LLM Uncertainty Estimation

LLM: Large Language Model

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38 papers in the last four weeks, up 111% on the four weeks before. 0.4% of all new papers.

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Latest papers 298

Jun 15, 2026cs.CL

Speaking in Self-Assessing Tongues: On the Verbalized Confidence of LLMs in Machine Translation

The rapid rise in popularity of large language models (LLMs) for translation calls for a thorough study of the reliability of their confidence in their own outputs. Unlike many generation tasks, translation errors and confidence levels can be useful at different levels of granularity (tokens, words, or spans). Unsupervised approaches based on internal signals like predicted probabilities can be misleading because they reflect certainty among alternatives rather than correctness. In addition, they require access to such internal signals. Here, we devise five verbalized methods of extracting an LLM's per-token confidence without those shortcomings and compare their reliability with that of the model's internal signals of certainty. We evaluate reliability using two forms of alignment: fine-grained error detection and calibration. For both, internal and verbalized methods perform similarly, although results vary by model. Interestingly, we find little to no correlation between internal and verbalized methods.

Ali Marashian, Alexis Palmer, Katharina von der Wense

University of Colorado Boulder, USA · Johannes Gutenberg University Mainz, Germany

Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation MT Evaluation

Jun 14, 2026cs.AI

Heteroskedastic Signals in Budgeted LLM Verification: Structural Heterogeneity Limits Optimization Gains

Large language model (LLM) systems increasingly use uncertainty signals to allocate limited computation across verification, test-time scaling, tool execution, and other selective-compute decisions. Such policies rely on a \emph{global signal comparability assumption}: equal scores should carry comparable decision value across inputs. Using budgeted verification as a controlled diagnostic setting, we identify a failure mode of this assumption: uncertainty quality is heteroskedastic across cost strata, with some regions exhibiting near-random discriminability despite concentrating many errors. Under an explicit local model, we characterize the resulting distortion of global allocation and show that its upper bound scales with cross-stratum signal-quality dispersion. We separate weak signals, optimization instability, and structural heterogeneity through a controlled intervention hierarchy: Threshold, MP-Adapt, MP-Strat, and a deliberately simple cost-stratified thresholding intervention (CST). Across MBPP and MATH using Qwen3-8B, LLaMA3-8B, and GPT-4o-mini, global online adaptation yields inconsistent gains over static thresholding; MP-Strat partially recovers performance, while CST improves hit rate by up to 17 percentage points in strongly heterogeneous settings without gradient updates. These results identify structural heterogeneity, rather than optimizer weakness alone, as the primary bottleneck in the observed settings. More broadly, misaligned feedback structure cannot always be repaired by stronger optimization.

Jinlong Yang

Northwestern Polytechnical University

Large Language Model-Guided Optimization LLM Uncertainty Estimation Inference-Time Compute Allocation

Jun 12, 2026cs.CL

CoRA: Confidence-Rationale Alignment for Reliable Chain-of-Thought Reasoning

Chain-of-thought (CoT) reasoning can improve LLM performance, but high answer confidence may be misleading when the accompanying CoT rationale is plausible yet incomplete or poorly supported. We study confidence--rationale alignment: whether a model's confidence in its committed answer is justified by its generated rationale. We introduce a GRPO-based reinforcement learning framework that jointly rewards answer correctness, committed-answer probability, and rubric-based rationale support, where the rubric assesses grounding, coherence, task match, and connection to the selected answer without revealing the gold answer to the judge. Across MedQA, MathQA, and OpenBookQA using three open-weight LLMs, our method reduces the confidence--rationale alignment error by up to 26.51% compared with untuned checkpoints, SFT, and correctness-only GRPO, while maintaining competitive accuracy and often improving calibration. These results show that reliable CoT reasoning requires not only confident answers, but rationales that substantively support them.

Juming Xiong, Weixin Liu, Kevin Guo +9

Vanderbilt University · Vanderbilt University Medical Center · Intuit AI Research

CoT Reasoning RL for Language Model Reasoning LLM Reliability LLM Uncertainty Estimation

Jun 11, 2026cs.CL

Operadic consistency: a label-free signal for compositional reasoning failures in LLMs

Detecting LLM reasoning failures at inference time without ground-truth labels has motivated a wide range of confidence baselines, including self-consistency, semantic entropy, and P(True), built on within-question sampling and self-evaluation. Operad theory, the formalism for systems built by iterated substitution, suggests a complementary diagnostic: a model's direct answer to a compositional query should agree with the answer it produces by composing a stated decomposition of the same query. We instantiate this idea as operadic consistency (OC), a per-question signal. Across twelve instruction-tuned LLMs (4B to 671B parameters, open-weights and closed-source) on four multi-hop QA datasets, OC is strongly correlated with accuracy on every dataset (Pearson

r \in [0.86, 0.94]

