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REVIEW 5 major objections 4 minor 24 references

How to Choose a Threshold for an Evaluation Metric for Large Language Models

T0 review · 5 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A recipe for picking LLM evaluation thresholds from risk tolerance using conformal prediction.

desk verdict Practical recipe for LLM metric thresholds, but the conformal prediction claim overreaches: coverage is not the same as the Type I/II error rate the recipe needs. read the letter →

arxiv 2412.12148 v1 pith:GFLXO3LQ submitted 2024-12-10 stat.ML cs.CLcs.LGq-fin.STstat.AP

Bhaskarjit Sarmah , Mingshu Li , Jingrao Lyu , Sebastian Frank , Nathalia Castellanos , Stefano Pasquali , Dhagash Mehta This is my paper · ORCID
classification stat.MLcs.CLcs.LGq-fin.STstat.AP
keywords thresholdselectionLLMevaluationmetricsconformalpredictionmodelriskmanagementfaithfulnessmetrichallucinationdetectiongeneralizedadditivemodels
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 proposes a step-by-step methodology for choosing a threshold on an LLM evaluation metric, borrowing model risk management practices from regulated finance. The method starts with identifying the risks of the specific LLM application and the risk tolerance of its stakeholders, then translates that tolerance into a statistical confidence level, and finally computes a threshold from ground-truth data. As a demonstration, the authors apply the recipe to the Faithfulness metric for RAG hallucinations, using three public implementations and the HaluBench dataset. Their central empirical claim is that conformal prediction—especially with GAM or polynomial logistic regression as the underlying calibrator—identifies thresholds with better discriminative power than KDE, empirical recall, or standard logistic regression, while maintaining guaranteed coverage.

What carries the argument

The load-bearing machinery is split conformal prediction combined with Platt-style probability calibration. Faithfulness scores are first mapped to calibrated probabilities of the label using a classifier; the paper compares standard logistic regression, polynomial logistic regression, and Generalized Additive Models (GAMs). These calibrated probabilities are turned into conformity scores $s_i = 1 - \hat{\mu}(X_i)_{Y_i}$ on a hold-out set, and the $(1-\alpha)$-quantile of those scores defines a prediction set $\hat{C}_\alpha(X_{test}) = \{y : \hat{\mu}(X_{test}) \geq 1 - Q_{1-\alpha}\}$ that is guaranteed to contain the true label with confidence $1-\alpha$. The threshold on the original faithfulness score is obtained by mapping this quantile back to the feature space, and narrower prediction sets indicate more informative thresholds.

What would settle it

Run the same threshold recipe on an LLM evaluation metric whose scores are roughly uniformly distributed instead of bimodal; if GAM-based conformal prediction no longer produces narrower prediction sets than standard logistic regression, the claimed advantage is an artifact of the bimodal faithfulness scores used here.

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Extended reading notes

Core claim

On the paper's own terms, the central claim is that threshold selection for LLM evaluation metrics should not be a heuristic choice but a disciplined procedure that starts from stakeholder risk appetite and ends with a statistically grounded cutoff. The authors establish this by translating financial model risk management guidance into a concrete recipe, and they argue that split conformal prediction with flexibly calibrated probabilities—via GAMs or polynomial logistic regression—gives the best thresholds: it achieves the claimed coverage at each confidence level while producing narrower, more informative prediction sets than KDE, empirical recall, or standard logistic regression. The demonstration on Faithfulness scores from RAGAS, DeepEval, and UpTrain against human labels in HaluBench shows that the simpler baselines collapse to zero thresholds at high confidence levels, whereas conformal prediction continues to produce non-trivial cutoffs.

Load-bearing premise

The whole recipe rests on the assumption that a stakeholder's risk tolerance can be translated into a specific statistical confidence level; the paper states this translation as a requirement but gives no procedure for doing it, and the experiments simply pick confidence levels from 80% to 99%.

