Formal Barrier Limits Tabular Foundation Models' Operational Reasoning

New research reveals a fundamental limitation for tabular foundation models: they struggle to reason about data generated by operational systems unless explicitly provided with the rules governing those systems. The study introduces an "Operational Turing Test" where pairs of legal and rule-violating database states are constructed to be statistically indistinguishable based on simple column-value distributions. Despite their statistical similarity, values-only classifiers, including advanced models like XGBoost, TabICL, and TabPFN, fail to differentiate these states, achieving near-random accuracy. This highlights that merely observing data values is insufficient for understanding operational integrity. Only classifiers augmented with executable, rule-derived audits can achieve perfect classification accuracy. Even large language models (LLMs), when given schema, trigger sources, rule tables, and state files, perform poorly, indicating that the barrier is one of identifiability rather than model capacity or data scale. This suggests that simply increasing model size or data volume will not overcome this inherent limitation.