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Entropy Sentinel: Probing Entropy Traces for LLM Monitoring

Pedro Memoli Buffa, Luciano Del Corro

arXiv:2601.09001v6cs.CL

TL;DR

As deployed LLM traffic shifts, practitioners need scalable ways to locate underperformance and prioritize interventions; Entropy Sentinel uses top-k entropy traces to estimate slice quality. Estimates often track held-out accuracy on verifiable tasks, while several models closely recover subjective judge scores, suggesting usefulness where the coupling holds.

  • Problem

    Practitioners lack scalable ways to identify where deployed LLMs underperform on shifting heterogeneous traffic and where to intervene.

  • Method

    Entropy Sentinel summarizes each response’s entropy trajectory into a compact vector, predicts instance-level quality with a lightweight classifier, and aggregates predictions into slice-level estimates.

  • Results

    Estimates often track held-out accuracy on verifiable STEM tasks, while several models track subjective judge scores closely, reaching r up to 0.91.

  • Takeaways & Limitations

    Where entropy–quality coupling holds, cheap decoding signals can support monitoring and prioritization at a fraction of judge-based evaluation’s cost.

  • Takeaways & Limitations

    Subjective-task quality is defined by a single LLM judge, so the claims concern recovering that judge’s assessments rather than quality itself.

Abstract

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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.

1 Introduction

The paper proposes using compact top-k entropy traces from standard inference to monitor slice-level quality and prioritize interventions without repeated judge-based evaluation. Across verifiable and subjective tasks, the approach often tracks held-out accuracy or judge scores, though coupling varies by LLM.

  • Motivation: Deployed LLMs face shifting heterogeneous traffic, but practitioners need scalable ways to locate underperformance and prioritize interventions.Existing approaches rely on expensive, slow-to-update benchmarks or judge evaluation whose cost scales linearly with traffic, leaving most production data unmonitored.
  • Approach: Top-k entropy signals offer a cheap monitoring alternative because they arise during decoding, are much smaller than hidden states, and are exposed by most model-serving APIs.A probe can score production slices without repeated labeling or external large models, while inducing rankings for intervention prioritization.
  • Verifiable tasks: 10 STEM QA benchmarks support an exhaustive evaluation of out-of-distribution accuracy estimation across varying supervision compositions.The study trains on benchmark subsets and estimates accuracy on remaining benchmarks for k ∈ {1, 2, 3, 4}.
  • Verifiable tasks: >160,000 configurations show that estimates often track held-out accuracy closely, with some LLMs exhibiting almost perfect calibration.The evaluation spans nine LLMs from 3B–20B across six families, and supervision composition emerges as the dominant design factor.
  • Subjective tasks: On 11-category multi-turn chat slices, entropy probes test whether they recover judge category scores and rankings for realistic monitoring.Where alignment holds, entropy signals support monitoring and prioritization at a fraction of judge-based evaluation cost on the target model and task distribution.

2 From Signatures to Quality Estimates

Entropy Sentinel converts top-k logprob traces into compact entropy features, predicts instance-level quality with a lightweight probe, and averages predictions to estimate slice-level quality. Calibration supports accuracy monitoring when correctness is verifiable and judge-score monitoring when it is subjective.

  • Method: Entropy Sentinel uses two stages: summarize each response’s entropy trajectory into a compact feature vector, then predict instance quality and aggregate predictions by slice.The probe outputs an estimated quality measure for each response, whose predictions are averaged over domain instances.
  • Method: Top-k entropy approximates next-token uncertainty by truncating the Shannon-entropy sum to probabilities exposed by standard inference APIs.The approximation omits probability mass outside the top-k token set.
  • Quality estimation: Averaged probe predictions estimate domain quality, with correctness probabilities yielding slice accuracy when labels are verifiable.If the probe is well-calibrated, the averaged estimate is a consistent estimator of the true domain measure.
  • Quality estimation: For production traces without objective correctness, the probe can instead be trained on an external judge quality score normalized to [0, 1].This extends the same monitoring framework to continuous subjective quality labels.
  • Related work: ES generalizes the binary ATC baseline by accepting multi-feature inputs and continuous labels, making it suitable for broader monitoring.ATC uses a hard threshold on a single score to produce binary votes and applies only to binary labels.

3 A Compact Entropy Signature

The section develops a fixed-dimensional entropy signature from top-k log-probabilities to probe response correctness. Across models and benchmarks, entropy summaries generally discriminate correct from incorrect responses, but the most predictive statistic varies by setting.