, all

p \leq 0.0004

), and is the only signal we evaluate with

r \geq 0.85

uniformly across all four datasets. Chain-of-thought self-consistency (CoT-SC; Wang et al., 2023) matches OC on HotpotQA and DROP (

r = 0.93, 0.87

) but drops to

r \approx 0.45

on MuSiQue and StrategyQA. At the per-question level, OC contributes information beyond CoT-SC and semantic entropy on every dataset (cluster-robust

p \leq 10^{-16}

for the OC coefficient), and the conclusion is robust to additionally controlling for constructed decomposition-aware baselines (

p \leq 10^{-13}

). The same signal yields selective-prediction improvements (accuracy at fixed coverage) over a tuned CoT-SC baseline at the equal-cost

K = 3

budget (AUARC lifts of +0.086 to +0.096 and AUROC lifts of +0.092 to +0.164; 95% CIs exclude zero on every cell). On five frontier thinking models, where the decomposition is extracted from the model's own chain of thought, the same equal-cost comparison gives positive selective-prediction point-estimate lift on all 16 (dataset, budget, metric) cells tested, with 95% CIs excluding zero on 12 of the 16.

Nathaniel Bottman, Yinhong Liu, Kyle Richardson

Incubilate · University of Cambridge · Allen Institute for Artificial Intelligence

Compositional Reasoning Reasoning Consistency in Language Models LLM Reliability LLM Uncertainty Estimation

Jun 10, 2026cs.CL

LLMs Can Better Capture Human Judgments--With the Right Prompts

Are large language models (LLMs) bad at capturing human judgment? Two commonly stated limitations are that LLMs fail to capture full distributions of responses, and that their judgments are unstable across wording variations. We demonstrate simple prompting strategies that mitigate these limitations. Across two datasets--a U.S.-representative set of 144 moral scenarios and 38 moral beliefs from the International Social Survey Programme's Family and Changing Gender Roles module covering 32 countries--we show how simple elicitation techniques help improve AI-human alignment. First, prompting models to report standard deviations and response proportions recovers the full range of human responses better than common strategies. Second, ensuring scenarios are clear to human participants--as reflected in human confusion ratings--boosts model alignment, and LLMs can track human confusion ratings. At the same time, we find that LLMs' estimates of their own error are poorly calibrated, though they can predict human variability relatively well. These results suggest that asking better questions to LLMs can yield better answers.

Danica Dillion, Chen Cecilia Liu, Baihui Wang +5

Complexity Science Hub, Vienna · The Ohio State University · University of Cambridge +2

Human Preference Evaluation LLM Alignment Moral Reasoning in Language Models Human Preference Modeling LLM Prompting LLM Uncertainty Estimation

Jun 9, 2026cs.CL

SAGE: Answer-Conditioned Uncertainty Targets for Verbal Uncertainty Alignment

Large language models increasingly express uncertainty through natural-language statements, yet these expressions often fail to reflect the model's sampled behavior. We study verbal uncertainty alignment as a distributional calibration problem: the appropriate uncertainty target for a prompt should be estimated from repeated model outputs rather than from an isolated response. However, group rollouts alone are insufficient, since the resulting target must provide a useful training signal. Existing targets only partially satisfy this requirement. We propose SAGE, Semantic-Answer Guided Entropy, a group-level uncertainty target that constructs an answer-conditioned uncertainty geometry over sampled responses. SAGE preserves categorical, numeric, and symbolic answer distinctions while maintaining a smooth and scale-preserving calibration signal. We further apply this target through Group-Uncertainty Preference Optimization, or GUPO, an uncertainty-channel training framework that supervises verbal uncertainty expressions rather than the full response. Experiments across factual, mathematical, and multiple-choice reasoning tasks show improved uncertainty ranking, lower calibration error, and reduced overconfidence.

