Statistically Indistinguishable, Operationally Distinct: A Formal Barrier for Tabular Foundation Models
Tabular foundation models cannot reason about data produced by running systems without access to the rules that govern them. We make this statement falsifiable. The \emph{Operational Turing Test} (OTT) constructs pairs of legal and rule-violating database states whose $1$- and $2$-way column-value marginals match to a total variation of $<0.02$; Le~Cam's lemma then bounds any values-only classifier at $\geq0.49$ Bayes error. Three values-only baselines (XGBoost, TabICL, TabPFN) hit the bound exactly (accuracy $0.50$, pre-registered two one-sided tests (TOST) $p<0.002$), raw row-level access does not help, exposing relational value consistency closes most of the gap, and only a classifier ...
| Authors | Tassilo Klein, Johannes Hoffart |
|---|---|
| Primary category | cs.LG |
| Published | 27 June 2026 |
| Last updated at source | 27 June 2026 |
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