REVIEW 4 major objections 5 minor 3 cited by
SConU: Selective Conformal Uncertainty in Large Language Models
T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash
Pith's one-line read A conformal p-value lets LLMs abstain when a question is an uncertainty outlier.
desk verdict The central claim of rigorous post-filter coverage is undone by an invalid proof of the refined conformal p-value; the broad empirical work does not rescue the missing theory. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is the conformal p-value. In SConU, Eq. (1) computes $p_{N+1} = (1 + \sum_{i=1}^N \mathbf{1}\{u_i \ge u_{N+1}\})/(N+1)$, with $u_i$ the predictive entropy of the model on question $i$; small p-values reject the null hypothesis that the calibration set can provide coverage for the new point. SConU-Pro uses Eq. (2), $p'_{N+1} = (1 + \sum_{i=1}^N \mathbf{1}\{u_i \ge u_{N+1},\, y_i^* \in \mathcal{E}(x_i,\mathcal{D}_{\rm cal},\alpha)\})/(N+1)$, which only counts calibration points whose own conformal prediction set contains the true answer. The p-value carries the argument because it turns the exchangeability precondition into a testable per-sample statement, and the calibration-set prediction status is the mechanism that gives SConU-Pro its tighter control.
What would settle it
Construct a calibration set in which no sampled candidate set contains the true answer; then in Eq. (2) the refined count $k'$ is always 0, so $p'_{N+1} = 1/(N+1)$ for every test point. At any risk level $\delta > 1/(N+1)$, the procedure rejects every exchangeable test point, contradicting the claimed validity and the statement that the remaining samples meet user-specified marginal coverage.
Extended reading notes
Core claim
The paper's central claim is that the miscoverage anomalies observed in existing conformal uncertainty frameworks are caused by uncertainty data outliers — test points whose uncertainty scores sit outside the calibration distribution — and that significance tests can remove those outliers before the conformal quantile step. Eq. (1) defines the base conformal p-value; Eq. (2) defines the refined version. After filtering, the paper argues, the remaining test samples are expected to satisfy user-specified marginal coverage even when the original exchangeability condition is violated, and the experiments on MMLU-Pro show empirical miscoverage rates at or below the target risk level across calibration/test subject pairs. The framework also introduces the minimum manageable risk level, quantifies when a calibration set can support a given error rate, and keeps calibration samples that earlier methods would discard.
Load-bearing premise
The whole guarantee rests on the claim that the refined conformal p-value in Eq. (2) is a true p-value under the null hypothesis; the proof in Appendix C uses an inequality, $P(k' \le m) \le (m+1)/(N+1)$, that is asserted without proof and can fail, and if it fails the miscoverage guarantee collapses.
Editorial extensions
If this is right
- A deployed QA system can abstain on out-of-distribution questions instead of emitting empty or unreliable prediction sets.
- The minimum risk level tells a practitioner the lowest error rate a given calibration set can support with finite sampling.
- Because the filter is score-agnostic, it layers onto logit-based, frequency-based, and black-box conformal uncertainty methods.
- The experiments indicate that refined outlier filtering reduces cross-domain empirical miscoverage rates to within the target risk level and trims average prediction set size toward 1.
- Semantic deduplication cuts average prediction set size from roughly 8–9 to about 1 in open-domain QA, making prediction sets actionable.
Reading between the lines
- If the refined p-value validity holds, the same filtering logic could be ported to semantic-entropy or word-sequence-entropy uncertainty scores, potentially catching hallucinations that predictive entropy misses.
- The framework's abstention rule is equivalent to a data-dependent refusal set; a natural diagnostic is whether the rejected questions are the same ones a human expert would flag as out-of-domain.
- When the refined p-value is not a valid p-value (e.g., if the asserted inequality in Appendix C fails), the observed cross-domain improvement may come from selective abstention rather than conformal control; comparing coverage on filtered-in versus filtered-out test points would separate the two.
- The minimum-risk-level analysis suggests a practical deployment rule: measure the minimum manageable risk level after model deployment, and refuse any task whose required risk level falls below it.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript introduces SConU and SConU-Pro, two procedures that compute conformal p-values from an LLM's uncertainty scores and filter out test samples deemed to violate exchangeability with the calibration set; the remaining samples are then fed to a standard conformal uncertainty framework. The paper also derives a 'minimum risk level' to justify keeping calibration points whose sampled candidate sets do not contain a correct answer. It claims rigorous management of miscoverage rates in single-domain and cross-domain QA tasks and reports experiments on MMLU, MMLU-Pro, MedMCQA, TriviaQA, and CoQA, together with ablations over risk level, sampling size, and uncertainty measures.