Kaiwen Shi, Zheyuan Zhang, Yanfang Ye

University of Notre Dame

Confidence Estimation in Language Models Preference Optimization LLM Uncertainty Estimation Uncertainty Calibration

Jun 9, 2026cs.CL

Early-Token Confidence Predicts Reasoning Quality in Multi-Agent LLM Debate

Evaluating reasoning quality in multi-agent LLM systems is challenging, especially for open-ended tasks without reference answers. We investigate whether intrinsic confidence signals, token-level log-probabilities from decoding, can predict reasoning quality as assessed by LLM-as-judge evaluation. Using a debate-based essay scoring framework, we compare confidence proxies against rubric-based judge scores across two ASAP essay sets. We find that early-token confidence, particularly within the first few generated tokens, is consistently the strongest predictor of reasoning quality, outperforming full-sequence statistics. Analysis of log-probability trajectories shows that the opening phase of generation is the most heterogeneous and therefore most informative. We also observe a systematic asymmetry between agent roles, with stronger alignment between confidence and quality for supportive reasoning than for adversarial critique. These results suggest that early decoding dynamics provide a lightweight and effective signal for estimating reasoning reliability in multi-agent LLM systems.

Ali Keramati, Justin Cheok, Jacob Horne +1

University of California, Irvine

LLM Agent Evaluation Multi-Agent Debate LLM Uncertainty Estimation

Jun 9, 2026cs.CL

The Confident Liar: Diagnosing Multi-Agent Debate with Log-Probabilities and LLM-as-Judge

Multi-agent debate systems are typically evaluated only on whether the final answer is correct, overlooking the quality of the intermediate reasoning that debate is designed to produce. This paper studies the relationship between three signals in multi-agent debate: token-level log-probability distributions over reasoning tokens, LLM-as-judge rubric scores assigned to those tokens, and final task accuracy. We examine whether internal confidence signals predict externally evaluated reasoning quality, and whether either signal aligns with task correctness, across three domains: rubric-based scoring, mathematical reasoning, and factual question answering. Our framework pairs a two-agent debate architecture -- a Constructor and an Auditor -- with an LLM-as-judge that scores each agent's reasoning along instruction following, justification quality, and evidence grounding, together with a critical-failure flag. Experiments in the rubric-scoring domain reveal a consistent four-phase confidence trajectory and a substantial role asymmetry: confidence aligns with judged reasoning quality roughly twice as strongly for the Constructor as for the Auditor, and confidence-based detection of critical reasoning failures is markedly more reliable for the Constructor (AUROC 0.804) than for the Auditor (0.634). These findings motivate the broader cross-domain investigation proposed in this paper.

Ali Keramati, Justin Cheok, Jacob Horne +1

University of California, Irvine

LLM Agent Evaluation Multi-Agent Debate LLM Uncertainty Estimation

Jun 8, 2026cs.SE

FASE: Fast Adaptive Semantic Entropy for Code Quality

Multi-agent code generation offers a promising paradigm for autonomous software development by simulating the human software engineering lifecycle. However, system reliability remains hindered by LLM hallucinations and error propagation across interacting agents. While semantic entropy provides a principled way to quantify uncertainty without ground-truth answers, current methods often rely on costly LLM-driven equivalence checks. In this work, we introduce Fast Adaptive Semantic Entropy (FASE), a novel metric that approximates functional correctness based on the minimum spanning tree of structural and semantic dissimilarity graphs. Evaluations on HumanEval and BigCodeBench demonstrate that FASE outperforms state-of-the-art semantic entropy by LLM entailment, achieving a 25% average improvement in Spearman correlation and a 19% increase in ROCAUC score against Pass@1 from ground-truth test cases when using the Qwen3-Embedding-8B model. Furthermore, by eliminating costly LLM-driven equivalence evaluation, FASE incurs negligible computational overhead, requiring only approximately 0.3% of the runtime cost of traditional semantic entropy approaches. These results position FASE as a practical, cost-effective solution for optimizing uncertainty quantification in real-world multi-agent workflows.

Shizhe Lin, Ladan Tahvildari

University of Waterloo, Canada

Semantic Entropy LLM Uncertainty Estimation Code Generation Evaluation

Jun 8, 2026cs.CL

Code Is More Than Text: Uncertainty Estimation for Code Generation

Large language models (LLMs) are increasingly deployed as code generators, where silently wrong programs pose real safety and reliability risks. Reliable uncertainty estimation (UE) is essential for selective prediction, human-in-the-loop review, and downstream agentic decisions. Yet most existing code UE methods are inherited from natural language (NL) generation and ignore properties that make code distinct. We argue that code differs from NL in three ways: a single wrong token can break an entire program (token fragility); algorithmic intent and concrete implementation can disagree independently (intent-code gap); and programs can be executed (executability). We instantiate these properties as three orthogonal uncertainty axes: lexical (Top-K token entropy), algorithmic (pseudo-code consistency), and functional (behavioral consistency). Across five code LLMs, our three-axis ensemble improves average AUROC from 0.696 for the strongest NL-derived baseline to 0.776 (+8.1 points). Notably, on Qwen3-14B, our single-pass Top-K token entropy matches the strongest multi-pass baseline while being over 3x cheaper; across models, it remains a competitive low-cost signal. These results suggest that code UE deserves code-specific design rather than direct NL ports.

