Entropy Sentinel: Probing Entropy Traces for LLM Monitoring

Luciano Del Corro; Pedro Memoli Buffa

REVIEW 2 major objections 6 minor 38 references

A compact entropy profile extracted from top-20 decoding probabilities, averaged over a domain, estimates LLM accuracy on unseen STEM benchmarks for most models tested.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · deepseek-v4-flash

2026-08-04 06:20 UTC pith:K4D5DVC7

load-bearing objection Solid, useful STEM result with an exhaustive evaluation; the metadata abstract overclaims subjective tasks and the single-validator labeling needs more support. the 2 major comments →

arxiv 2601.09001 v6 pith:K4D5DVC7 submitted 2026-01-13 cs.CL

Entropy Sentinel: Probing Entropy Traces for LLM Monitoring

Pedro Memoli Buffa , Luciano Del Corro This is my paper

classification cs.CL

keywords entropy monitoringLLM accuracy estimationtop-k logprobsdomain shiftuncertainty quantificationcorrectness predictionSTEM benchmarks

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper asks whether a cheap by-product of normal LLM inference—the probabilities assigned to the top-20 next tokens at each decoding step—can reveal where a model is performing badly. It compresses each response's entropy trajectory into a compact vector, trains a lightweight classifier to predict whether the response is correct, and averages those predictions over a domain to estimate accuracy. Across exhaustive train/test splits over ten STEM benchmarks and nine models, the estimates often track held-out accuracy and rank domains correctly, although reliability varies by model. The most concrete finding is that the composition of the training domains matters more than the estimator: two benchmarks that span easy and hard tasks generalize better than more elaborate setups. If this transfers to production traffic, monitoring slice-level accuracy would require no extra judge calls, only logs that serving APIs already emit.

Core claim

The paper's central claim is that domain-level accuracy of an LLM can be estimated from the entropy of its own decoding trace, without labels on the target domain. For each response, a 17-dimensional profile summarizes the truncated top-20 entropy trajectory; a calibrated probabilistic classifier maps that profile to a per-instance correctness probability; and Eq. (1) averages those probabilities to produce an accuracy estimate for any slice. Tested on ten STEM benchmarks with all train/test splits of sizes one to four, across nine open-weight models from six families, the estimates often track held-out benchmark accuracy closely and achieve high rank agreement, with the best cases showing n

What carries the argument

The entropy profile: per generated token, entropy is approximated as -Σ p_i log p_i over the top-20 next-token probabilities (omitting the mass outside the top-k set); the trajectory of these values is condensed into 17 statistics (max, mean, standard deviation, quantiles Q10–Q90, skewness, kurtosis, and accumulation metrics such as SEA and NLL sums). A lightweight classifier—often a random forest—turns this vector into an estimated probability that the response is correct, and domain accuracy is the averaged predicted probability (Eq. 1). The load-bearing idea is that token-level uncertainty couples with answer correctness, so the profile is an accuracy signal rather than just a relative co

Load-bearing premise

All correctness labels and all 'true' benchmark accuracies are produced by a single external validator model, checked against human judgment only on 300 instances; if that validator is systematically biased on a benchmark, the training labels and the target it is compared against are biased in the same direction.

What would settle it

Hand-label a held-out benchmark that the estimator ranks poorly, using two independent human annotators, and compare the entropy-based accuracy estimates to human-labeled accuracy. If the estimates track the validator's labels but diverge from human truth, or if the entropy-correctness AUROC drops to chance under human labels, the transfer claim collapses.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

A monitoring system could estimate slice accuracy from standard inference logs, without additional judge or human evaluation for every slice.
Two well-chosen supervision benchmarks—one easy, one hard—often transfer to the other eight domains, suggesting a low-cost calibration procedure for deployment.
The choice of which domains provide supervision dominates performance; difficulty-diverse training sets are substantially better than difficulty-homogeneous ones.
Single accumulation metrics (NLLsum, SEsum) are competitive with the full 17-dimensional profile, so a minimal variant is available when only one scalar is practical.
Reliability must be validated per target model; some models show weak entropy–correctness coupling even under maximal supervision.