  • Setup: k=20 top-k log-probabilities provide the entropy trajectories, matching the maximum exposed by commercial APIs.A full-vocabulary ablation shows little difference.
  • Entropy statistics: AUROC > 0.5 for the vast majority of statistics indicates correct responses concentrate in lower-entropy regions while incorrect responses shift higher.This pattern is illustrated by the max-entropy density comparison for PHI-3.5-MINI on MATH.
  • Entropy statistics: Q10/Q25 are most predictive on MATH, Std on GSM8K, and SEA and NLLsum consistently rank among the strongest signals.Higher-order moments help in some settings but collapse toward chance in others.
  • A compact discriminative signature: 17D entropy-profile vectors summarize central tendency, dispersion, distributional tails, shape, accumulation, and white-box uncertainty metrics.The vectors truncate vocabulary sums to the top k=20 tokens where applicable, enabling lightweight quality classification.

4 Estimating OOD Accuracy on Verifiable STEM Tasks

Entropy profiles support OOD accuracy estimation on verifiable STEM tasks by training instance-level correctness predictors and aggregating their probabilities across unseen benchmarks. Performance depends primarily on supervision composition, while estimator design has smaller effects.

  • RQ1: Accuracy estimation under deployment-plausible defaults: Eight of nine models achieve r ≥ 0.90 with low MAE of 0.03–0.13 when estimating accuracy out of domain.The Extremes training group is consistently stronger than Intermediate; PHI-3.5-MINI reaches MAE 0.03 and r = 0.99, while QWEN3-8B is weakest with MAE 0.13–0.17 and r = 0.84–0.90.
  • RQ1: Accuracy estimation under deployment-plausible defaults: Slice-level MAE is largely decoupled from per-instance AUROC, with R2 < 0.1, because averaging cancels noisy instance-level errors.Estimates remain accurate even when the instance-level discriminator is near chance.
  • RQ2: Comparison to ATC: The flexible configuration ties for the lowest error on Extremes at .09 MAE and can outperform ATC for particular models, including PHI with MAE 0.03 vs. ATC’s 0.06.This shows that nonlinear models over multi-feature signatures can match or exceed the ATC baseline in some settings.
  • RQ3: Supervision composition: Increasing the number of supervision benchmarks from k=1 to k=4 lowers median MAE from 0.20–0.27 to 0.06–0.16 and compresses IQR to 0.03–0.04.Training composition is therefore a first-order factor in flexible ES performance for these tasks.
  • RQ3: Supervision composition: Intermediate-difficulty training groups with weighted accuracy around 0.4–0.65 minimize held-out error, whereas very easy or very hard groups generalize worse.The U-shaped relationship is attributed to difficulty-diverse supervision exposing both success and failure patterns.
  • RQ4: Estimator design: Estimator design changes median MAE by at most 0.02–0.03, calibration and balancing have near-zero effects, and Pearson r remains at ≈0.94.Random forests and the full 17D profile perform best, while MLPs degrade slightly under limited supervision.

5 Monitoring LLM Traffic

The section evaluates whether entropy profiles can monitor open-ended LLM traffic by predicting LLM-judge quality without ground-truth scores. Entropy–quality coupling is substantial for some models but model-dependent, and where it holds, entropy signals support lower-cost monitoring beyond response length alone.

  • Setup: The study tests entropy-based quality probes on open-ended WildBench conversations scored by an external LLM judge across 11 task categories.Conversations are capped at two turns, with responses limited to 16,384 tokens and judge scores normalized to [0, 1].
  • RQ1: OOD category monitoring with entropy signals: |r| > 0.85 is achieved by several individual entropy features in strong models, whereas weak models never exceed |r| ≈0.67.Simple averages and upper quantiles perform best, while accumulation metrics reach just r = 0.14 for PHI-3.5-MINI.
  • RQ2: Studying the length confound: Length alone reaches r = 0.75 only for LLAMA-3.1-8B, while adding length to entropy changes results by at most ∆r = +0.05 and is often negative.This indicates that strong entropy-based results are not explained solely by the judge’s known preference for longer responses.
  • RQ1: OOD category monitoring with entropy signals: Four of nine models show significant OOD entropy–judge coupling, with r = 0.79–0.91 and all 95% CIs excluding zero.Two models also separate the judge’s worst categories at significance under an exact permutation test.
  • Limitations and implications: Entropy-based monitoring does not consistently transfer to subjective tasks, so it should be validated on each target model and on real traces clustered post hoc.Where coupling holds, the results suggest monitoring at a fraction of judge-based evaluation cost.