Editorial extensions

If this is right

  • Practitioners get a defensible route from stakeholder risk appetite to a specific cutoff on an LLM evaluation metric, instead of an ad hoc choice.
  • Conformal prediction with flexible calibration supplies thresholds that come with a guaranteed coverage rate, so the stated confidence level is an actual bound.
  • KDE and empirical recall thresholds degrade to zero at high confidence levels, so they are not suitable for high-stakes settings.
  • The recipe is metric-agnostic and intended to carry over from Faithfulness to other LLM and GenAI evaluation metrics.
  • The paper positions the procedure as a foundation for systematic threshold selection in any generative AI application, not just LLMs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The missing risk-tolerance-to-confidence translation could be made operational by fitting Prospect Theory utility functions to stakeholder choices and deriving the implied acceptable error rates, a step the paper flags but leaves to future work.
  • Because conformal prediction only requires exchangeability, the recipe could be adapted to streaming or drift-monitoring settings by re-calibrating thresholds on rolling windows.
  • A natural next experiment is to test whether GAM-based conformal thresholds remain superior when the ground-truth labels are noisy or when the LLM judge used in the metric changes.
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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

5 major / 4 minor

Summary. The paper proposes a step-by-step recipe for choosing a threshold on a continuous LLM evaluation metric. The recipe begins with identifying application risks and stakeholder risk tolerance, translates that tolerance into a statistical confidence level, prepares ground-truth data, and then derives a threshold using one of several statistical methods: Z-scores, kernel density estimation, empirical recall, AUC-ROC, or split conformal prediction. The methods are demonstrated on the HaluBench dataset using three faithfulness implementations (RAGAS, DeepEval, UpTrain) with gpt-4o-mini as the judge. The paper reports thresholds at confidence levels from 80% to 99% and claims that conformal prediction, especially when based on GAM or polynomial logistic regression, has better discriminative power than the other methods.

Significance. If the proposed methodology were fully validated, it would give practitioners a defensible, risk-aware procedure for threshold selection in LLM evaluation, which is currently an underexplored part of LLM deployment. The paper's main strengths are its clear problem framing, its use of publicly available data and libraries, and its explicit discussion of stakeholder risk as a starting point. These strengths make the paper potentially useful as an applied recipe. However, the contribution is not supported by a new statistical derivation, and the empirical comparison has several load-bearing gaps, so the practical claims should be treated as provisional until the evaluation criteria are aligned across methods.

major comments (5)
  1. [Section 2.3.5, Table 1] The central claim that conformal prediction yields better thresholds is not established because the mapping from conformal prediction sets to a single faithfulness threshold is never defined. Equations (4)-(6) produce set-valued predictions that can be {FAIL}, {PASS}, or {FAIL, PASS}, and the text only says that thresholds are 'mapped back to feature space' without giving a rule. Table 1 then reports a single threshold per confidence level, but no derivation is provided from those equations. Since the paper itself notes in Section 4.5 that the thresholds in Tables 1 and 2 are not directly comparable, the comparison of conformal methods with KDE, empirical recall, and ROC-based methods is not valid evidence for the claimed 'better discriminative power.' The evaluation should define the operational threshold classifier (e.g., using one boundary of the ambiguous region or a decision rule for the two-label set), and then report the same error metrics for all methods.
  2. [Section 2.1.3] The foundational step of the recipe is asserted rather than operationalized. The paper states that risk preferences 'should be translated into a corresponding statistical confidence level' and gives the example 'only 5% hallucination is accepted ... required confidence level is 95%,' but it provides no procedure for this translation. The experiments simply choose confidence levels from 80% to 99% without any stakeholder-elicitation method. Because this translation is the input to every downstream method, the recipe cannot be used by practitioners as written. The authors should either supply a concrete elicitation and mapping procedure or reformulate the recipe so that risk tolerance directly specifies quantities such as acceptable false-positive and false-negative rates.
  3. [Section 3.3, Table 2] The non-conformal methods are evaluated only by recall, which is insufficient for a risk-tolerance framework whose stated quantities are Type I and Type II error rates. Table 2 reports recall values of 100% at high confidence levels, but without precision or false-positive rates it is impossible to tell whether those thresholds are sensible or simply classify almost everything as passing. The paper should report a full confusion-matrix-based comparison for every method, including the conformal classifier after a threshold is extracted, so that methods are compared on the same operational quantities.
  4. [Section 3.1, Section 3.2] The data preprocessing is not justified with sensitivity analysis. The original HaluBench dataset is described as containing around 15K samples, but filtering by answer length and removing NaN scores reduces it to 7,703 samples. The paper does not characterize what is lost by this filtering, nor does it check whether the thresholds are stable under different filtering choices. In addition, all faithfulness scores come from a single judge (gpt-4o-mini) with default hyperparameters and single draws, so no estimate of judge or sampling variability is provided. A robustness analysis should be added to support the generality of the reported thresholds.
  5. [Section 4.5] The sentence 'Overall, all methods achieve valid coverage aligned with the pre-specified confidence levels' is not supported by the tables. Table 2 reports recall, not coverage, and Table 1 shows coverage values that are often substantially higher than the nominal level (e.g., 90% nominal coverage reported as 98.35% for Uptrain). The claim should be restricted to conformal prediction, and even there the exact coverage should be reported rather than described as 'aligned.'
minor comments (4)
  1. [Section 2.3.5, Equations (4)-(5)] The notation in Equations (4) and (5) is ambiguous: the subscript on the calibrated probability in Equation (5) appears to be missing, and the text following Equation (4) does not clearly define whether the expression is the probability of the observed label or of each candidate label.
  2. [Section 2.3.1, Equation (1)] Equation (1) is a confidence interval for the population mean, not a threshold for an individual score. The paper notes in Appendix C that the resulting bounds are outside [0,1], but the conceptual mismatch should be stated explicitly in the main text so that readers do not interpret the method as a quantile estimator.
  3. [Section 4.3.1] There is a typo in the first sentence: 'The results od KDE' should read 'The results of KDE.'
  4. [Section 2.3.5] The split conformal workflow is described only informally. The paper should specify how the training set I1, the calibration set I2, and the test set are created inside the stratified 5-fold cross-validation, and how the calibrated probabilities are obtained for each fold.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the thresholds are standard supervised estimators trained on ground-truth labels and validated on held-out folds; the paper's admitted coverage-vs-recall mismatch is a correctness caveat, not a derivation loop.