Where Pith is reading between the lines

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

Because the interface is top-20 logprobs, the same pipeline would run on closed models that expose such probabilities; the paper scopes validation to open-weight models, so this is an extension rather than a claim.
The near-parity of single accumulated metrics suggests an even cheaper operational route: calibrate one scalar like SEsum per model, and use it to triage domains before committing to a full profile.
An operator could apply the same estimator to subjective quality scores (as the abstract reports for judge scores) to flag low-quality traffic slices; the ranking signal appears in both verifiable and subjective settings, but transfer to new judge rubrics needs separate validation.
The paper's caveat that AEE remains non-trivial for several models implies using the method for prioritization and targeted inspection, not for high-stakes decisions based on absolute accuracy values.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

Solid, useful STEM result with an exhaustive evaluation; the metadata abstract overclaims subjective tasks and the single-validator labeling needs more support.

read the letter

Colleague,

The paper is worth a real look. It shows that a compact entropy-profile vector from top-k logprobs, fed through a lightweight classifier and averaged over a slice, gives accuracy estimates that transfer to unseen STEM benchmarks for several of nine tested LLMs. The evaluation is genuinely extensive—385 train/test benchmark splits, multiple classifier families and feature subsets, over 160k configurations—and the body is carefully hedged about model dependence. The finding that supervision diversity matters more than estimator architecture is concrete and actionable.

What's new is the aggregation protocol: people have used entropy features for instance-level uncertainty, but estimating domain-level accuracy under domain shift with a trained classifier and validating it exhaustively is a legitimate extension. The paper also honestly reports that simple baselines like NLLsum and SEsum are nearly as good, which is useful for practitioners.

Two soft spots, in proportion. First, the arXiv metadata abstract claims subjective-task correlations up to 0.91 and near-perfect worst-category detection, but the manuscript text is about STEM only, and the Limitations explicitly defer open-ended tasks to future work. That's an overclaim in the public record, and it needs fixing—either supply the experiments or revise the abstract. It looks like a versioning accident, but it's still the version people will read.

Second, the stress-test note is right: all correctness labels and all 'true' accuracies come from GROK-4.1-FAST-REASONING as the sole validator, with a 300-instance human audit. If the validator's errors correlate with entropy—say, it tends to accept verbose low-entropy wrong answers—then the training signal and the evaluation target contain the same bias, which can inflate the apparent transfer. That's not fatal for STEM math, where answer equivalence is fairly mechanical, but it's load-bearing for any absolute AEE claim. The authors should report per-benchmark validator agreement and ideally run a second validator on a sample. The overall 97% agreement is too thin to rule out a concentrated bias.

Minor: the code link in the text is a placeholder, no actual URL.

Who's this for? Practitioners monitoring LLM deployments and researchers in uncertainty quantification. It deserves a serious referee—the empirical question is important and the protocol is careful. I'd send it to review with a request to address the abstract mismatch and strengthen the validator analysis.

Recommendation: conditional acceptance after those revisions, or major revision with a clear path.

Referee Report

2 major / 6 minor

Summary. The paper proposes a lightweight, API-compatible method for estimating domain-level LLM accuracy from decoding traces. For each response, it computes a 17-dimensional entropy-profile vector from top-20 next-token log-probabilities, trains a probabilistic classifier to predict instance correctness, and averages the predicted probabilities over a domain (Eq. 1) to obtain an accuracy estimate. The method is evaluated on ten STEM benchmarks across nine LLMs (3B–20B) with an exhaustive train/test sweep over all subsets of size k=1..4 (385 groups), multiple classifier families, feature subsets, and calibration choices, totaling over 160,000 configurations. The central findings are that entropy-profile estimators often track held-out benchmark accuracy and rank domains well, that supervision composition (especially difficulty diversity) matters more than estimator architecture, and that reliability is model-dependent.