Yuling Shi, Caiqi Zhang, Yuexian Li +4

Shanghai Jiao Tong University · University of Cambridge

Confidence Estimation in Language Models LLM Reliability LLM Uncertainty Estimation Code Language Models LLM Code Generation

Jun 7, 2026cs.AI

Inference-Time Conformal Reasoning with Valid Factuality Control for Large Language Models

Large language models (LLMs) increasingly perform multi-step reasoning, where intermediate claims form implicit directed acyclic graphs whose node correctness is structurally conditioned on their ancestors. This makes factuality uncertainty structural, rather than a trivial accumulation of node-wise errors, and necessitates inference-time uncertainty quantification over the reasoning structure. While conformal prediction (CP) offers flexible user-specified factuality control, existing work remains post-hoc and cannot intervene during generation. To fill the gap between CP's flexibility and its post-hoc limitation, we propose an \emph{Inference-Time Conformal Reasoning (ITCR)} framework that integrates CP directly into reasoning graph generation. ITCR learns a structure-level factuality uncertainty function that aggregates claim-level factuality signals over reasoning graphs without complex modeling assumptions. We then design the non-conformity score based on graph-level factuality uncertainty and calibrate the conformal threshold to decide when to stop generation. We theoretically show such generation is nested, yielding valid coverage guarantees for factuality control. Experiments over multiple datasets and coverage objectives demonstrate empirically valid coverage. In downstream reasoning tasks, inference-time calibrated graphs yield more accurate generation than post-hoc pruned graphs.

Ting Wang, Yuanjie Shi, Yan Yan +1

University of Illinois Urbana-Champaign · School of EECS, Washington State University.

LLM Inference LLM Reasoning with Graphs Conformal Prediction LLM Uncertainty Estimation LLM Reasoning

Jun 7, 2026cs.CL

Calibration of Structured Ignorance Certificates for Diagnosing Unknown Unknowns in Reasoning Models

Large language models frequently fail in a characteristic way: rather than acknowledging ignorance, they produce fluent but incorrect answers to questions that lie beyond their knowledge boundaries. We introduce \textbf{Structured Ignorance Certificates} (SICs), a JSON-formatted output schema that demands a model explicitly name the missing domain intersection, enumerate required concepts, and propose a productive retrieval query rather than hallucinating an answer. To train models to produce high-quality SICs we construct a 7,347-sample \emph{Unknown-Unknown} (UU) dataset by prompting Qwen3-14B to stitch together questions from seven domains (physics, biology, engineering, CS, economics, medical, legal) into novel cross-domain queries that no single-domain expert could answer. We fine-tune a 14B-parameter model with Group Relative Policy Optimization (GRPO) using a composite reward that combines retrieval utility, concept specificity, and output-format validity. A paraphrase-divergence probe trained on model responses confirms that SIC-tuned outputs systematically exhibit higher unknown-unknown probability scores. Evaluation on 735 held-out UU questions achieves a 99.46% JSON validity rate, a mean Certificate Specificity Score of 0.967, and a 3.6% ROUGE-L improvement over the base model on retrieval-grounded generation -- demonstrating that explicit epistemic structuring is a learnable and measurable capability.

Subramanyam Sahoo

Independent Researcher.

Hallucination in Language Models Language Model Calibration LLM Reliability LLM Uncertainty Estimation Metacognition in Language Models

Jun 5, 2026cs.CL

The ACUTE Protocol: Operationalizing Language Model Activations for Better Calibration, Utility, and Trust

As language models improve and become increasingly deployed to solve a variety of tasks, trustworthiness becomes essential. Calibration is a good proxy for trust: well-calibrated confidence estimates help inform the risk versus reward tradeoff when trusting a specific model output. Unfortunately, even as models improve, they remain poorly calibrated, often biasing towards overconfidence. Additionally, calibration can be gamed: a policy that always predicts the base rate is perfectly calibrated, but completely uninformative. To resolve this, we develop a new metric, expected utility renormalized by the oracle (EURO), that balances calibration and informativeness. We also propose a general-purpose activation-based confidence, utility, and trust estimation protocol (ACUTE) to appropriately adjudicate uncertainty. The ACUTE protocol provides flexible, sample-efficient, and compute-efficient confidence estimators for 3 tasks including multiple choice question answering, tool-calling, and scientific document summarization across 6 models from 4 model families. ACUTE outperforms strong baselines on EURO, while maintaining low calibration error. Taken together, our work shows that equipping LLMs with the ACUTE protocol can improve calibration, utility, and trustworthiness in numerous settings.

