfer zero-shot to dynamic and stochastic tasks from a static supervised initialization and improve through complete-route adaptation. These adaptation gains recur across training lineages. The study establishes a basis for simplification that accounts for both residual-task sufficiency and learned computational dependence, with deletion and re-encoding evaluated by the quality of the resulting routes.