Significance. If the empirical claims hold, the paper makes a useful practical contribution: a cheap, log-only signal for continuous accuracy monitoring and data-acquisition prioritization, together with a rigorous evaluation protocol that exhaustively varies supervision and estimator design. The strengths are the scope of the experiments, the honest reporting of model dependence, the comparison against strong single-metric baselines, and the clear identification of supervision composition as the dominant factor. The main caveat is that all correctness labels and all 'true' accuracies are produced by a single external LLM validator, and the robustness of the transfer results to validator bias is not established. With additional validation of the labeling pipeline, the paper could be a solid empirical contribution to LLM monitoring.

major comments (2)

[Section 4 ('Instance labeling'); Appendix C.2; Eq. (1)] The correctness labels z from GROK-4.1-FAST-REASONING are used both as supervision for the classifier and as the ground-truth accuracy target when computing AEE and Spearman. If the validator's errors correlate with the entropy features being used — for example, if it accepts long, low-entropy reasoning variants more often than terse correct answers — the classifier can learn the validator's bias, and the evaluation target contains the same bias, inflating the apparent transfer. The manual audit of 300 instances (97% agreement) gives only an overall error rate and cannot detect bias concentrated in particular model–benchmark cells. Please provide a stratified human-label comparison across models and benchmarks (or at least across response-length/format strata), report the validator's confusion matrix against human labels, and test whether validator disagreements are associated with the e
[Abstract (arXiv metadata); Section 8] The arXiv metadata abstract claims subjective-task correlations up to r=0.91 and near-perfect detection of worst-performing categories, but the manuscript body contains no subjective-task experiments; Section 8 (Limitations) explicitly defers open-ended tasks as future work. This is an unsupported claim in the paper's front matter. Either remove the subjective-results claim from the abstract or include the experiments that support it. As written, the paper supports only the STEM-domain claims.

minor comments (6)

[Section 4 ('Benchmarks')] The text says 'eleven STEM reasoning benchmarks,' but the list that follows contains ten benchmarks (GSM8K, SVAMP, GSM-Symbolic, MATH, TheoremQA, SciBench, MatSciBench, OlympiadBench, LiveMathBench, GPQA). The count of 385 groups is consistent with ten benchmarks (sum_k C(10,k)), so 'eleven' appears to be a typo.
[Table 1 caption] The caption says 'across 3 benchmarks and 4 models,' but the table reports three models (PHI-3.5-MINI, MINISTRAL-3 8B, GPT-OSS 20B). The caption should say '3 models' or otherwise be corrected.
[Section 1 footnote] The footnote 'Code for the paper can be found here' contains no URL. Please provide a working repository link so that the experiments can be independently reproduced.
[Section 3; Appendix B] The feature vector is described as 17-dimensional in Section 3, while Appendix B concludes with a 'joint eleven-dimensional profile.' Section 4 also refers to a 10-dimensional entropy-distribution subset. Please harmonize the numbering and define clearly which components belong to which subset.
[Table 3] The presentation of median and IQR as subscripted pairs (e.g., '.95 .05') is difficult to read. Consider reporting median and IQR in separate columns or as error bars, especially since the table is central to the RQ2 comparison.
[Section 3] Some abbreviations (SEA, NLL, LNTP, MTP) are used in Table 1 before they are defined in Appendix A. Please define them at first occurrence in the main text, or move a brief definition to Section 3.

Circularity Check

0 steps flagged

No significant circularity: entropy-derived features, GROK-provided labels, and held-out benchmark accuracy targets are not identified by construction.

full rationale

The derivation chain is self-contained. Entropy-profile features are computed from decoding logprobs, the correctness labels z are produced by an external validator (GROK-4.1-FAST-REASONING) and used only as supervision, and the evaluation uses held-out benchmarks disjoint from the training groups via exhaustive 385 train/test compositions. AEE and Spearman values compare aggregated classifier outputs against these held-out labels, not against quantities fitted into the estimator. No equation defines the target accuracy in terms of the fitted classifier, and no load-bearing result depends on a self-citation or on importing a uniqueness theorem. The paper also reports a 300-instance manual audit with 97% agreement, giving the label source some independent grounding. The reliance on a single LLM validator for both training and evaluation labels is a legitimate external-validity concern—systematic, entropy-correlated judge errors could inflate apparent transfer—but it is an annotation-choice limitation, not circularity under the required construction-based standard. Therefore the appropriate finding is no significant circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The central claim is empirical, not derived. The method's free parameters are standard ML/engineering choices (top-k, temperature, feature set, hyperparameters). The main non-empirical commitments are that truncated top-20 entropy is an adequate signal and that a single external LLM judge can supply trustworthy labels; both are stated but only weakly validated.

free parameters (5)

