Beyond Fit: Intervention-Aware Hypothesis Search for OOD Tabular Regression

Modern tabular predictors perform strongly in-distribution but often degrade under out-of-distribution (OOD) shifts, especially when deployment requires extrapolation beyond observed support. A key difficulty is that fitting the source data does not uniquely determine how predictions should continue outside that support: different predictive rules can explain the observed data yet imply very different extrapolations. This suggests that OOD tabular regression requires not only learning or selecting a strong predictor, but also constructing alternative predictive hypotheses and deciding which of them should be used at deployment. We introduce Intervention-Aware Hypothesis Search (IAHS), a framework that separates these two problems by constructing executable hypotheses through representations, predictor families, predictive roles, and compositions, and then using source-derived evidence, permitted unlabeled deployment information, and deployment-specific constraints to guide protocol-conditioned adoption without target labels. On TabularMath, hypothesis construction increases the retrospective mean per-task best OOD $R^2$ from 0.3006 to 0.8177, while Source-score Top-1 selection on the same candidate pool reaches only 0.0625 compared with 0.5829 for IAHS. Across additional regression benchmarks, IAHS improves mean OOD $R^2$ over TabPFN v3 by 0.619 while maintaining comparable non-OOD performance. These results show that reliable extrapolation depends on both which predictive alternatives are made available and how they are selected under the evidence available at deployment.