OrdinalICL: Making Tabular Foundation Models Ordinal-Native

Ordinal targets arise in ratings, disease stages, and educational attainment: their categories are ordered, but the distances between them are unknown. General tabular foundation models usually ignore this structure and predict nominal classes. We ask a controlled question: if the backbone, trainable capacity, data, initialization, optimizer, and compute are held fixed, does giving the model an ordinal target interface help? We introduce OrdinalICL, which represents a declared variable-cardinality scale by ordered thresholds and returns a coherent class distribution with exact reversal symmetry. A TabICLv2 ordinal adapter and a compact model trained from scratch first establish that the interface learns and uses order. The original survey identifies TabDPT-Turbo v1.2 as the best-performing surveyed backbone that supports an exactly matched training experiment. We keep this backbone unchanged and attach equally sized prediction-correction modules that differ only in target geometry: the control uses class identities; OrdinalICL uses rank coordinates and ordered boundary decisions. Two independently prespecified evaluations on unseen synthetic mechanisms favor the ordinal module for every seed, class count, mechanism, and coverage stratum. Across a unified 40-family real benchmark, the final model also improves both its matched nominal control and released TabDPT, with family-level intervals excluding zero. The synthetic experiments provide the architecture test, while the real-data analysis measures transfer beyond the synthetic generator. Under matched training conditions, explicitly modeling target order improves TabDPT on ordinal problems.