Top-k logprob truncation k = 20
Chosen to match the maximum logprobs exposed by commercial serving APIs; the truncated entropy approximation depends on this limit.
Decoding temperature = 0.5
Set to 0.5 following Kuhn et al. for entropy estimation; it shapes all entropy trajectories and therefore all features.
Feature subset choice = 17D / 10D / 3D / 1D variants
Feature sets were defined from the AUROC screening in Section 3; the choice is manual and evaluated as an ablation, not fitted to held-out accuracy.
Classifier hyperparameters = grid-searched per training group
RF max_depth and min_samples_split, MLP hidden sizes, class balancing and isotonic calibration are selected by 5-fold CV on each training group—a standard but data-dependent modeling choice.
Answer post-processing rules = benchmark-specific heuristics
Final answers are extracted with benchmark-specific rules (e.g., last boxed expression); errors here translate into label noise.

axioms (4)

domain assumption Top-20 logprob entropy is an adequate approximation of full-vocabulary entropy for the studied models.
Section 3 defines the entropy signal by truncating the sum to top-20; if the omitted tail mass is large, the feature vector is a distorted uncertainty signal.
domain assumption GROK-4.1-FAST-REASONING labels are a valid ground truth for all benchmarks.
Section 4 and Appendix C.2; only 300 instances are manually audited (97% agreement). This grounds both training labels and evaluation error.
domain assumption Correctness is well-defined for all instances after removing answer options.
For GPQA and SciBench the multiple-choice options are stripped, making answer equivalence less standardized; the paper assumes benchmark-specific extraction resolves this.
domain assumption Decoding at temperature 0.5 produces representative confidence signals for the entropy estimator.
Temperature changes the token distribution; the paper adopts 0.5 from prior entropy-estimation work without ablating it.

pith-pipeline@v1.3.0-alltime-deepseek · 104 in / 13551 out tokens · 149176 ms · 2026-08-04T06:20:31.247892+00:00 · methodology

0 comments

read the original abstract

Deploying LLMs raises two coupled challenges: (1) monitoring---estimating where a model underperforms as traffic drifts---and (2) prioritization---deciding where to intervene to close the largest performance gaps. We explore whether top-$k$ logprobs---cheap, consumer-accessible signals from standard inference---can serve as reliable proxies for domain-level quality of both verifiable and subjective tasks. We summarize each response's output-entropy profile into a compact vector, predict instance quality with a lightweight classifier, and then average predictions to yield a domain-level estimate. On verifiable tasks (ten STEM benchmarks, nine LLMs, exhaustive train/test compositions), estimates often track held-out accuracy, with several models showing near monotonic calibration. On subjective tasks, trained on LLM-judge scores over categorized real user conversations, several models track the judge's slice scores remarkably closely ($r$ up to $0.91$) and detect the worst-performing categories near-perfectly, though this is not the case for all LLMs. Where coupling holds, results suggest that entropy signals can support monitoring at a fraction of the cost of judge-based evaluation.

Figures

Figures reproduced from arXiv: 2601.09001 by Luciano Del Corro, Pedro Memoli Buffa.

**Figure 2.** Figure 2: Max-entropy density for PHI-3.5-MINI on MATH (correct vs. incorrect). Incorrect responses shift to higher entropy, indicating greater uncertainty. which aspects matter for correctness in a given setting, without brittle manual feature selection. 4 Robustness Evaluation Protocol We now evaluate whether the methodology supports domain-level accuracy estimation under domain shift: we train instance-level c… view at source ↗

**Figure 3.** Figure 3: Accuracy estimations from a random-forest classifier trained exclusively on compact entropy-profile [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Relationship between training group difficulty [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

Review history (2 revisions) →

discussion (0)

Reference graph

Works this paper leans on

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online" 'onlinestring :=

ENTRY address archivePrefix author booktitle chapter edition editor eid eprint eprinttype howpublished institution journal key month note number organization pages publisher school series title type volume year doi pubmed url lastchecked label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block STRING...
[39]

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" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

[1] [1]

Gustaf Ahdritz, Tian Qin, Nikhil Vyas, Boaz Barak, and Benjamin L. Edelman. 2024. Distinguishing the knowable from the unknowable with language models. arXiv preprint arXiv:2402.03563

Pith/arXiv arXiv 2024

[2] [2]