Nishant Subramani, Palash Goyal, Yiwen Song +4

Carnegie Mellon University · Google · Scale AI

Confidence Estimation in Language Models Language Model Calibration LLM Reliability LLM Uncertainty Estimation Metacognition in Language Models

Jun 5, 2026cs.AI

Exploring Agentic Tool-Calling Decisions via Uncertainty-Aligned Reinforcement Learning

Large language model (LLM)-based agents often make suboptimal tool-use decisions, including unsupported tool invocation and hallucinated direct responses, which may accumulate errors throughout multi-step interactions. Existing approaches mainly improve these behaviors through inference-time correction or coarse-grained reward signals based on decision outcomes and structured checklists, leaving the uncertainty characteristics of agent decisions underexplored. We observe that decision-oriented reinforcement learning tends to weaken the uncertainty separation between correct and incorrect actions, resulting in overconfident mistakes and weaker exploration signals. Therefore, we propose TRUST, which incorporates uncertainty quantification into reward design as a repulsive force for maintaining uncertainty separation, and labels lightweight key-turn annotations for unified post-training of multi-turn trajectories. Experimental results across diverse tool-use benchmarks show that TRUST consistently enhances both decision quality and agent performance while maintaining more reliable uncertainty estimates during optimization.

Yijin Zhou, Linqian Zeng, Xiaoya Lu +4

Shanghai Jiao Tong University, China · Shanghai Artificial Intelligence Laboratory, China · Shanghai Innovation Institute, China

Reinforcement Learning LLM Uncertainty Estimation LLM Agent Reliability RL for Tool Use

Jun 4, 2026cs.CL

How Language Models Fail: Token-Level Signatures of Committed and Persistent Reasoning Failures

Failures in language model reasoning emerge through distinct processes that leave identifiable signatures in the reasoning trace. We characterize these failures using token-level uncertainty signals, finding they arise through two empirically distinguishable processes. The first is committed failure, in which a model locks onto an incorrect reasoning path early in its trace. A central diagnostic signature is the commitment point, beyond which considering additional tokens hurt rather than help failure detection. In the second, persistent uncertainty, uncertainty instead accumulates throughout, and the full trace is needed to best distinguish failing from successful completions. These signatures reproduce across 23 model-dataset configurations, with the framework's falsifiable predictions holding in 20 of 23 cases, well above chance across both failure modes. Finally, we demonstrate our failure mode framework has direct implications for self-consistency, identifying when uncertainty signals complement it and when it can be selectively skipped. These results offer a foundation for understanding when LLM reasoning failures become detectable and for adapting detection strategies accordingly.

Tanvi Thoria, Kiana Jafari, Marc R. Schlichting +1

Department of Computer Science, Stanford University · Department of Aeronautics and Astronautics, Stanford University

Language Model Error Detection LLM Reliability LLM Uncertainty Estimation

Jun 4, 2026cs.LG

CaliDist: Calibrating Large Language Models via Behavioral Robustness to Distraction

Existing calibration methods for Large Language Models (LLMs) often overlook a critical dimension of trustworthiness: a model's {\em behavioral robustness} to irrelevant or misleading information. In this paper, we argue that a model's true confidence should reflect its stability under cognitive pressure. We introduce \textsc{CaliDist}, a novel post-hoc calibration approach that directly measures and penalizes a model's susceptibility to distraction. \textsc{CaliDist} quantifies how an LLM's predictions and uncertainty change when its input prompt is perturbed with semantic \textit{distractors}. This stability (or lack thereof) signal is then used to adaptively scale the model's initial confidence score. Our extensive experiments on seven Natural Language Understanding classification benchmarks using six distinct LLMs show that \textsc{CaliDist} consistently achieves lower Expected Calibration Error (ECE) and Brier Score compared with strong baselines. Remarkably, our method reduces the ECE from 23% to 7% on average--a relative improvement of 70%--demonstrating that behavioral stability is a powerful signal for calibration. We make our code and datasets available at github.com/m-anas-j/CaliDist.

Mohammad Anas Jawad, Cornelia Caragea

Computer Science, University of Illinois Chicago, USA.

