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arxiv: 2606.02289 · v1 · pith:RAAO4ABBnew · submitted 2026-06-01 · 💻 cs.CL

DECK: A Consistency x Confidence Taxonomy of LLM Hallucinations

Mohit Singh Chauhan This is my paper

Pith reviewed 2026-06-28 14:54 UTC · model grok-4.3

classification 💻 cs.CL
keywords LLM hallucinationsuncertainty quantificationtaxonomyconsistencyconfidencedetectabilityblind spotoutput-level UQ
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The pith

The DECK taxonomy partitions LLM hallucinations into four regimes along consistency and confidence axes, each tied to specific uncertainty scorers, while exposing a universal blind spot for confident repeatable fabrications.

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

The paper introduces a taxonomy that classifies LLM errors according to the signals that uncertainty scorers can read rather than by the semantic nature of the mistake. It creates a 2x2 grid using inter-sample consistency and token-level confidence to define Drift, Entrenched, Confabulation, and Knotted regimes. Each cell maps to the scorer families expected to catch errors in that regime, with black-box consistency methods covering some cells, token-probability methods covering others, and only an independent LLM judge reaching the Entrenched cell. Validation across models and datasets shows external labels land in the predicted cells and that scorer disagreements align with the partition. The work additionally demonstrates that every output-level uncertainty method fails by construction on knowledge-gap cases where the model produces confident, repeatable wrong answers.

Core claim

The DECK taxonomy is a 2x2 partition along inter-sample consistency and token-level confidence into four behavioural regimes (Drift, Entrenched, Confabulation, Knotted), each mapping to a specific scorer family that can detect it, with black-box consistency scorers having signal in Drift and Confabulation, white-box token-probability scorers having signal in Knotted and Confabulation, and only an LLM-as-a-Judge with independent pretraining able to detect Entrenched; cell membership is operationalised by a Youden's J optimal split on each scorer axis, external labels align with predicted cells, and all output-level UQ families collapse on knowledge-gap inputs that produce confident repeatable

What carries the argument

The DECK 2x2 taxonomy that classifies hallucinations by their detectability signature using inter-sample consistency and token-level confidence.

If this is right

  • Black-box consistency scorers detect errors in the Drift and Confabulation regimes.
  • White-box token-probability scorers detect errors in the Knotted and Confabulation regimes.
  • Only an independent LLM-as-Judge reaches the Entrenched regime.
  • All output-level uncertainty quantification methods fail on knowledge-gap inputs that elicit confident repeatable fabrications.
  • A linear probe on hidden states also collapses to chance on those same inputs.

Where Pith is reading between the lines

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

  • The blind spot may require methods that look beyond output-level signals or single-model activations.
  • Hybrid scorers that combine consistency and token-probability signals could cover three of the four regimes.
  • The taxonomy could guide selection of detection methods for specific application domains where one regime dominates.

Load-bearing premise

That the four cells defined by optimal splits on consistency and confidence axes capture genuinely distinct detectability regimes rather than merely reflecting the scorers chosen to draw the splits.

What would settle it

External labels from SelfAware, HaluEval, or PopQA fail to land preferentially in the predicted DECK cells when measured across multiple models, or scorer-pair disagreements show no alignment with the taxonomy partition.

Figures

Figures reproduced from arXiv: 2606.02289 by Mohit Singh Chauhan.

Figure 1
Figure 1. Figure 1: Top scorer per family with best AUROC across all twelve dataset–model combinations (four datasets [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Pairwise scorer-family disagreement on hallucinated samples, one subplot per dataset. Each bar’s height [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Per-method AUROC across all twelve dataset–model combinations (rows: GPT-4o, Llama-3-8B, Gemini [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
read the original abstract

Existing hallucination taxonomies classify LLM errors by what is wrong with the output -- memorised misconceptions, reasoning failures, fluent fabrications. These taxonomies are useful for diagnosis but cannot answer a different question: which uncertainty scorer would have caught this error? We propose a complementary taxonomy that classifies errors by their detectability signature -- the signal a scorer family would read. The DECK taxonomy is a 2x2 partition along inter-sample consistency and token-level confidence into four behavioural regimes (Drift, Entrenched, Confabulation, Knotted), each mapping to a specific scorer family (or families) that can detect it: black-box consistency scorers have signal in D and C, white-box token-probability scorers have signal in K and C, and only an LLM-as-a-Judge with independent pretraining can detect E. Cell membership is operationalised by a Youden's J optimal split on each scorer axis. Across three models and four datasets we validate the taxonomy two ways: by analysing scorer-pair disagreement, and by checking that external labels (SelfAware unanswerable, HaluEval adversarial, PopQA entity popularity) land in the predicted DECK cells, with model-scale and content-specific secondary-cell refinements. We further identify a universal blind spot of output-level UQ: on knowledge-gap inputs where the generator emits confident, repeatable fabrications, every output-level family collapses by construction. A linear probe on Llama-3-8B's hidden states also collapses to chance, giving preliminary evidence that the failure may persist at the activation level; richer internal-state methods (UQ heads, information-theoretic estimators) remain to be tested.

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.

Referee Report

3 major / 1 minor

Summary. The paper proposes the DECK taxonomy, a 2x2 partition of LLM hallucinations along axes of inter-sample consistency and token-level confidence, yielding four regimes (Drift, Entrenched, Confabulation, Knotted) each associated with specific uncertainty scorer families. It operationalizes cell membership via Youden's J optimal splits, validates the taxonomy on three models and four datasets via scorer-pair disagreement patterns and placement of external labels (SelfAware unanswerable, HaluEval adversarial, PopQA popularity), and reports a universal blind spot for output-level UQ on knowledge-gap inputs producing confident repeatable fabrications, with preliminary evidence from a linear probe on Llama-3-8B hidden states.

