# Statistically Indistinguishable, Operationally Distinct: A Formal Barrier for Tabular Foundation Models

arXiv: https://arxiv.org/abs/2606.29091 · HTML: https://mlsanity.com/paper/2606.29091/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 27 Jun 2026.

## Builds on (most cited first, 12 of 12)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [TabICL: A Tabular Foundation Model for In-Context Learning on Large Data](https://mlsanity.com/paper/2502.05564/) (2025)
- [TabArena: A Living Benchmark for Machine Learning on Tabular Data](https://mlsanity.com/paper/2506.16791/) (2025)
- [TabPFN-2.5: Advancing the State of the Art in Tabular Foundation Models](https://mlsanity.com/paper/2511.08667/) (2025)
- [CARTE: Pretraining and Transfer for Tabular Learning](https://mlsanity.com/paper/2402.16785/) (2024)
- [Griffin: Towards a Graph-Centric Relational Database Foundation Model](https://mlsanity.com/paper/2505.05568/) (2025)
- [Relational In-Context Learning via Synthetic Pre-training with Structural Prior](https://mlsanity.com/paper/2603.03805/) (2026)
- [NameGuess: Column Name Expansion for Tabular Data](https://mlsanity.com/paper/2310.13196/) (2023)
- [SALT: Sales Autocompletion Linked Business Tables Dataset](https://mlsanity.com/paper/2501.03413/) (2025)
- [Position: Foundation Models for Tabular Data within Systemic Contexts Need Grounding](https://mlsanity.com/paper/2505.19825/) (2025)

## Built on by (most cited first, 1 of 1)

- [Relational Learning as World Modeling](https://mlsanity.com/paper/2610.16763/) (2026)

## Abstract (arXiv)

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 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 ≥0.49 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 fed by seven executable rule-derived audits reaches 1.00 classification accuracy. In three matched 100-state frontier large-language-model (LLM) runs, models given the schema, trigger source, rule tables, and state files classify at most 2/50 legal states as LEGAL; GPT-5.5 accepts 0/50 legal states even with higher reasoning effort and a Structured Query Language (SQL) executor. The access-ladder pattern also appears on a second schema with structurally distinct rule families (banking ledger: cross-row balance, cumulative aggregate). The barrier is identifiability, not capacity: scale, data, and richer features cannot cross it without operational grounding.