arxiv: 2604.12373 · v5 · submitted 2026-04-14 · 💻 cs.CL

Recognition: unknown

Masked by Consensus: Disentangling Privileged Knowledge in LLM Correctness

Tomer Ashuach , Shai Gretz , Yoav Katz , Yonatan Belinkov , Liat Ein-Dor

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Pith reviewed 2026-05-10 15:40 UTC · model grok-4.3

classification 💻 cs.CL

keywords LLM correctness predictionprivileged knowledgeself-representationsdisagreement subsetsfactual vs mathhidden statesmodel introspectionlayer-wise analysis

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The pith

LLMs hold domain-specific privileged knowledge about answer correctness that only self-representations can access on disagreement cases.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether large language models possess internal, privileged information about the correctness of their own answers that external observers cannot access through other models. Standard evaluations show no advantage for self-probes over peer-model probes because models tend to agree on correctness. By restricting analysis to cases where models produce conflicting answers, the work isolates a clear pattern: self-representations improve correctness prediction for factual questions but provide no benefit for math reasoning. This asymmetry appears gradually in middle layers of the model, pointing to internal memory retrieval as the source of the factual edge. A reader would care because it suggests new ways to detect and correct model errors precisely where consensus breaks down.

Core claim

On disagreement subsets where models give conflicting answers, self-representations consistently outperform peer representations when predicting correctness for factual knowledge tasks, while showing no such advantage for math reasoning tasks. The factual advantage emerges progressively from early-to-mid layers onward, consistent with access to model-specific memory, whereas math reasoning exhibits no consistent layer-wise advantage.

What carries the argument

correctness classifiers trained on a model's own hidden states versus external peer-model hidden states, evaluated on disagreement subsets to separate consensus from privileged internal signals

If this is right

Factual error detection can improve by probing the model's own states when external models disagree.
Math reasoning correctness may depend more on patterns observable across multiple models.
Layer-wise analysis can identify the point at which model-specific factual memory becomes accessible.
Disagreement subsets provide a sharper test for uncovering internal knowledge than full agreement datasets.
Self-probes may serve as a targeted tool for model self-correction in factual domains.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This approach could extend to other domains like code generation or commonsense reasoning by creating disagreement subsets.
Multi-model systems might use self-probes to decide which model's answer to trust when outputs conflict.
The layer localization suggests interventions that target mid-layer states for factual knowledge access.
Consensus-based evaluation of LLMs may systematically underestimate individual model strengths in factual recall.

Load-bearing premise

Performance differences between self and peer probes on disagreement subsets reflect genuine privileged knowledge rather than biases in how those subsets were selected or differences between the factual and math benchmarks.

What would settle it

Finding equivalent performance between self and peer correctness classifiers on disagreement subsets after rebalancing those subsets to equalize difficulty, data source distribution, and answer patterns across factual and math domains.

Figures

Figures reproduced from arXiv: 2604.12373 by Liat Ein-Dor, Shai Gretz, Tomer Ashuach, Yoav Katz, Yonatan Belinkov.

**Figure 1.** Figure 1: Overview of the experimental framework. Questions are input to a target model and to external models, yielding representations htarget and hext. Probes trained on these representations predict answer correctness. We evaluate probe performance using mean AUC averaged over layers and define the premium gap as the performance advantage of self over external probes. conflicting correctness labels. By restricti… view at source ↗

**Figure 2.** Figure 2: Premium Gap. Mean AUC for correctness prediction, averaged over layers, on two task types: factual knowledge (TriviaQA) and mathematical reasoning (MATH). Bars compare Random, Embedding, and Best Cross-Model baselines to the Self-Probe (Self) across three target models. Semi-transparent overlays indicate the performance gain (or lack thereof) of Self relative to each baseline. Error bars denote 95% confide… view at source ↗

**Figure 3.** Figure 3: Target Model Correctness Prediction. Heatmap of correctness prediction differences across target models, datasets, and test subsets. Each cell reports the AUC difference (∆AUC = Self − Best External), with the percentage of the gap closed shown in parentheses, computed as Self−Best External 1−Best External × 100. The y-axis lists target models, and cell colors indicate the best-performing source model for … view at source ↗