Confidence Estimation in Language Models Language Model Calibration LLM Reliability LLM Uncertainty Estimation

Jun 2, 2026cs.LG

Calibrating Overconfidence Without Sacrificing Confidence: Probe-Conditioned Head Intervention for LLMs

Large language models often express high confidence in answers that are wrong. Standard calibration remedies typically act globally or at the score level, reducing unwarranted confidence but also risking erosion of warranted confidence on correct answers. We introduce Probe-Conditioned Head Intervention (PCHI), an inference-time method that uses a frozen probe to detect likely wrong-but-confident responses and conditionally rescales downstream attention-head outputs during confidence generation. On Qwen3-4B-Instruct solving OpenMathInstruct problems with a structured binary confidence field, readout-token PCHI converts 82.2% of originally wrong-yes confidence readouts to

\texttt{no}

, while a joint intervention across upstream confidence-template tokens reduces ECE from 21.9% to 9.2% and damages only 5.1% of originally correct-yes readouts. The readout-token effect also appears on Gemma3-4B, though upstream interventions are weaker and more mask-dependent. These results show that verbalized overconfidence can be selectively reduced through conditionally applied internal intervention, partially decoupling the suppression of unwarranted confidence from the loss of warranted confidence.

Ke Li, Chongzhe Zhang, Zifan Zeng +3

Huawei Heisenberg Research Center · EPFL · TU Berlin +1

Confidence Estimation in Language Models Language Model Calibration LLM Reliability LLM Uncertainty Estimation Causal Interventions in Language Models

Jun 2, 2026cs.LG

Integrating Local and Global Entropy for Uncertainty Quantification in LLMs

Large language models hallucinate confidently, making uncertainty quantification (UQ) essential for reliable deployment. Existing methods rely predominantly on token-level signals, leaving the geometric structure of intermediate hidden states underused. In this paper, we take the geometric complexity of hidden-state matrices as a measure of the global uncertainty of LLMs, while treating token-level uncertainty estimation as a local metric. We show that hidden-state geometric entropy (global uncertainty) and token-level entropy (local uncertainty) are statistically near-orthogonal, capturing distinct failure regimes for reliability prediction. In particular, global geometry recovers the confident-but-wrong failure mode that local signals systematically miss. Building on this, we propose Global-Local Uncertainty (GLU), an unsupervised, single-pass score that fuses the two signals via a multiplicative gate. Across three model families and six benchmarks, GLU matches or outperforms all unsupervised baselines while requiring only a single forward pass and remaining length-normalized and architecture-agnostic.

Johanne Medina, Tianyi Zhou, Keivin Isufaj +2

Qatar Computing Research Institute, HBKU Doha, Qatar · KTH Royal Institute of Technology Stockholm, Sweden

Uncertainty Quantification Confidence Estimation in Language Models LLM Reliability LLM Uncertainty Estimation

Jun 2, 2026cs.CL

Quantifying Faithful Confidence Expression in Large Reasoning Models

Reliable uncertainty communication is critical to the trustworthiness of LLMs, yet faithful calibration (FC)--the alignment between models' intrinsic and (linguistically) expressed confidence--is a persistent failure mode. This challenge is key for large reasoning models (LRMs), whose extended reasoning traces are often interpreted by users as evidence of deliberation, competence, and confidence. Despite the importance of FC and wide usage of LRMs, the extent to which LRMs can faithfully express their confidence remains poorly understood. Moreover, the prevailing paradigm to measure FC does not generalize well to the long chain-of-thought outputs generated by LRMs, which tend to lack clear step boundaries, involve inconsistent step structure, and encode complex conditional dependencies throughout the trace--complicating estimation of intrinsic confidence. To address this challenge, we introduce a novel framework to systematically quantify FC of LRMs. Our framework analyzes linguistic decisiveness relative to three sources of internal uncertainty, based on token probabilities, hidden states, and sampled response consistency. We also devise a prefix-conditioned sampling approach to control for conditional and structural variation across traces. Applying our framework to a diverse suite of leading models, datasets, and prompts, we find that faithful confidence expression is a significant challenge for LRMs. Reasoning behaviors do not automatically translate to improved FC, and prompt interventions for non-reasoning models do not improve faithfulness in the reasoning setting. Different confidence estimators further produce divergent assessments of the same traces, revealing fragility in prior evaluation methodologies. Taken together, our work establishes FC as a distinct reliability and alignment target for LRMs, particularly as such systems are increasingly deployed in high-stakes contexts.