Guillaume Alain and Yoshua Bengio. 2017. Understanding intermediate layers using linear classifier probes. In ICLR Workshop

2017

[3] [3]

Riccardo Ali, Francesco Caso, Christopher Irwin, and Pietro Li\` o . 2025. https://arxiv.org/abs/2502.16570 Entropy-lens: The information signature of transformer computations . Preprint, arXiv:2502.16570. Preprint. Under review

arXiv 2025

[4] [4]

Anonymous. 2025. Livemathbench: A contamination-resistant dynamic math reasoning benchmark. arXiv preprint arXiv:2505.15340

arXiv 2025

[5] [5]

Amos Azaria and Tom Mitchell. 2023. The internal state of an LLM knows when it's lying. arXiv preprint arXiv:2304.13734

Pith/arXiv arXiv 2023

[6] [6]

Yonatan Belinkov. 2022. Probing classifiers: Promises, shortcomings, and advances. Computational Linguistics, 48(1):207--219

2022

[7] [8]

Dylan Bouchard, Mohit Singh Chauhan, David Skarbrevik, Ho-Kyeong Ra, Viren Bajaj, and Zeya Ahmad. 2025 b . https://arxiv.org/abs/2507.06196 Uqlm: A python package for uncertainty quantification in large language models . Preprint, arXiv:2507.06196

arXiv 2025

[8] [9]

Chao Chen, Kai Liu, Ze Chen, Yi Gu, Yue Wu, Mingyuan Tao, Zhihang Fu, and Jieping Ye. 2024. INSIDE : LLMs ' internal states retain the power of hallucination detection. arXiv preprint arXiv:2402.03744

Pith/arXiv arXiv 2024

[9] [10]

Jiuhai Chen and Jonas Mueller. 2023. Quantifying uncertainty in answers from any language model and enhancing their trustworthiness. arXiv preprint arXiv:2308.16175

Pith/arXiv arXiv 2023

[10] [11]

Wenhu Chen and 1 others. 2023. Theoremqa: A theorem-driven question answering dataset. In Proc. EMNLP

2023

[11] [12]

Karl Cobbe and 1 others. 2021. Training verifiers to solve math word problems. In arXiv preprint arXiv:2110.14168

Pith/arXiv arXiv 2021

[12] [13]

Hanyu Duan, Yi Yang, and Kar Yan Tam. 2024. Do LLMs know about hallucination? an empirical investigation of LLM 's hidden states. arXiv preprint arXiv:2402.09733

Pith/arXiv arXiv 2024

[13] [14]

Ekaterina Fadeeva, Aleksandr Rubashevskii, Artem Shelmanov, Sergey Petrakov, Haonan Li, Hamdy Mubarak, Evgenii Tsymbalov, Gleb Kuzmin, Alexander Panchenko, Timothy Baldwin, Preslav Nakov, and Maxim Panov. 2024. Fact-checking the output of large language models via token-level uncertainty quantification. arXiv preprint arXiv:2403.04696

Pith/arXiv arXiv 2024

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Google DeepMind . 2025. https://ai.google.dev/gemma/docs/core/model_card_3 Gemma 3: Multimodal open models built from gemini technology . Technical report, Google

2025

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Chaoqun He and 1 others. 2024. Olympiadbench: A challenging benchmark for promoting agi with olympiad-level bilingual multimodal scientific problems. In Proc. ACL

2024

[16] [17]

Dan Hendrycks and 1 others. 2021. Measuring mathematical problem solving with the math dataset. In Proc. NeurIPS, pages 1--15

2021

[17] [18]

Saurav Kadavath, Tom Conerly, Amanda Askell, Tom Henighan, Dawn Drain, Ethan Perez, Nicholas Schiefer, Zac Hatfield-Dodds, Nova DasSarma, Eli Tran-Johnson, Scott Johnston, Sheer El-Showk, Andy Jones, Nelson Elhage, Tristan Hume, Anna Chen, Yuntao Bai, Sam Bowman, Stanislav Fort, and 17 others. 2022. Language models (mostly) know what they know. arXiv prep...

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ENTRY address archivePrefix author booktitle chapter edition editor eid eprint eprinttype howpublished institution journal key month note number organization pages publisher school series title type volume year doi pubmed url lastchecked label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block STRING...

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write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...