Leaf Values as Coordinates: Exact Contrastive Explanation for Gradient-Boosted Ensembles

Gradient-boosted ensembles predict by summing one leaf value per tree. The conventional view treats these values as intermediate results; this paper proposes reading them directly as coordinates in M-dimensional space. Each instance becomes a point, and the model score is the sum of coordinates. This perspective turns the model into a linear function in that space, making contrastive explanation exact rather than approximate. The difference vector between two instances is zero on coordinates where they share a leaf; thus, the gap between a rejected applicant and an accepted one is carried by a few coordinates, each traceable to a real split in a real tree. No surrogate fitting, sampling, or additive-feature assumption is needed—additivity already exists in the right space. The authors build a recourse method on this representation and evaluate it on five tabular datasets under repeated cross-validation. The recommendation reconstructs the model's own decision to 6.2×10^-15, allowing an auditor to re-check arithmetic without the model. On credit datasets, the method is Pareto-non-dominated on effort against realism. When recommendations are restricted to changes the subject can actually make (not age, not settled delinquency), it retains 58% of its validity where the strongest baseline retains 41%—a distinction standard evaluation cannot see because it never asks whether a recommendation is feasible.