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Confidence Calibration in Large Language Models

T0 review · 3 major / 4 minor · reviewed 2026-07-13 · grok-4.5

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Pith's one-line read Like people, large language models are overconfident on hard tasks and underconfident on easy ones.

desk verdict Solid preregistered multi-model demo of average overconfidence plus a classic hard-easy effect in LLMs, with a useful new continuous-difficulty probe (LifeEval); contamination is real but does not erase the pattern. read the letter →

arxiv 2605.23909 v1 pith:7FYDCXWR submitted 2026-04-03 cs.AI cs.LG

Noam Michael , Daniel BenShushan , Jacob Bien , Don A. Moore This is my paper · ORCID
classification cs.AIcs.LG
keywords confidencecalibrationlargelanguagemodelshard-easyeffectoverconfidenceLifeEvalexpectederrorreasoning
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether commercially available large language models know how sure they should be of their own answers. Across eleven models and six task families, the models report confidence that exceeds actual accuracy on average—about nine percentage points of overconfidence. That average, however, hides a strong hard-easy pattern: overconfidence is largest on difficult items, while easy items produce substantial underconfidence. To isolate difficulty from other confounds, the authors introduce LifeEval, a lifespan-prediction task whose difficulty can be dialed continuously using actuarial life tables. The same pattern appears there, and reasoning-oriented models produce more graded confidence reports than ordinary chat models. The practical stakes are straightforward: if a model cannot dial its stated certainty down when the problem gets harder, users cannot safely treat its confidence as a reliability signal.

What carries the argument

LifeEval: a lifespan-prediction probe that varies sex, minimum age, and accuracy radius so that difficulty is defined as 1 minus the Maximum Achievable Score (the actuarial probability mass inside the optimal radius). Model point estimates and stated confidences are scored against the true conditional probabilities from Social Security period life tables.

What would settle it

Re-run the same models on a LifeEval-style task whose ground-truth distribution is guaranteed never to have appeared in training; if the hard-easy slope of overconfidence versus Maximum Achievable Score disappears or reverses, the isolation claim fails.

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Extended reading notes

Core claim

Current large language models are, on average, overconfident: stated confidence exceeds accuracy. This overconfidence is moderated by a hard-easy effect—overconfidence grows with task difficulty and flips into underconfidence on easy tasks. LifeEval, a new continuous-difficulty Bayesian-style task grounded in actuarial probabilities, isolates the effect while holding other task features fixed.

Load-bearing premise

The claim that LifeEval cleanly measures difficulty rests on the premise that its actuarial ceiling is free of training-data contamination and other confounds, so that changes in radius truly isolate how models respond to hardness.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper reports a preregistered multi-model study of verbal confidence calibration for 11 LLMs (5 reasoning, 6 chat) on six English question sets. Aggregate results show overconfidence (mean stated confidence ~88% vs. accuracy ~79%), moderated by a hard-easy effect: overconfidence is largest on difficult items (LSAT-AR, small-radius LifeEval) while easy items (SciQ, SAT-EN, large-radius LifeEval) produce underconfidence. Reasoning models are better calibrated, less prone to 5% rounding, and more correlated with true probabilities. The novel LifeEval task elicits point estimates of age-at-death plus radius-specific confidence, scored against SSA actuarial probabilities (Eqs. 2-4) to yield a continuous exogenous difficulty measure (1-MAS). ECE (Eq. 9) and overconfidence (Eq. 10) are computed throughout; Appendix G audits SSA contamination and re-runs key plots on the clean subset.

