- The paper demonstrates that statistical indistinguishability of database states does not ensure operational equivalence, establishing a formal barrier for tabular foundation models.
- It introduces the Operational Turing Test, using tight marginal matching to yield a Bayes error lower bound near chance accuracy (≈ 0.50) for values-only classifiers.
- It shows that augmenting models with explicit, rule-derived audits achieves perfect accuracy, emphasizing the need for operational grounding in tabular reasoning.
Problem Statement and Motivation
This work establishes a formal, falsifiable barrier in the efficacy of tabular foundation models to reason about data generated by operational systems, specifically when rule-based logic is not available for grounding. The central claim is that statistical indistinguishability of database states does not entail operational equivalence, fundamentally constraining any architecture that lacks executable access to underlying system rules.
Theoretical Framework: The Operational Turing Test (OTT)
The Operational Turing Test (OTT) is introduced as a generalization of classical indistinguishability frameworks. The test operationalizes the concept by generating pairs of database states—one legal, one illegal—such that all observable $1$- and $2$-way column-value marginals are tightly matched (TV<0.02). Under these constraints, Le Cam's lemma yields a Bayes error lower bound of $0.49$ for any marginal-statistics-based classifier. This impossibility result is architecture-agnostic: induction capacity, feature engineering, and training set size cannot supersede the identifiability limitations imposed by information-theoretic considerations (2606.29091).
Experimental Protocol and Empirical Findings
The pipeline is instantiated on an order-to-cash schema encompassing customers, orders, and order items tables. Four operational rule categories are enforced: declarative referential consistency, cardinality constraints, value transformation logic, and transition constraints embedded in triggers/application code. Rule-violating states are generated to preserve all measured value marginals.
Models Evaluated
Three classes of values-only models are tested:
- XGBoost (gradient-boosted trees)
- TabICL (Tabular In-Context Learning via transformers)
- TabPFN (Transformer pre-trained on synthetic tabular tasks)
All models are evaluated under a rigorous two one-sided tests (TOST) procedure and permutation-null checks for sanity.
Key empirical results:
- All values-only models converge to chance accuracy (≈0.50), exactly matching the information-theoretic lower bound.
- Inclusion of relational features (e.g., foreign key coverage, within-row value pairs) improves recall for certain violation types (FK and cardinality) up to $0.89$, but value transformation logic remains inaccessible.
- Augmenting the feature space with outputs of seven executable, rule-derived audits immediately yields $1.00$ accuracy across all violation types.
- Increasing model scale or switching from aggregate to row-level representations offers no benefit in the absence of operational grounding.
LLMs with Full Access to Schema and Rules
Frontier LLMs (Kimi-K2.6, GPT-5.5) are also challenged on the OTT in settings where the entire schema, triggers, rule tables, and state files are given in-context. Across 100-state evaluations, no variant of GPT-5.5 accepts any legal states as LEGAL, and Kimi-K2.6 accepts $2/50$ legal states (with empty outputs on a significant fraction). Even with SQL execution scaffolding, LLM outputs reflect gaps in specification and code-induced audit logic, particularly missing value transformation and subtle semantic checks.
Implications: Practical and Theoretical
Identifiability Versus Capacity
The results unequivocally attribute the observed failures to identifiability, not inductive capacity. This distinction is critical—the source of the limitation is the information content available at inference, not architectural expressiveness or model size. As a consequence, larger models, richer representations, and more pre-training do not bridge the gap in the absence of explicit operational grounding.
Table Representation Learning and Benchmark Gaps
Prevailing tabular learning benchmarks, especially those focused on single-table, values-only, or even relational structure-aware tasks, inherently miss operational constraints that are routine in real-world data systems. The work demonstrates that benchmarks must include operational reasoning—the translation of executable rules, constraints, and trigger code into model-accessible logic—for measured progress to reflect practical deployability. The spectrum of evaluation must move from values-only to full operational audits, as operational errors can neither be anticipated nor detected by statistical pattern recognition alone.
LLMs and Prompted Code
The inability of LLMs to pass the OTT, despite prompt access to all relevant schema and rule artifacts, exposes deficits in prompt-based code/logic compilation for system state discrimination. This suggests that robust, reliable system-level AI for tabular data will require mechanisms for explicit rule parsing, code compilation, or symbolic execution, beyond large-scale language modeling and retrieval-augmented pipelines.
Toward Operational Grounding
The authors' operational grounding hypothesis is direct: reliable system-level tabular intelligence requires models to access, interpret, and execute explicitly encoded domain logic. This is orthogonal to scaling, architecture, or unsupervised representation learning. Audits and operational checks must become first-class features, integrated either by hybrid system design or by neural–symbolic methods capable of ingesting and executing code and logic.
Conclusion
This paper formalizes and validates an operational barrier for tabular foundation models, showing that statistical indistinguishability does not guarantee operational equivalence. The impossibility is rooted in information-theoretic identifiability and is independent of capacity, model sophistication, or training data scale. Achieving reliable tabular reasoning in operational settings requires explicit access and grounding in executable rule logic. Any future development of foundation models for structured data must address operational reasoning directly, either by design or by extending the scope of foundation modeling to encompass and interpret procedural database logic (2606.29091).