Areeb Gani, Asal Meskin, Gabrielle Kaili-May Liu +1

1Yale University

LLM Evaluation Confidence Estimation in Language Models Language Model Calibration LLM Reliability LLM Uncertainty Estimation Trust in AI+1

Jun 2, 2026cs.CL

Clustered Self-Assessment: A Simple yet Effective Method for Uncertainty Quantification in Large Language Models

Large language models (LLMs) demonstrate remarkable performance across diverse tasks, but they often generate responses that appear plausible while being factually incorrect. This problem is compounded by the lack of explicit uncertainty estimates, which makes it difficult for users to judge the reliability of model outputs. Existing uncertainty quantification methods typically rely on indirect signals, such as entropy across sampled generations. These signals can be difficult to interpret and do not fully leverage the model's ability to assess its own uncertainty. We propose a simple yet effective self-assessment method for uncertainty quantification in LLMs. Our approach groups sampled generations into semantically distinct clusters, converts them into answer options in a structured multiple-choice question, and uses the probability assigned by the LLM to each option as a confidence estimate. Experiments across multiple models and datasets show that our method consistently outperforms baseline approaches. Notably, it achieves competitive performance with as few as two additional samples, demonstrating both its effectiveness and efficiency.

Qi Cao, Takeshi Kojima, Andrew Gambardella +3

The University of Tokyo, Japan

LLM Evaluation Uncertainty Quantification Confidence Estimation in Language Models Language Model Self-Assessment LLM Reliability LLM Uncertainty Estimation+1

Jun 2, 2026cs.CL

Large Language Models Are Overconfident in Their Own Responses

Prior work has shown that instruction-tuned large language models (LLMs) are less well calibrated than their base pre-trained counterparts. However, little is known about the frequently used chat template's effect on the calibration of conversational LLMs. In this work, we investigate the mechanisms driving this miscalibration by decoupling the effects of the post-training algorithm and the chat format. We find that, while instruction tuning fundamentally harms calibration, the chat template aggravates the issue through an "ownership bias" -- models are significantly more confident in their own answers than in identical answers provided by a user. Extensive experiments across six recent open-weight LLMs, three benchmarks, and three confidence elicitation methods show that models assign up to 26% higher confidence to their own responses. Leveraging this insight, we propose a simple inference-time strategy: framing the model's answer as user input during confidence elicitation. This approach significantly reduces overconfidence and improves calibration by up to 26% without the need for retraining, narrowing the gap between base and instruction-tuned models.

Mario Sanz-Guerrero, Manuel Mager, Katharina von der Wense

∇Johannes Gutenberg University Mainz, Germany · ♠University of Colorado Boulder, USA

Confidence Estimation in Language Models LLM Prompting LLM Fine-Tuning Language Model Calibration LLM Reliability LLM Uncertainty Estimation

Jun 2, 2026cs.AI

Uncertainty-Aware Clarification in LLM Agents with Information Gain

Large Language Model (LLM) agents often operate under underspecified user instructions, where latent uncertainty over user intent leads to erroneous tool actions. To address this challenge, we propose a goal-oriented clarification framework that aligns clarification behavior with ambiguity resolution. Central to our approach is the Information Gain Reward, a metric that quantifies the utility of clarification questions by measuring the Bayesian belief update towards the ground-truth goal induced by the clarification exchange. We train the clarifier (LLM) using this reward to optimize for high information gain, ensuring that clarifications effectively reduce uncertainty and improve task completion within the agent-tool-user environment. We validate our framework within a clarification-enhanced

τ

-Bench environment, conducting cross-agent evaluations across five heterogeneous backbones. Empirical results demonstrate that our method consistently improves the success rate by 3.7% over the no-clarification baseline, while adding only 0.3 total interaction steps on average.

Mengyi Deng, Zhiwei Li, Xin Li +4

Information Hub, HKUST(GZ) · Jilin University · et al.

Clarification Question Generation Tool-Using Agents LLM Uncertainty Estimation LLM Agent Training

Jun 1, 2026cs.CL

The Ghost Annotator: a Framework to Explore Human Label Variation in Content Moderation through Conformal Prediction

Current research primarily focuses on model performance, while comparatively less attention has been devoted to uncertainty estimation, particularly in settings where LLMs are increasingly used to generate annotated data. We introduce a framework combining conformal prediction with Collaborative Filtering-style annotators' representation to model LLM behavior in relation to human annotators and to analyze patterns of agreement and disagreement. Using Non-Conformity Scores, we introduce the Ghost Prediction metric and the Ghost Annotator representation to quantify cases in which model predictions diverge from all available human annotations. We compute cosine similarity measures to explore differences in model behavior across sociodemographic axes. We evaluated four LLMs of different size and families across four content moderation datasets. Our finding shows that while we find that all models uncertainty increases with annotator disagreement, larger models tend to be more confident in the classification of texts that are not aligned with any human annotation. Finally, the Ghost Annotator framework reveals a consistent and robust pattern of demographic misalignment, suggesting a structural bias likely rooted in pretraining corpora.

