When Interpretability Meets Generalization: Delta-GAM for Robust Extrapolation in Out-of-Distribution Settings

Out-of-Distribution (OOD) extrapolation, where test data feature values extend beyond the training range, poses significant challenges in machine learning. While existing solutions often sacrifice interpretability, resulting in limited applicability in high-stakes applications where interpretability is a a critical requirement. In this paper, we propose Delta-GAM, an interpretable Generalized Additive Model (GAM) that achieves robust extrapolation in OOD scenarios. Our method jointly learns (1) feature-target relationships and (2) functional adaptations for extrapolating beyond the training distribution by reformulating GAM fitting as a second-order interaction problem between features and their distributional offsets. We theoretically show that smooth GAM shape functions induce an approximately low-rank structure in these interactions, enabling efficient decomposition via a specialized neural network. Experiments on synthetic and real-world data demonstrate Delta-GAM's superior performance in OOD extrapolation tasks while preserving model interpretability, bridging a key gap in trustworthy machine learning.