**Figure 4.** Figure 4: Agreement vs. Disagreement Rates. Stacked bar chart showing the proportion of questions on which models agree (blue) or disagree (orange) on correctness across datasets, averaged over all model pairs. models. In mathematical reasoning, both embedding model and cross-model probes match selfprobe performance, yielding a non-existent premium gap. This initial finding suggests that correctness prediction d… view at source ↗

**Figure 5.** Figure 5: Per-Layer Premium Gap. Premium gap (self-probe AUC − best external-probe AUC) on the disagreement subset as a function of normalized layer depth. Shaded regions denote 95% confidence intervals. (a) For factual tasks, the gap is near zero in early layers and grows progressively toward deeper layers across all models, indicating that privileged knowledge emerges in early-to-mid representations. (b) For math… view at source ↗

**Figure 6.** Figure 6: Premium Gap (Remaining Datasets). Mean AUC for correctness prediction, averaged over layers, on two task types: factual knowledge (Mintaka, HotPotQA) and mathematical reasoning (GSM1K). Bars compare Random, Embedding, and Best Cross-Model baselines to the Self-Probe (Self) across three target models. Semitransparent overlays indicate the performance gain (or lack thereof) of Self relative to each baseline… view at source ↗

**Figure 7.** Figure 7: Target Model Correctness Prediction (MLP Probes). Heatmap of correctness prediction differences across target models, datasets, and test subsets. Each cell reports the AUC difference (∆AUC = Self − Best External), with the percentage of the gap closed shown in parentheses, computed as Self−Best External 1−Best External × 100. The y-axis lists target models, and cell colors indicate the best-performing ext… view at source ↗

**Figure 8.** Figure 8: Disagreement Gap: Factual Knowledge Breakdown (Linear Probes). Detailed performance on the disagreement subset across Mintaka, TriviaQA, and HotPotQA. Self-probes consistently outperform external probes across all factual datasets, reinforcing the existence of privileged knowledge in factual tasks. stripped input. If correctness prediction is driven by entity-level familiarity, entity tokens alone should r… view at source ↗

**Figure 9.** Figure 9: Disagreement Gap: Mathematical Reasoning Breakdown (Linear Probes). Detailed performance on the disagreement subset across GSM1K and MATH. Unlike factual tasks, mathematical correctness shows no consistent premium gap, indicating that reasoning difficulty is a public feature accessible to external models. 0.50 0.55 0.60 AUC Score Qwen-2.5-7B Llama-3.1-8B Embedding Model Embedding Model Qwen-2.5-7B Gemma-2-… view at source ↗

**Figure 10.** Figure 10: Disagreement Gap: Factual Knowledge Breakdown (MLP Probes). Detailed disagreement subset performance using MLP probes. The premium gap is even more pronounced with non-linear probes, with Selfrepresentations outperforming Best External probes in 9 out of 9 configurations. lexical tokens encode mathematical topic indicators (e.g., “eigenvalue”, “asymptote”) that correlate with difficulty. In contrast, G… view at source ↗

**Figure 11.** Figure 11: Disagreement Gap: Mathematical Reasoning Breakdown (MLP Probes). Detailed disagreement subset performance using MLP probes across GSM1K and MATH. Consistent with linear results, increased probe expressivity does not uncover hidden privileged info in math tasks; external models remain effective predictors. Apache 2.0. • GSM1K (Zhang et al., 2024) and MATH (Hendrycks et al., 2021) are licensed under the MIT… view at source ↗

**Figure 12.** Figure 12: Premium Gap (MLP Probes). Mean AUC for correctness prediction, averaged over layers. Bars compare Random, Embedding, and Best Cross-Model baselines to the Self-Probe (Self) across three target models. Semi-transparent overlays indicate the performance gain (or lack thereof) of Self relative to each baseline. Error bars denote 95% confidence intervals. (a) Core comparison on TriviaQA and MATH, mirroring th… view at source ↗