6 Related Work

Prior work estimates out-of-distribution performance using confidence or agreement signals, while LLM uncertainty quantification often relies on repeated generations, external judges, or hidden-state probes. Entropy Sentinel instead uses single-pass decoding traces and adapts ATC per metric as an in-method baseline.

  • Estimating OOD performance: OOD performance estimation for classification networks leverages correlations between in-distribution and out-of-distribution accuracy.This line of work includes Garg et al. (2022), Chen et al. (2021), and Miller et al. (2021).
  • Estimating OOD performance: The ATC baseline thresholds a single confidence score but is not adapted to LLM token sequences.Saxena et al. (2024) extend “agreement on the line” to foundation models, requiring inference from multiple models.
  • Estimating OOD performance: Entropy Sentinel uses single-pass decoding traces and adapts ATC per metric as an in-method baseline.The method avoids the multiple-model inference described as prohibitive for continuous monitoring.
  • Uncertainty quantification: LLM uncertainty quantification methods sample multiple generations, invoke external judges, or probe hidden states.The cited methods include Shorinwa et al. (2024), Huang et al. (2025), Kuhn et al. (2023), Azaria and Mitchell (2023), Chen et al. (2024), and Zhang et al. (2025a).

7 Conclusion

The study finds that top-k entropy signals can support slice-level quality monitoring, but their reliability varies by task and model. Verifiable-task estimates often track held-out accuracy, whereas subjective-task coupling with judge scores requires per-model validation.

  • Conclusion: Top-k entropy signals were studied as probes for slice-level quality monitoring.The approach uses cheap decoding signals to estimate quality at the slice level.
  • Conclusion: On verifiable STEM tasks, entropy-based estimates often track held-out accuracy closely.Supervision composition is the dominant factor affecting this relationship.
  • Conclusion: On subjective monitoring, coupling with judge scores is real but model-dependent.Performance in the verifiable setting does not guarantee transfer to subjective monitoring.
  • Conclusion: Per-model validation remains necessary before relying on entropy signals for monitoring.Where coupling holds, cheap decoding signals can support monitoring.

8 Limitations

The study leaves unexplained why entropy–quality coupling varies across models and settings, and its subjective-task claims rely on a single LLM judge. Entropy traces are also sensitive to serving and formatting choices, requiring retraining when configurations change.

  • Unexplained model-dependence: Entropy–quality coupling varies strongly across models, and verifiable-task coupling strength does not predict subjective-task coupling strength.The architectural or training properties driving this dependence remain unidentified.
  • Judge-relative supervision: Subjective-task monitoring treats scores from a single LLM judge as ground truth, leaving agreement with other judges, ensembles, or humans untested.The resulting claims are therefore judge-relative.
  • Sensitivity to decoding and formatting: Entropy traces depend on temperature, maximum length, stop criteria, prompting style, answer formatting, and post-processing.These changes can shift entropy distributions without reflecting true capability changes.
  • Sensitivity to decoding and formatting: A deployed entropy sentinel should be retrained whenever the serving configuration changes.Configuration changes include decoding choices, prompt instructions, answer formatting, and post-processing.

A Baseline White Box UQ Metrics · B Effect of logprob truncation on predictive power

The paper benchmarks nine white-box uncertainty metrics derived from single-pass output logprobs and uses top-20 truncation for entropy profiles. For Phi-3.5-mini, replacing top-20 logprobs with the full vocabulary barely changes predictive power, aside from larger skewness and kurtosis shifts on harder benchmarks.

  • A Baseline White Box UQ Metrics: Nine standard uncertainty-quantification baselines use only output-token logprobs from a single forward pass, providing cheap signals for continuous performance monitoring.Most baselines are available in the uqlm library and directly match the signals accessible through standard inference.
  • A Baseline White Box UQ Metrics: Shannon Entropy computes token-level uncertainty over vocabulary V and is accumulated across response tokens as Shannon Entropy Accumulation.In practice, the entropy sum is truncated to the top k = 20 tokens.
  • A Baseline White Box UQ Metrics: Negative Log-Likelihood averages the negative log probability assigned to each generated token.The metric is defined tokenwise as NLL(y_i) = −log P(y_i | x, y_<i) before aggregation.
  • A Baseline White Box UQ Metrics: Length-Normalized Token Probability uses the geometric mean of token probabilities as a response-level uncertainty metric.This baseline is attributed to Malinin and Gales (2021).
  • A Baseline White Box UQ Metrics: Minimum Token Probability identifies the weakest token probability in a response.MTP(y) = min_i P(y_i | x, y_<i).
  • A Baseline White Box UQ Metrics: Perplexity is computed as exp(NLLavg(y)), providing a standard transformation of average negative log-likelihood.This baseline is attributed to Fadeeva et al. (2024).
  • B Effect of logprob truncation on predictive power: 0.002 is the typical AUROC shift when Phi-3.5-mini entropy profiles use full-vocabulary rather than top-20 logsoftmax values.Every location and scale statistic moves by less than 0.01; skewness and kurtosis shift by ≈0.03 on MATH and OlympiadBench and ≈0.003 on GSM8K.

