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arxiv: 2605.04295 · v1 · submitted 2026-05-05 · 💻 cs.LG · cs.AI

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· Lean Theorem

LLMs Uncertainty Quantification via Adaptive Conformal Semantic Entropy

Hamed Karimi, Reza Samavi, Vaishali Meyappan

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Pith reviewed 2026-05-08 17:48 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords large language modelsuncertainty quantificationsemantic entropyconformal predictionadaptive clusteringhallucination detectiondistribution-free guarantees
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The pith

Adaptive Conformal Semantic Entropy quantifies LLM prompt uncertainty by clustering responses according to semantic similarity and applies conformal calibration to bound error rates on accepted outputs.

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

The paper introduces Adaptive Conformal Semantic Entropy to quantify uncertainty in large language model responses at the prompt level. It generates multiple diverse answers to the same prompt, clusters them by semantic similarity, and derives an adaptive uncertainty score from the entropy inside each cluster. Conformal calibration then sets acceptance thresholds that deliver finite-sample, distribution-free guarantees keeping the error rate among accepted responses below a user-chosen tolerance. Existing lexical and probabilistic uncertainty measures often overlook meaning-level variation and lack such guarantees, which matters for safe deployment where overconfident hallucinations can cause harm. Experiments across models and datasets show higher AUROC, better calibration, and stronger conformal coverage than token-entropy and other baselines.

Core claim

The central claim is that prompt-level uncertainty can be estimated by adaptively measuring semantic dispersion through clustering of multiple responses, combined with conformal calibration to provide finite-sample distribution-free guarantees that the error rate among accepted responses is bounded by a user-specified tolerance.

What carries the argument

The adaptive uncertainty scoring function based on clustering semantic entropy of diverse responses to the same prompt, with conformal calibration for accept/abstain decision rules.

Load-bearing premise

That clustering responses by semantic similarity reliably captures meaningful dispersion in model knowledge and that adaptive adjustments based on cluster features produce valid uncertainty scores without bias or post-hoc tuning that would violate the conformal guarantees.

What would settle it

Observing that the empirical error rate among accepted responses exceeds the user-specified tolerance on held-out data from multiple LLMs and datasets would show the guarantee does not hold in practice.

Figures

Figures reproduced from arXiv: 2605.04295 by Hamed Karimi, Reza Samavi, Vaishali Meyappan.

Figure 1
Figure 1. Figure 1: ACSE Pipeline. (a) To calibrate a pretrained LLM, for each prompt view at source ↗
Figure 3
Figure 3. Figure 3: Comparing ACSE uncertainty against baseline confidences, view at source ↗
Figure 5
Figure 5. Figure 5: Sensitivity analysis on clustering threshold view at source ↗
read the original abstract

LLMs' overconfidence, particularly when hallucinating, poses a significant challenge for the deployment of the models in safety-critical settings and makes a reliable estimation of uncertainty necessary. Existing approaches for uncertainty quantification typically prioritize lexical or probabilistic measures; however, these techniques often ignore the semantic variance of different responses with similar meaning. In this paper, we propose Adaptive Conformal Semantic Entropy (ACSE), a method for estimating prompt-level uncertainty by adaptively measuring semantic dispersion in LLMs outputs. Our uncertainty scoring function is based on clustering semantic entropy of multiple diverse responses to the same prompt. The function adaptively adjusts the uncertainty score based on semantic features of each cluster. To ensure statistical reliability of our score, we use conformal calibration to apply a decision rule to accept/abstain the prompts, providing a finite-sample, distribution-free guarantee such that the error rate among the accepted responses remains bounded by a user-specified tolerance. Our extensive experimental evaluations using different LLMs and datasets, demonstrate that our approach consistently outperforms state-of-the-art uncertainty quantification baselines using discriminative performance, conformal guarantees, and probabilistic calibration indicators. As a highlight, for TriviaQA dataset, AUROC of our approach is 0.88 compared to 0.65 produced by the token entropy approach.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes Adaptive Conformal Semantic Entropy (ACSE) for prompt-level uncertainty quantification in LLMs. Multiple diverse responses are generated per prompt, clustered by semantic entropy, and an uncertainty score is computed that adaptively adjusts based on semantic features of each cluster. Conformal calibration is then applied to produce a decision rule for accepting or abstaining from prompts, with a claimed finite-sample, distribution-free guarantee that the error rate among accepted responses is bounded by a user-specified tolerance. Experiments across LLMs and datasets (e.g., TriviaQA) report superior AUROC (0.88 vs. 0.65 for token entropy) and better performance than baselines on discriminative, conformal, and calibration metrics.