full rationale

The paper's derivation chain is self-contained. Each threshold method (Z-score, KDE with Bayes rule, empirical recall, ROC/logistic/GAM classifiers, split conformal prediction) takes ground-truth labels and metric scores as input, computes a cutoff from a training split, and evaluates it on a held-out test split; none of these procedures fits a parameter and then relabels that fit as a prediction of the same quantity. There is no load-bearing self-citation: reference [17] (Sudjianto and Neppalli) and the other cited works are external to the authors, and the footnote in Sec. 2.3.5 explicitly says the comparison was set up from scratch because Ref. [17]'s setup was unclear. The conformal coverage guarantee is a mathematical property of Eqs. (4)-(6), so Table 1's coverage near the target is expected rather than an empirical discovery, but the paper's central comparative claim about 'better discriminative power' is carried by prediction-set width, which is an empirical, non-tautological outcome. The paper itself flags the main validity limitation in Sec. 4.5: the risk levels in Tables 1 and 2 'differ slightly—coverage rate for conformal prediction versus recall for precision-recall curves—making the corresponding thresholds not directly comparable'; this is a correctness/comparability gap, not circular reasoning. Similarly, Sec. 2.1.3 explicitly assumes the stakeholder risk-tolerance-to-confidence translation is available ('we assume that we have this specific information'), which is an unfulfilled input to the recipe rather than a circular definition. No equation in the paper reduces to its own input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard statistical assumptions plus the asserted but unimplemented risk-tolerance-to-confidence translation. The main free parameters are the confidence level and hidden hyperparameters of the threshold methods, which are not fully reported.