**Figure 13.** Figure 13: Per-Layer AUC: Gemma-2-9B. Absolute AUC at each probed layer on the disagreement subset. Lighter bars: best external probe; darker bars: self-probe. (a) For factual datasets, the self-probe advantage grows visibly from mid-layers onward, particularly in TriviaQA. (b) For mathematical reasoning, bars are of similar or reversed height, consistent with the absence of a premium gap. Error bars denote 95% conf… view at source ↗

**Figure 14.** Figure 14: Per-Layer AUC: Llama-3.1-8B. Absolute AUC at each probed layer on the disagreement subset. Lighter bars: best external probe; darker bars: self-probe. (a) For factual datasets, the self-probe advantage emerges in early-to-mid layers. (b) For mathematical reasoning, bars are of similar or reversed height, consistent with the absence of a premium gap. Error bars denote 95% confidence intervals from cross-va… view at source ↗

**Figure 15.** Figure 15: Per-Layer AUC: Qwen-2.5-7B. Absolute AUC at each probed layer on the disagreement subset. Lighter bars: best external probe; darker bars: self-probe. (a) For factual datasets, the self-probe advantage emerges in early-to-mid layers. (b) For mathematical reasoning, bars are of similar or reversed height, consistent with the absence of a premium gap. Error bars denote 95% confidence intervals from cross-val… view at source ↗

**Figure 16.** Figure 16: Lexical-Only vs. Original Question. Mean AUC for correctness prediction, averaged over layers, of probes trained on the Original Question versus the Lexical-Only input (named entities and nouns only), aggregated across all models (Gemma-2-9B, Llama-3.1-8B, Qwen-2.5-7B). The gap between conditions reflects the contribution of syntactic and contextual processing beyond entity identity. Error bars denote 95%… view at source ↗

read the original abstract

Humans use introspection to evaluate their understanding through private internal states inaccessible to external observers. We investigate whether large language models possess similar privileged knowledge about answer correctness, information unavailable through external observation. We train correctness classifiers on question representations from both a model's own hidden states and external models, testing whether self-representations provide a performance advantage. On standard evaluation, we find no advantage: self-probes perform comparably to peer-model probes. We hypothesize this is due to high inter-model agreement of answer correctness. To isolate genuine privileged knowledge, we evaluate on disagreement subsets, where models produce conflicting predictions. Here, we discover domain-specific privileged knowledge: self-representations consistently outperform peer representations in factual knowledge tasks, but show no advantage in math reasoning. We further localize this domain asymmetry across model layers, finding that the factual advantage emerges progressively from early-to-mid layers onward, consistent with model-specific memory retrieval, while math reasoning shows no consistent advantage at any depth.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper finds self-representations beat peers on factual correctness only in disagreement cases and only from mid-layers, but the split may trace to how those subsets are filtered rather than to real privileged knowledge.

read the letter

The main result is that hidden states from the model itself help predict whether its answer is correct more than hidden states from peer models, but this edge appears only on factual questions where the models disagree and only starting around the middle layers. Math questions show no self-advantage at any depth. On the full test sets the self and peer probes perform about the same, which the authors attribute to high agreement across models on correctness labels.

Referee Report

2 major / 2 minor

Summary. The paper investigates whether LLMs possess privileged internal knowledge about answer correctness by training binary correctness classifiers on hidden-state representations from the target model itself versus external peer models. On full evaluation sets, self-probes show no advantage over peer probes. The authors then restrict analysis to disagreement subsets (where target and peer models produce conflicting answers) and report that self-representations outperform peers on factual-knowledge tasks but not on math-reasoning tasks; they further localize the factual advantage to progressive emergence in early-to-mid layers, interpreting this as evidence of model-specific memory retrieval.