Significance. If the conformal validity holds, ACSE would offer a semantically grounded uncertainty measure that improves upon purely lexical or probabilistic baselines while retaining distribution-free guarantees, which is valuable for safety-critical LLM deployment. The integration of semantic clustering with conformal prediction is a potentially useful direction, though its statistical soundness requires verification.

major comments (3)
  1. [§3.2] §3.2 (Adaptive Uncertainty Scoring): The uncertainty score is defined to adaptively adjust based on semantic features extracted from clusters of responses generated for the specific test prompt. This per-instance, data-dependent adaptation is not shown to preserve the exchangeability between calibration and test points that is required for the distribution-free guarantee asserted in the abstract and §4.
  2. [§4] §4 (Conformal Calibration): No modified procedure (e.g., split-conformal with the adaptation function frozen on calibration data only, or inductive conformal treating the full adaptive map as a fixed nonconformity function) is described. Standard conformal thresholds applied to an adaptively computed score on test data do not automatically inherit the finite-sample coverage bound.
  3. [§5.2] Table 2 / §5.2 (Empirical Results): The reported AUROC gains and conformal coverage are presented without ablations that isolate the contribution of the adaptive adjustment versus the base semantic-entropy clustering; without such controls it is unclear whether the gains are robust or whether they rely on post-hoc choices that could invalidate the claimed guarantees.
minor comments (2)
  1. [Abstract] The abstract and §1 claim 'parameter-free' guarantees, yet the clustering step implicitly depends on the choice of embedding model and number of responses; clarify whether these are treated as fixed hyperparameters or part of the method.
  2. [§3.2] Notation for the adaptive score (e.g., how cluster features enter the nonconformity function) is introduced without an explicit equation; adding a compact definition would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback, particularly on the statistical validity of the conformal guarantees and the empirical analysis. We address each major comment below and will make the necessary revisions to clarify the method and strengthen the claims.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (Adaptive Uncertainty Scoring): The uncertainty score is defined to adaptively adjust based on semantic features extracted from clusters of responses generated for the specific test prompt. This per-instance, data-dependent adaptation is not shown to preserve the exchangeability between calibration and test points that is required for the distribution-free guarantee asserted in the abstract and §4.

    Authors: We agree that the per-instance adaptation described in §3.2, which relies on semantic features from test-prompt-specific clusters, does not automatically preserve exchangeability and thus may not support the claimed distribution-free guarantee. To address this, we will revise the uncertainty scoring function to derive all adaptive parameters (including cluster-based semantic feature adjustments) exclusively from the calibration data, treating the full scoring map as fixed. This change will be explicitly stated in the revised §3.2, ensuring the nonconformity scores remain exchangeable between calibration and test points. revision: yes

  2. Referee: [§4] §4 (Conformal Calibration): No modified procedure (e.g., split-conformal with the adaptation function frozen on calibration data only, or inductive conformal treating the full adaptive map as a fixed nonconformity function) is described. Standard conformal thresholds applied to an adaptively computed score on test data do not automatically inherit the finite-sample coverage bound.

    Authors: The referee is correct that the manuscript does not describe a modified conformal procedure accounting for the adaptation. We will update §4 to specify inductive conformal prediction with the complete adaptive scoring function (semantic clustering and feature adjustment) learned and frozen solely on the calibration set. Test-point scores will be computed using this fixed function, inheriting the standard finite-sample, distribution-free coverage bound. A formal statement of the revised guarantee will be added. revision: yes

  3. Referee: [§5.2] Table 2 / §5.2 (Empirical Results): The reported AUROC gains and conformal coverage are presented without ablations that isolate the contribution of the adaptive adjustment versus the base semantic-entropy clustering; without such controls it is unclear whether the gains are robust or whether they rely on post-hoc choices that could invalidate the claimed guarantees.

    Authors: We acknowledge that the current experiments lack ablations isolating the adaptive adjustment from the base semantic-entropy clustering. In the revision, we will add new experiments and a supplementary table in §5.2 comparing ACSE against a non-adaptive baseline (fixed semantic entropy clustering without per-cluster adjustment), using the frozen adaptation function from the updated conformal procedure. This will clarify the contribution of the adaptive component while maintaining the revised guarantees. revision: yes

Circularity Check

0 steps flagged

No circularity: ACSE score construction and conformal guarantee are independent of self-definition or fitted inputs.

full rationale

The paper defines its uncertainty scoring function explicitly from clustering of semantic entropy across multiple LLM responses to a prompt, followed by an adaptive adjustment using per-cluster semantic features. It then applies standard conformal calibration on this score to obtain acceptance/abstention thresholds with the usual finite-sample distribution-free coverage guarantee. No equation or step reduces the claimed guarantee or score to a tautology by construction (e.g., no fitted parameter is relabeled as a prediction, no self-citation supplies a uniqueness theorem, and no ansatz is smuggled via prior work). The derivation chain is self-contained against external conformal prediction theory and does not rely on renaming known results or self-referential definitions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the assumption that semantic clustering of LLM responses provides a meaningful proxy for uncertainty and that conformal calibration can be applied directly to the resulting scores without violating distribution-free properties.

axioms (2)
  • domain assumption Semantic similarity between LLM responses can be measured reliably enough to form clusters that reflect true epistemic uncertainty.
    The method depends on this to define dispersion; abstract invokes it when describing clustering of semantic entropy.
  • domain assumption Multiple diverse responses to the same prompt are available and sufficient to estimate semantic dispersion.
    Core to the uncertainty scoring function described in the abstract.
invented entities (1)
  • Adaptive Conformal Semantic Entropy (ACSE) no independent evidence
    purpose: Prompt-level uncertainty score that adapts based on semantic cluster features
    Newly introduced scoring function; no independent evidence provided beyond the paper's own experiments.

pith-pipeline@v0.9.0 · 5520 in / 1417 out tokens · 40956 ms · 2026-05-08T17:48:05.790303+00:00 · methodology

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