Significance. If robust, the work is a clear contribution: it documents that contemporary LLMs exhibit the classic human hard-easy pattern, with direct implications for user trust, hallucination risk, and possible RLHF-induced overconfidence. Strengths that raise the paper above typical LLM evaluation studies include the preregistration, explicit formulas for ECE and overconfidence, systematic comparison of reasoning vs. chat models, the continuous-difficulty LifeEval construction grounded in public actuarial tables, and the contamination audit that re-analyzes the no-evidence subset. These elements make the central empirical claims falsifiable and relatively careful. The discussion of reflection-style debiasing and the three forms of overconfidence also usefully connects the AI results to the psychological literature.

major comments (3)
  1. [Appendix G, Tables 4-5, Figure 8] Appendix G / Tables 4-5 / Figure 8: Contamination rates for the strongest reasoning models are high (DeepSeek-R1 71.5%, Gemini-2.5-Pro 71%, GPT-o3 50.1% strong evidence). The no_evidence subset therefore shrinks to N=35-45 for those models. While hard-easy coefficients remain positive, the tiny samples and the selection process itself (clean responses are those that do not cite table values) leave open the possibility that overconfidence on low-MAS items simply reflects inability to compute the actuarial p(k,r|a,s) of Eq. 3 rather than the claimed noisy-confidence mechanism. This undercuts the claim that LifeEval isolates a pure, exogenous difficulty effect (Section 4.5). Either supply CIs/power calculations on the clean subset or substantially qualify the isolation language in the abstract and Discussion.
  2. [Table 2, Section 7] Table 2 and Section 7: The Hard-Easy regression coefficients (overconfidence on 1-MAS) are presented as point estimates without standard errors, confidence intervals, or any inferential statistics. Reasoning-model averages are modest (0.168) while chat-model averages are large (0.732); without uncertainty quantification it is impossible to judge whether the 'powerful' hard-easy effect is reliable for the better-calibrated models that matter most. Bootstrap or mixed-effects intervals are needed before the central claim can be taken as established.
  3. [Appendix A, Section 4.5] Appendix A and Section 4.5: LifeEval scoring was changed after preregistration from a binary 'within-radius' indicator to the continuous actuarial probability (Eq. 3). The continuous metric is preferable for calibration analysis, yet it is a material deviation on the paper's flagship task. Sensitivity of the hard-easy slopes and ECE numbers to the original binary scoring should be reported as a robustness check.
minor comments (4)
  1. [Introduction] Introduction (p. 2): typographical error 'based on of quantitative elements'.
  2. [Figures 2-4, 8-12] Figures 2-4 and 8-12 lack error bars or confidence bands; given the varying N across models and contamination strata, visual uncertainty would help readers.
  3. [Table 1] Table 1 and Section 4: HaluEval answer field is listed as N/A; a one-sentence clarification that the model only supplies confidence (not an answer) would improve readability.
  4. [Section 4.5 / Table 2] Notation for Maximum Achievable Score (MAS) appears first in the LifeEval results without a formal definition until later; move the definition earlier or add a short glossary.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: purely empirical comparison of stated confidence against external accuracy or actuarial ground truth, with no fitted parameters or self-referential definitions in the metrics.

full rationale

The paper's central claims (average overconfidence of ~9%, moderated by a hard-easy effect) rest on direct, non-circular comparisons: stated confidence (prompted numerical probabilities, normalized if needed via Eq. 5) versus observed accuracy (Eq. 6) or actuarial success probability (Eqs. 1-4 from public SSA Period Life Tables). Overconfidence is defined as conf(Q) - acc(Q) (Eq. 10); ECE is the standard binned absolute difference (Eq. 9). LifeEval difficulty is 1 - MAS, where MAS is the maximum probability mass inside the optimal radius under the external life tables (Figure 5, Eq. 3); this is independent of any model output and is not estimated from the LLMs. The hard-easy regression simply correlates this exogenous difficulty with the already-computed overconfidence. No parameters are fitted to the evaluation data and then re-used as 'predictions'; no uniqueness theorems or ansatze are imported via self-citation; related-work citations are to external psychology and calibration literature. Contamination screening (Appendix G) is a post-hoc robustness check, not part of the metric definitions. The derivation chain is therefore self-contained against external benchmarks and exhibits zero circular reduction.