Significance. If the central empirical pattern survives controls for subset selection, the work offers a concrete, domain-differentiated probe for internal versus external knowledge in LLMs and supplies layer-localization evidence that could inform mechanistic interpretability. The purely empirical design avoids circular derivations and the layer-wise analysis constitutes a positive methodological step beyond aggregate accuracy comparisons.

major comments (2)

[Experimental setup and disagreement-subset definition] The construction of disagreement subsets (described after the standard-evaluation results) is performed post-hoc without reported balancing or regression controls for subset-level statistics such as question length, answer entropy, model confidence, or ground-truth difficulty. Because factual and math benchmarks may differ systematically in these properties, the observed domain asymmetry and layer-wise pattern could be an artifact of the filtering procedure rather than evidence of privileged knowledge; explicit controls or matched-subset re-analysis are needed to support the claim.
[Results on disagreement subsets] The abstract and results sections state that self-probes 'consistently outperform' peers on factual disagreement subsets, yet no exact subset sizes, confidence intervals, or statistical significance tests for the self-versus-peer gap are provided. Without these quantities it is impossible to assess whether the reported advantage is robust or driven by small or imbalanced subsets.

minor comments (2)

[Layer-wise analysis] The layer-localization plots would benefit from explicit error bars or shaded regions indicating variability across random seeds or cross-validation folds.
[Methods] Notation for 'self-representations' versus 'peer representations' is used consistently but could be introduced with a short table of probe architectures and training objectives for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive comments. We appreciate the concerns about potential confounds in the disagreement-subset construction and the need for more complete statistical reporting. We address each major comment below and commit to revisions that strengthen the empirical claims.

read point-by-point responses

Referee: The construction of disagreement subsets (described after the standard-evaluation results) is performed post-hoc without reported balancing or regression controls for subset-level statistics such as question length, answer entropy, model confidence, or ground-truth difficulty. Because factual and math benchmarks may differ systematically in these properties, the observed domain asymmetry and layer-wise pattern could be an artifact of the filtering procedure rather than evidence of privileged knowledge; explicit controls or matched-subset re-analysis are needed to support the claim.

Authors: We agree that the post-hoc filtering on model disagreement could introduce confounds if factual and math benchmarks differ systematically in length, entropy, confidence, or difficulty. In the revision we will add (i) regression controls that include these covariates when predicting probe accuracy and (ii) a matched-subset re-analysis in which disagreement examples are balanced across domains on the listed statistics. These controls will allow us to test whether the domain asymmetry and layer-wise localization survive after accounting for subset-level differences. revision: yes
Referee: The abstract and results sections state that self-probes 'consistently outperform' peers on factual disagreement subsets, yet no exact subset sizes, confidence intervals, or statistical significance tests for the self-versus-peer gap are provided. Without these quantities it is impossible to assess whether the reported advantage is robust or driven by small or imbalanced subsets.

Authors: We acknowledge that the current manuscript lacks the quantitative details needed to evaluate robustness. The revised version will report the exact number of examples in each disagreement subset, bootstrap or analytic confidence intervals around the self-minus-peer accuracy differences, and the results of paired statistical tests (e.g., McNemar or Wilcoxon signed-rank) for every domain and layer comparison. These additions will make the magnitude and reliability of the reported advantages transparent. revision: yes

Circularity Check

0 steps flagged

No circularity: purely empirical probing with independent evaluations

full rationale

The paper conducts an empirical study by training correctness classifiers on hidden-state representations from self and peer models, then measuring accuracy differences on standard vs. disagreement subsets across factual and math tasks, with layer-wise localization. No equations, derivations, or first-principles results are presented that reduce by construction to fitted parameters, self-definitions, or self-citation chains. Subset construction and performance reporting are direct experimental outputs rather than renamed inputs or ansatzes smuggled via prior work. The analysis is self-contained against external benchmarks and does not invoke uniqueness theorems or load-bearing self-citations.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard probing assumptions plus empirical subset selection; no new entities are postulated.

free parameters (1)

disagreement subset definition
Criteria for selecting conflicting predictions are chosen by the authors and directly affect which examples enter the privileged-knowledge test.

axioms (1)

domain assumption Hidden states encode extractable information about answer correctness
Invoked when training linear or MLP probes on representations from both self and peer models.

pith-pipeline@v0.9.0 · 5478 in / 1077 out tokens · 47556 ms · 2026-05-10T15:40:54.769485+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages · 2 internal anchors

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