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

• URL: http://arxiv.org/abs/2606.29091v1
• Date: Sat, 27 Jun 2026 21:14:06 GMT
• Title: Statistically Indistinguishable, Operationally Distinct: A Formal Barrier for Tabular Foundation Models
• Abstract summary: We show that Tabular foundation models cannot reason about data produced by running systems without access to the rules that govern them.<n>In three matched $100$-state frontier large-lemma-model (LLM) runs, models given the schema, trigger source, rule tables, and state files classify at most $2/50$ legal states as Legal.<n>The barrier is identifiability, not capacity scale, data, and richer features cannot cross it without operational grounding.
• Score: 6.240573495762223
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 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.

Related papers

• Reference-Based Bias Detection in LLMs via Relative Representations of Hidden States [4.505185728893222]
  We propose a reference-based method that audits bias in hidden-state representations across related model variants.<n>Because fine-tuning reshapes representation geometry, absolute hidden states are not directly comparable.<n>We measure how target groups shift in their association with positive and negative attributes.
  arXiv  Detail & Related papers  (2026-09-09T11:33:35Z)
• Which Model Is Actually Serving You? IRIS: Budgeted Black-Box Auditing of Model Substitution and Routing Dilution in LLM Gateways [6.964275075635626]
  We present $mathrmIRIS$, an audit that needs only the returned text.<n>A cheap pilot fits the exponential query-error decay and freezes that budget before any suspect query is issued.<n>$mathrmIRIS$ matches or beats detection on shared tasks, and adaptive allocation lifts the matched-budget target-hit rate from $73$% to $87$%.
  arXiv  Detail & Related papers  (2026-07-23T02:32:08Z)
• Isolating LLM Alignment from Regex: Zero Coverage and Metric-Dependent Divergence Under Adversarial Mutation [51.56484100374058]
  Previous work found no measurable coverage gain from adding a live Gemini backend behind an active filter.<n>We introduce $L_5$-no-regex -- identical to $L_4$-real (Gemini-2.5-flash, token-budget cap, rate limit, output scrub) but with the nine-pattern filter disabled.<n>We evaluate it against adversarial probes across three sub-languages.
  arXiv  Detail & Related papers  (2026-06-12T18:54:24Z)
• A Mathematical Theory of Value: a synthesis on goal-directed agency under resource constraints [6.057587531186626]
  We show that value, the quantity goal-directed agents create, destroy, and exchange, is a lawful structural quantity in the same category as information.<n>For populations, value is frame-relative while price is frame-independent; a fleet that pools its resource and fuses its perception inherits the ceiling.
  arXiv  Detail & Related papers  (2026-06-10T16:11:04Z)
• Imbuing Large Language Models with Bidirectional Logic for Robust Chain Repair [44.80087038178069]
  We introduce Teleological Reasoning Infilling (TRI), a training framework that endows decoder-only transformers with a native emphgoal-conditioned bridging capability.<n>At inference, TRI operates as a surgical repair module within a dual-system loop.<n>Experiments on three benchmarks demonstrate that TRI achieves state-of-the-art performance across all tasks, while reducing per-problem token expenditure by 31.2%.
  arXiv  Detail & Related papers  (2026-06-03T15:58:48Z)
• Which Defense Closes Which Threat? Attributing OWASP-LLM-Top-10 Coverage and Its Brittleness Under Paraphrasing [51.56484100374058]
  Production LLM applications stack several defense families -- refusal-phrase filters, tokenbudget controls, model allowlists, rate limits, tool-registry authentication -- yetBAS benchmarks report a single aggregate coverage number.<n>We add four-LLM-Top-10-aware agents to a 21-agent baseline scanner and target a lattice of four synthetic LLM endpoints.
  arXiv  Detail & Related papers  (2026-06-01T19:39:25Z)
• What Do EEG Foundation Models Capture from Human Brain Signals? [64.48249643001402]
  Modern EEG foundation models learn directly from raw signals via self-supervised pretraining.<n>We decompose into three sub-questions: emphwhat does the model learn, emphwhat does the model use, and emphhow much can be explained<n>The audit covers three foundation models (CSBrain, CBraMod, LaBraM), five clinical tasks (MDD, Stress, ISRUC-Sleep, TUSL, Siena), and a 6-family 63-feature lexicon.
  arXiv  Detail & Related papers  (2026-05-12T01:57:53Z)
• Logic-Regularized Verifier Elicits Reasoning from LLMs [63.65875399266337]
  We propose LOVER, an unsupervised verifier regularized by logical rules.<n>Lover treats theverifier as a binary latent variable, utilizinginternal activations and enforcing three logical constraints.<n>Lover significantly outperforms unsupervised baselines.
  arXiv  Detail & Related papers  (2026-05-07T09:03:49Z)
• RSAT: Structured Attribution Makes Small Language Models Faithful Table Reasoners [0.0]
  RSAT produces step-by-step reasoning cell-level citations grounded in table evidence.<n>Phase 1 teaches a structured output format from verified reasoning traces.<n>RSAT improves faithfulness 3.7$times$ over SFT alone (0.224$rightarrow$0.826), with near-perfect citation validity.
  arXiv  Detail & Related papers  (2026-04-30T20:25:41Z)
• PAR$^2$-RAG: Planned Active Retrieval and Reasoning for Multi-Hop Question Answering [57.89576196160413]
  Large language models (LLMs) remain brittle on multi-hop question answering (MHQA)<n>We propose textbfPlanned Active Retrieval and Reasoning RAG (PAR$2$-RAG), a two-stage framework that separates emphcoverage from emphcommitment.
  arXiv  Detail & Related papers  (2026-03-30T23:52:54Z)
• Consistency-Guided Decoding with Proof-Driven Disambiguation for Three-Way Logical Question Answering [4.878198984786631]
  Three-way logical question answering (QA) assigns $True/False/Unknown$ to a hypothesis $H$ given a premise set $S$.<n>We present CGD-PD, a lightweight test-time layer that queries a single 3-way classifier on both $H$ and a mechanically negated form of $H$.
  arXiv  Detail & Related papers  (2026-03-12T18:26:16Z)
• ProofWala: Multilingual Proof Data Synthesis and Theorem-Proving [53.67926215943612]
  $rm Psmall ROOFWsmall ALA$ allows interaction between neural theorem-provers and two established interactive proof assistants (ITPs)<n>We show that a model trained on a mix of $rm Psmall ROOFWsmall ALA$-generated Coq and Lean data outperforms Lean-only and Coq-only models on the standard prove-at-$k$ metric.
  arXiv  Detail & Related papers  (2025-02-07T05:35:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.