C Additional Entropy Profile Features Results … F Decoupling between slice MAE and per-instance AUROC

The appendices show that entropy-feature separability varies substantially by model and task, while temperature robustness and aggregate calibration support monitoring even when instance discrimination is weak. They also document the STEM evaluation setup and validator-based labeling procedure.

  • C Additional Entropy Profile Features Results: 0.9196 AUROC is achieved by QWEN-3 4B on MATH, while QWEN-3 8B shows near-chance AUROCs on several statistics.The results indicate substantial heterogeneity across model families and sizes, including within the same family.
  • C Additional Entropy Profile Features Results: Q10 and Q25 are most predictive on difficult tasks like MATH, whereas Mean and Std Dev perform better on elementary tasks like GSM8K.Individual statistics’ discriminatory potential is highly dependent on model and domain.
  • D Feature Temperature Sensitivity Analysis: 0.78–0.84 is the AUROC range maintained by SEA, NLLsum, Q10, and Q25 across all twenty temperature runs.Although several bulk and average-likelihood statistics drift monotonically upward with temperature, feature ordering remains preserved.
  • E Experimental Setup Details for STEM Evaluation; E.1 Benchmark Preprocessing: STEM experiments use zero-shot prompts with free-form answers, benchmark-specific preprocessing, and test splits when available.GPQA and SciBench options are removed, OlympiadBench is restricted to text-only math and physics, and LiveMathBench uses the v202505_all_en subset.
  • E.2 Instance Labeling; E.3 Evaluation and Verification Prompt: 99% agreement with human judgment was obtained in a manual audit of 1000 randomly sampled instances labeled by an external validator LLM.The validator compares the question, model response, and reference answer to produce a binary correctness label.
  • E.4 Feature Interface: Top-20 decoding logprobs define the feature interface to match common logprob-returning serving stacks.The paper notes an ablation against the full-vocabulary distribution in Appendix B.
  • E.5 Estimator Configurations: Over 160,000 configurations span 9 models, 385 train/test groups, 3 classifier families, 2×2 training options, and 4 feature subsets.The evaluated classifiers are logistic regression, random forest, and MLP, with cross-validated hyperparameter selection for the latter two.
  • E.6 Hardware and Compute; F Decoupling between slice MAE and per-instance AUROC: Pearson R2 is 0.005 and 0.097 for the two estimator settings, with low slice-level error across the full AUROC range.Averaging allows per-instance errors to cancel, so aggregate estimation depends on calibration rather than discrimination; experiments ran on one NVIDIA A6000 GPU over approximately a week.

G Additional Training Sensibility Results · H Per Model Feature Correlation · J Use of AI-Assitants

Supplementary analyses show that difficulty-diverse training compositions improve accuracy estimation, while additional sections document per-model feature correlations and limited AI-assistant use. The appendix also reports low slice-level error across the AUROC range.

  • G Additional Training Sensibility Results: Best-performing benchmark groups occupy the intermediate accuracy regime (0.4–0.7), corroborating the U-shaped relationship from Figure 3.Table 11 identifies the highest- and lowest-performing combinations at each k using weighted average group accuracy.
  • G Additional Training Sensibility Results: For k ≥2, pairing GSM8K with OLYMPIADBENCH spans difficulty levels and exposes estimators to low-entropy successes and high-entropy failures.This composition enables robust transfer to unseen domains.
  • G Additional Training Sensibility Results: 0.087 median MAE is achieved by the k = 2 GSM + OLY combination, matching the best k = 4 configuration with half the supervision.The result supports difficulty diversity as the main driver of better accuracy estimation.
  • H Per Model Feature Correlation: Per-model correlations for each feature are presented in Table 12, with the largest absolute correlation per row bolded.The supplied appendix passage provides the table reference but no individual correlation values.
  • J Use of AI-Assitants: AI assistants were used for spell checking, proofreading, and minor utility scripts, but no AI-generated text was included directly in the paper.The authors conducted all research, methodology, and analysis.
  • J Use of AI-Assitants: Pearson R2 = 0.005 for Extremes and R2 = 0.097 for Intermediate, while slice-level error remains low across the full AUROC range.Each plotted point represents one (LLM, held-out benchmark) pair.
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