free parameters (5)
  • confidence level (1-α) = 0.80, 0.90, 0.95, 0.975, 0.99
    Chosen by the authors for experiments without a method to derive them from stakeholder risk tolerance; Step 1 prescribes eliciting this (Sec 2.1.3), but the experiments use arbitrary levels.
  • minimum answer token count = 3
    Data filter in Sec 3.1 removes short answers, reducing the dataset from ~15K to 9,616 samples and affecting score distributions and thresholds.
  • KDE bandwidth = not reported (library default)
    KDE thresholds (Sec 4.3.1, Appendix D) depend on kernel and bandwidth; the paper notes sensitivity but does not state the chosen value.
  • polynomial degree for polynomial logistic regression = not reported
    Used for AUC-ROC and conformal prediction; the degree is not reported and affects the thresholds.
  • GAM smoothness parameters = not reported
    GAM is used for AUC-ROC and conformal prediction; effective degrees of freedom and basis functions are not specified.
assumptions (5)
  • standard math Data exchangeability for split conformal prediction
    Conformal prediction validity relies on exchangeability of training, calibration, and test samples (Sec 2.3.5).
  • domain assumption Faithfulness scores from gpt-4o-mini are treated as stable inputs
    The LLM judge scores are stochastic and computed once with default hyperparameters (Sec 3.2); run-to-run variability is not accounted for.
  • domain assumption HaluBench human labels are ground truth for hallucination
    All threshold evaluations are measured against these labels (Sec 3.1); label noise would propagate into the results.
  • domain assumption The filtered dataset is representative of the deployment distribution
    Samples with short answers or NaN scores are removed (Sec 3.1); the paper does not analyze differences between excluded and included samples.
  • ad hoc to paper Risk tolerance can be translated into a statistical confidence level
    Sec 2.1.3 asserts this translation without providing a mechanism; experiments use arbitrarily chosen confidence levels.

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Cite this review

Pith. "Pith review of How to Choose a Threshold for an Evaluation Metric for Large Language Models." pith.science (2026). https://pith.science/paper/GFLXO3LQ

@misc{pith2026241212148,
  author       = {Pith},
  title        = {Pith review of: How to Choose a Threshold for an Evaluation Metric for Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GFLXO3LQ}},
  note         = {Machine review of arXiv:2412.12148}
}
read the original abstract

To ensure and monitor large language models (LLMs) reliably, various evaluation metrics have been proposed in the literature. However, there is little research on prescribing a methodology to identify a robust threshold on these metrics even though there are many serious implications of an incorrect choice of the thresholds during deployment of the LLMs. Translating the traditional model risk management (MRM) guidelines within regulated industries such as the financial industry, we propose a step-by-step recipe for picking a threshold for a given LLM evaluation metric. We emphasize that such a methodology should start with identifying the risks of the LLM application under consideration and risk tolerance of the stakeholders. We then propose concrete and statistically rigorous procedures to determine a threshold for the given LLM evaluation metric using available ground-truth data. As a concrete example to demonstrate the proposed methodology at work, we employ it on the Faithfulness metric, as implemented in various publicly available libraries, using the publicly available HaluBench dataset. We also lay a foundation for creating systematic approaches to select thresholds, not only for LLMs but for any GenAI applications.

Figures

Figures reproduced from arXiv: 2412.12148 by the authors.

Figure 1
Figure 1. compares the distributions of faithfulness scores from the libraries RAGAS, DeepEval, and Uptrain, respec￾tively, while also showing their relationship with binary labels, ”Pass” and ”Fail.” A correspondence between low scores and the ”Fail” label, high score and ”Pass” label would yield that the faithfulness metric is effective at de￾tecting hallucination in the generated outputs [PITH_FULL_IMAGE:figures/full_fig_… view at source ↗
Figure 2
Figure 2. demonstrates the ROC and precision-recall curves of various thresholding strategies. For the UpTrain and RAGAS datasets, the curves are nearly identical across all classifiers, indicating comparable performance. However, a significant improvement in performance is observed with GAM and polynomial logistic regression for the DeepEval dataset. For datasets with higher noise levels and lower relia￾bility, GAM and polyn… view at source ↗
Figure 3
Figure 3. Example visualizations of thresholds identified using local minimum. (a) UpTrain, (b) [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Example visualizations of thresholds identified using KDE. (a) UpTrain, (b) RAGAS, (c) [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: Visualizations of thresholds identified using empirical recall curve. (a) UpTrain, (b) RAGAS, [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Thresholds at different risk levels. (a): Thresholds vs type I error, (b): Thresholds vs [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Visualizations of conformal prediction performance at various confidence levels. (a) Up [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: Distribution of conformity scores with thresholds. (a) UpTrain, (b) RAGAS, (c) DeepEval. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

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