Significance. If the guarantees were valid, SConU would offer a practical way to combine outlier detection with conformal prediction for LLM question answering. The paper's strengths are its clear problem statement, the minimum-risk-level analysis in Section 3.2, the breadth of the empirical study, and the public code release. However, the central statistical claim rests on a p-value validity proof that is incorrect, and no theorem establishes coverage after filtering; the empirical EMR results are computed on the filtered set, so they do not substitute for a guarantee. As a statistical contribution the central claim is not established.
major comments (4)
- [Appendix C, Eq. (10)] Equation (10) states P(k≤m) ≤ (m+1)/(N+1), where k counts calibration points satisfying both u_i ≥ u_{N+1} and y*_i ∈ E(x_i, D_cal, α). Let K be the count of all calibration points with u_i ≥ u_{N+1}; since k ≤ K, the event {K ≤ m} implies {k ≤ m}, so P(k≤m) ≥ P(K≤m) = (m+1)/(N+1). The printed inequality has the wrong direction. A concrete counterexample with N=2, exchangeable iid uncertainties, and R_1=1, R_2=0 gives k = 1{U_1 ≥ U_3}, so P(k≤0)=1/2 > 1/3. Moreover, in the paper's own setting (Section 3.2 keeps calibration points even when no sampled response matches y*_i), if all calibration points have y*_i ∉ E then R_i=0 for all i, so p'_{N+1}=1/(N+1) regardless of the test uncertainty and P(p'≤δ)=1 for any δ>1/(N+1). Thus p'_{N+1} is not super-uniform and SConU-Pro's outlier test is not a valid significance test; the claimed finite-sample control for SConU-Pro is unsupported.
- [Section 3.2, Workflow of SConU; Section 4.2, Marginal Coverage] The paper asserts that after filtering out low-p-value test samples, "we conduct conformal procedures for samples within the remaining test set with finite-sample guarantees of correctness coverage" (Section 3.2), and claims "rigorous management of the miscoverage rates" (Abstract, Section 4.2). No theorem establishes that the selected test samples remain exchangeable with the calibration set, or that the standard conformal quantile provides coverage conditional on p_{N+1} > δ. Because the p-value is a function of the test uncertainty and the whole calibration set, conditioning on survival changes the distribution of the nonconformity scores used for the subsequent ConU step. This affects SConU, not only SConU-Pro, and is therefore load-bearing for the paper's central claim.
- [Tables 2–4 and Figures 3, 6, 8, 9] The EMR is computed only on test samples that pass the outlier filter, so the reported miscoverage rates measure performance on the surviving subset rather than on the full test stream. Since the filter is designed to remove high-uncertainty points, which are exactly the points most likely to violate coverage, the reported improvements are partly an artifact of abstention. The paper should report the full-test EMR with rejected points counted as errors, or provide a formal bound on the full-test miscoverage rate that accounts for the selection step. As it stands, the empirical results do not demonstrate the claimed guarantee.
- [Figure 1b and Appendix E] In the cross-domain experiments, the risk level α is not fixed by the user ex ante but is set as the maximum of the minimum manageable risk levels computed from the calibration set via Eq. (5). This data-dependent choice is legitimate for describing what risk is achievable, but it is not a user-specified level, and controlling EMR at a level chosen after seeing the calibration data is not the same as the guarantee advertised in the abstract. This should at least be stated explicitly in the main text and in the captions.
minor comments (5)
- [Appendix C, after Eq. (9)] The text says "if M < 0" but should say "if m < 0"; the variable m is also introduced after it is first used.
- [Section 3.2, Eq. (2)] The notation E(x_i, D_cal, α) is used in the definition of p' before the prediction-set construction is specified; define it formally in the main text.
- [Appendix B.2] The phrase "qIn order" is a typo for "In order".
- [Figures 1, 3, 8, and 9] The diagonal entries are set manually to α or 1; stating this only in the captions is insufficient, and the main text should clarify that these are not empirical measurements.
- [Table 3] Several entries have standard deviations exceeding the mean (e.g., 0.1056±0.1860 at size 3); reporting only mean±std for these highly skewed quantities is uninformative, and the authors should consider median or trimmed statistics.
Circularity Check
SConU-Pro's Appendix C proof asserts the super-uniformity inequality it needs to prove, and the reported EMR gains are measured on a self-selected low-uncertainty subset, so the central miscoverage claim is partly circular.
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other
[Appendix C, Eqs. (9)-(11)]
"If 0≤m≤N, we have P (k≤m)≤ m + 1 N + 1. Therefore, P (p′N+1≤δ)≤ m + 1 N + 1 ≤δ."
This inequality is exactly the super-uniformity bound required to prove that p′N+1 is a valid p-value, yet it is asserted without derivation. Since k counts only a subset of the calibration points satisfying ui≥uN+1, if K is the full count then k≤K, so {K≤m}⊆{k≤m} and P(k≤m)≥P(K≤m)=(m+1)/(N+1). The printed inequality has the wrong direction; the proof therefore assumes the conclusion it is meant to establish. Consequently, the claimed validity of SConU-Pro's significance test has no finite-sample support.
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fitted input called prediction
[Section 3.2 (workflow) and Section 4.2 (Marginal Coverage)]
"After filtering out uncertainty data outliers within the test set, we achieve rigorous management of the miscoverage rates in both single-domain and cross-domain QA datasets."