Assumptions & free parameters 2 free parameters · 3 assumptions · 1 invented entities

Empirical paper; load-bearing premises are standard statistical definitions plus the modeling choices that turn SSA tables into a difficulty continuum and that treat verbalized JSON confidence as the model's subjective probability.

free parameters (2)
  • ECE bin edges
    Ten equal-width bins plus a dedicated 1.0 bin; choice affects reported ECE magnitude though not the qualitative hard-easy pattern.
  • LifeEval radii set {1,5,10,20}
    Hand-chosen discrete difficulty levels; continuous difficulty is recovered via MAS but the discrete set still structures the main figures.
assumptions (3)
  • domain assumption Stated numerical confidence in the JSON field is a faithful report of the model's subjective probability of correctness.
    Core measurement assumption used for every ECE and overconfidence calculation (Section 5).
  • domain assumption SSA Period Life Tables supply the true conditional probabilities p(k,r|a,s) against which LifeEval confidence is scored.
    Ground-truth definition for LifeEval accuracy and MAS (Eqs. 2-4).
  • ad hoc to paper Maximum Achievable Score (MAS) is a pure exogenous difficulty measure that models can detect.
    Defines the continuous difficulty axis used for the hard-easy regression (Section 4.5).
invented entities (1)
  • LifeEval independent evidence
    purpose: Provide continuous, actuarially grounded difficulty while holding task format fixed, enabling clean measurement of the hard-easy effect.
    New benchmark constructed for this paper; independent evidence is the public SSA tables, but the specific question format and scoring are paper-specific.

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Cite this review

Pith. "Pith review of Confidence Calibration in Large Language Models." pith.science (2026). https://pith.science/paper/7FYDCXWR

@misc{pith2026260523909,
  author       = {Pith},
  title        = {Pith review of: Confidence Calibration in Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7FYDCXWR}},
  note         = {Machine review of arXiv:2605.23909}
}
read the original abstract

We investigate the calibration of large language models' (LLMs') confidence across diverse tasks. The results of our preregistered study show that the current crop of LLMs are, like people, too sure they are right: confidence exceeds accuracy, on average. Importantly, however, this tendency is moderated by a powerful hard-easy effect, wherein overconfidence is greatest on difficult tests; by contrast, easy tests actually show substantial underconfidence. We develop LifeEval, a test for evaluating model calibration across levels of difficulty.

Figures

Figures reproduced from arXiv: 2605.23909 by the authors.

Figure 1
Figure 1. LifeEval, from left to right: The user provides the LLM with sex, minimum age and radius. The LLM [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Aggregate calibration plots for each question set, showing accuracy conditional on confidence. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Overconfidence by question set and Model. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Overconfidence as a function of model and radius; [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: LifeEval allows for the monotonic decrease in task difficulty given age, sex, and radius. As the Maximum [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Best age to guess as a function of minimum age, sex, and radii. We see that the optimal age is constant until a [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Comparison between the calibration error of stated confidence versus token probability for models when [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: Overconfidence as a function of model and radius; difficulty decreases with larger accuracy radius. Specifically [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]
Figure 9
Figure 9. Figure 9: Side by side plots of all models (rows) and all question sets (columns). GPT-4o, Llama-3.1-70B, and [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]
Figure 10
Figure 10. Figure 10: Each plot displays the relationship between Stated Confidence and actual Score for various model families. [PITH_FULL_IMAGE:figures/full_fig_p024_10.png]
Figure 11
Figure 11. Figure 11: Accuracy for each model on all question sets. SAT-EN and SciQ had the highest performance while [PITH_FULL_IMAGE:figures/full_fig_p025_11.png]
Figure 12
Figure 12. Figure 12: ECE for each model on all question sets. Some questions sets like LSAT-AR and HaluEval saw high [PITH_FULL_IMAGE:figures/full_fig_p025_12.png]

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Forward citations

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Reviewed July 13, 2026 · model on record in the stance chip above.