Significance. If the 2x2 structure supplies signal beyond the underlying continuous scores, the taxonomy offers a useful organizing framework for matching hallucination types to detection methods and highlights a concrete limitation of current output-level UQ approaches. The identification of the blind spot and the attempt to ground the taxonomy in external labels are constructive contributions.

major comments (3)
  1. [Abstract] Abstract and validation description: Cell membership is defined by Youden's J splits on the same consistency and confidence axes used to assign regimes to scorer families, after which external labels are checked for placement in the predicted cells. This setup risks circularity; any label that correlates with consistency or confidence will appear to validate the taxonomy by construction, and the manuscript does not demonstrate that the discrete 2x2 partition adds explanatory power over the two continuous scores alone.
  2. [Abstract] Abstract: The scorer-pair disagreement analysis is presented as validation, yet disagreement is the expected statistical consequence of correlation between the two axes; this does not independently establish that the taxonomy supplies new signal.
  3. [Abstract] Abstract: The universal blind-spot claim (every output-level family collapses on knowledge-gap inputs emitting confident, repeatable fabrications) is load-bearing for the paper's contribution; the reported linear-probe result collapsing to chance requires the precise experimental setup, dataset construction, and baseline comparisons to be assessed for whether it supports the stronger claim that the failure may persist at the activation level.
minor comments (1)
  1. The mapping of regimes to scorer families (black-box consistency in D and C, white-box in K and C, LLM-as-Judge in E) should be stated with explicit citations to the relevant prior work on each family.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on the DECK taxonomy. We address each major comment below, acknowledging valid concerns about validation design and evidence strength while providing the strongest honest defense of the manuscript's contributions.

read point-by-point responses

  1. Referee: [Abstract] Abstract and validation description: Cell membership is defined by Youden's J optimal splits on the same consistency and confidence axes used to assign regimes to scorer families, after which external labels are checked for placement in the predicted cells. This setup risks circularity; any label that correlates with consistency or confidence will appear to validate the taxonomy by construction, and the manuscript does not demonstrate that the discrete 2x2 partition adds explanatory power over the two continuous scores alone.

    Authors: The Youden's J splits operationalize the continuous axes into regimes to test alignment with scorer-family predictions, rather than to claim the taxonomy is independent of the underlying scores. External labels serve as an out-of-sample check on whether known hallucination types fall into the expected detectability regimes. We agree the current presentation does not explicitly quantify incremental value of the discrete partition. In revision we will add a direct comparison (e.g., logistic regression or mutual information) showing whether quadrant membership improves label prediction beyond the raw consistency and confidence scores. revision: partial

  2. Referee: [Abstract] Abstract: The scorer-pair disagreement analysis is presented as validation, yet disagreement is the expected statistical consequence of correlation between the two axes; this does not independently establish that the taxonomy supplies new signal.

    Authors: Disagreement is indeed expected under imperfect correlation; the analysis is not offered as proof of statistical independence. Its purpose is to demonstrate that the observed disagreement patterns are consistent with the taxonomy's mapping of regimes to specific scorer families (black-box consistency vs. white-box token probability). We will revise the text to clarify this interpretive goal and supplement with quantitative measures of regime-specific signal. revision: partial

  3. Referee: [Abstract] Abstract: The universal blind-spot claim (every output-level family collapses on knowledge-gap inputs emitting confident, repeatable fabrications) is load-bearing for the paper's contribution; the reported linear-probe result collapsing to chance requires the precise experimental setup, dataset construction, and baseline comparisons to be assessed for whether it supports the stronger claim that the failure may persist at the activation level.

    Authors: The linear-probe result is presented as preliminary evidence only. We agree that full experimental details are necessary for readers to evaluate the strength of the claim. In the revised manuscript we will expand the methods and add an appendix containing the exact dataset construction, probe architecture, training procedure, baseline comparisons, and statistical results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; taxonomy is a definitional classification with external validation

full rationale

The DECK taxonomy is explicitly constructed as a 2x2 partition on the two input axes (consistency, confidence) with cell membership set via Youden's J splits and regimes mapped to scorer families by the scorers' known detection mechanisms; the blind spot is stated as holding 'by construction' without being presented as a derived result. Validation proceeds by checking alignment of independent external labels (SelfAware, HaluEval, PopQA) and scorer-pair disagreement patterns against the pre-defined cells. No equation or claim reduces a 'prediction' to a fitted parameter on the same data, no self-citation chain bears the central premise, and the external labels supply grounding outside the scorer definitions themselves. The derivation therefore remains self-contained as an organizational framework rather than a tautological fit.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The taxonomy rests on the domain assumption that Youden's J provides a valid operational split for cell membership and that the chosen external labels serve as independent validators of the predicted cells.

free parameters (1)
  • Youden's J optimal split thresholds
    Cell membership is operationalised by a Youden's J optimal split on each scorer axis.
axioms (1)
  • domain assumption Youden's J statistic yields appropriate classification thresholds for the consistency and confidence axes
    Used to define the four DECK cells from continuous scorer outputs.
invented entities (1)
  • DECK regimes (Drift, Entrenched, Confabulation, Knotted) no independent evidence
    purpose: To label the four cells of the consistency-by-confidence partition
    New behavioural regime labels introduced by the taxonomy.

pith-pipeline@v0.9.1-grok · 5829 in / 1438 out tokens · 30474 ms · 2026-06-28T14:54:53.402118+00:00 · methodology

discussion (0)

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