The filter rejects test points with low conformal p-value, i.e., high uncertainty uN+1 relative to the calibration set, and the same uncertainty scores drive the ConU prediction sets and their miscoverage: high-uncertainty samples are precisely the ones whose prediction sets are most likely to miss the true answer. EMR is then measured only on the surviving low-uncertainty samples, and no theorem shows that conditioning on p>δ preserves exchangeability or coverage for the remaining test points. The reported EMR control on the selected set is therefore substantially a consequence of the selection rule itself, not a prediction about the original test distribution.
full rationale
The paper's standard conformal p-value in Eq. (1) is proved correctly in Eq. (8), and the minimum-risk-level and sampling-size calibration derivations have independent content. I found no load-bearing self-citation: the cited prior ConU papers are used for nonconformity-score and uncertainty-measure conventions, not for the p-value validity claim. The circularity is concentrated in two places. First, Appendix C's proof that p′N+1 is a valid p-value reduces to asserting P(k≤m)≤(m+1)/(N+1), which is the very super-uniformity conclusion needed; since k is a subset of the full exceedance count, the true inequality has the opposite direction, so the proof is circular and the SConU-Pro significance test lacks a valid guarantee. Second, the empirical evaluation filters out high-uncertainty test points by the same uncertainty scores that determine miscoverage and then reports EMR on the remaining set; because conditioning on p>δ is not shown to preserve exchangeability or coverage, the reported gains are partly an artifact of the self-selected subset. These issues make the central 'rigorous management of miscoverage rates' claim partially self-referential, though the framework retains independent components, so the score is 6 rather than higher.
Assumptions & free parameters
free parameters (3)
- weights w_l and w_f in the nonconformity score =
w_l=1, w_f=0 or w_l=0, w_f=1 or w_l=0.5, w_f=0.5 depending on the setting
- significance level δ for the conformal p-value =
δ = α (user risk level)
- risk level α in cross-domain experiments =
Set to max α_l over calibration subjects (e.g., 0.28 for MMLU-Pro)
assumptions (3)
- domain assumption Calibration and test data are exchangeable under the null hypothesis for p-value validity.
- domain assumption The uncertainty score u_i is a meaningful proxy for the nonconformity score used in prediction set construction.
- ad hoc to paper The inequality P(k' ≤ m) ≤ (m+1)/(N+1) used in Appendix C.
Cite this review
Pith. "Pith review of SConU: Selective Conformal Uncertainty in Large Language Models." pith.science (2026). https://pith.science/paper/W2MFMN66
@misc{pith2026250414154,
author = {Pith},
title = {Pith review of: SConU: Selective Conformal Uncertainty in Large Language Models},
year = {2026},
howpublished = {\url{https://pith.science/paper/W2MFMN66}},
note = {Machine review of arXiv:2504.14154}
}
read the original abstract
As large language models are increasingly utilized in real-world applications, guarantees of task-specific metrics are essential for their reliable deployment. Previous studies have introduced various criteria of conformal uncertainty grounded in split conformal prediction, which offer user-specified correctness coverage. However, existing frameworks often fail to identify uncertainty data outliers that violate the exchangeability assumption, leading to unbounded miscoverage rates and unactionable prediction sets. In this paper, we propose a novel approach termed Selective Conformal Uncertainty (SConU), which, for the first time, implements significance tests, by developing two conformal p-values that are instrumental in determining whether a given sample deviates from the uncertainty distribution of the calibration set at a specific manageable risk level. Our approach not only facilitates rigorous management of miscoverage rates across both single-domain and interdisciplinary contexts, but also enhances the efficiency of predictions. Furthermore, we comprehensively analyze the components of the conformal procedures, aiming to approximate conditional coverage, particularly in high-stakes question-answering tasks.
Figures
Figures from the paper (11 more)
Forward citations
Cited by 3 Pith papers
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Conformal Prediction for Indoor Positioning with Correctness Coverage Guarantees
The paper applies split conformal prediction to indoor positioning on the UJIIndoLoc dataset, reporting approximate coverage, but the contributions are restatements and the experimental reporting is inconsistent.
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Conformal Segmentation in Industrial Surface Defect Detection with Statistical Guarantees
Applying conformal risk control to Mask R-CNN yields empirical FDR and FNR values below pre-specified risk levels on two steel defect datasets, but the paper adds little beyond reusing the existing CRC theorem.
-
Data-Driven Calibration of Prediction Sets in Large Vision-Language Models Based on Inductive Conformal Prediction
Split conformal prediction on multiple-choice visual question answering produces answer sets whose empirical miscoverage stays below a user-set alpha across eight vision-language models and two benchmarks.
Reference graph
Works this paper leans on
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The probability of each true class (label) is denoted as ˆf (Xi)Y∗ i
Given the calibration data set{(Xi,Y ∗ i )}n i=1 (i.i.d.) and pretrained model ˆf (·) ( ˆf (Xi)∈ [0, 1](K)). The probability of each true class (label) is denoted as ˆf (Xi)Y∗ i
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[2]
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Obtain the ⌈(n+1)(1−α)⌉ n quantile of{si}n i=1: ˆq = inf n q : |{i:si≤q}| n ≥ ⌈(n+1)(1−α)⌉ n o = s⌈(n+1)(1−α)⌉
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Create the prediction set forXtest following: C (Xtest) ={y∈ [K] : s (Xtest,y )≤ ˆq}
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