Mirko Lai, Alessandra Urbinati, Simona Frenda +2

Heriot-Watt University, Edinburgh, Scotland · aequa-tech, Torino, Italy · Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, MA, USA +2

Annotator Disagreement Conformal Prediction Content Moderation LLM Uncertainty Estimation Demographic Bias in Language Models

Jun 1, 2026cs.CL

DECK: A Consistency x Confidence Taxonomy of LLM Hallucinations

Existing hallucination taxonomies classify LLM errors by what is wrong with the output -- memorised misconceptions, reasoning failures, fluent fabrications -- but cannot answer a different question: which uncertainty scorer would have caught this error? We propose a complementary taxonomy that classifies errors by their detectability signature, the signal a scorer family would read. The DECK taxonomy is a 2x2 partition along inter-sample consistency and token-level confidence into four regimes (Drift, Entrenched, Confabulation, Knotted) that yields a falsifiable blind-spot map: black-box consistency scorers have signal in D and C, white-box token-probability scorers in K and C, and only an LLM-as-a-Judge with independent pretraining can detect E. Across three models and four short-form QA datasets we test this map two ways: judge-involving scorer disagreements concentrate in each family's predicted blind-spot cells, and external labels (SelfAware unanswerable, HaluEval adversarial, PopQA entity popularity) land in the predicted cells, robustly to cross-fitted thresholds. We further identify a universal blind spot of output-level UQ: on knowledge-gap inputs where the generator emits confident, repeatable fabrications, every output-level family collapses by construction. A linear probe on Llama-3-8B's final-layer hidden states also falls to chance, with or without quantisation, though an intermediate layer retains weak signal.

Mohit Singh Chauhan

Language Model Error Detection LLM Hallucination Detection LLM Uncertainty Estimation

Jun 1, 2026cs.CL

On the Salience of Low-Probability Tokens for AI-Generated Text Detection: A Multiscale Uncertainty Perspective

AI-generated text increasingly blends with human writing, raising practical risks such as misinformation, academic misuse, and corpora contamination. While statistical detectors are appealing for efficiency and generalization, they suffer from two key limitations. (i) Boilerplate dominance, boilerplate tokens shared across human and LLM writing can overwhelm discriminative signals. (ii) Brittle point estimates, relying on a single probability score yields unstable decisions under adversarial manipulations. To address these issues, we propose Uncertainty, a multiscale uncertainty estimator that focuses on informative low-probability tokens, which more clearly expose distributional discrepancies. Locally, it alleviates boilerplate dominance by averaging the log-probabilities of low-probability tokens; globally, it reduces brittleness by capturing the distributional shape of this low-probability region via Rényi entropy. We further extend the detector to Uncertainty++ via conditional independent sampling, yielding a more stable uncertainty estimation. Experiments across seven datasets and sixteen LLMs demonstrate high effectiveness, generalization, and robustness. Our code is available at https://github.com/guoyikai2000/Uncertainty-AIGT.

Yikai Guo, Bin Wang, Xilai Fan +2

Beijing Institute of Computer Technology and Application, Beijing, China · Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China · Southeast University, Nanjing, China +1

AI-Generated Text Detection LLM Uncertainty Estimation Robustness of Machine-Generated Text Detection

Jun 1, 2026cs.CL

The Role of Ambiguity in Error Prediction via Uncertainty Quantification

The task of Error Prediction, namely predicting whether a model output is correct, is commonly tackled with Uncertainty Quantification (UQ). However, while uncertainty metrics capture when models lack knowledge or capacity to make a prediction, they also reflect aleatoric uncertainty, which is inherent in the model input and context. This paper presents a method for improving error prediction for Large Language Models (LLMs), by disentangling input ambiguity from UQ signal. We conduct experiments on the task of Question Answering (QA) with six UQ metrics and show that UQ metrics are more predictive of errors on unambiguous instances than on questions with multiple plausible answers. We use Gated Experts and Selective Prediction to incorporate gold and predicted ambiguity labels into the error prediction pipeline. We find that ambiguity information improves error prediction scores across model families, training and evaluation paradigms, datasets (including allegedly unambiguous ones), and sources of aleatoric uncertainty, yielding improvements of over 10 points of PRR for individual UQ metrics on standard datasets.

Ieva Raminta Staliūnaitė, James Bishop, Andreas Vlachos

University of Cambridge · The Alan Turing Institute

Uncertainty Quantification LLM Uncertainty Estimation

Jun 1, 2026cs.AI

Does Compression Preserve Uncertainty? A Unified Benchmark for Quantized and Sparse LLMs via Conformal Prediction

Model compression techniques such as quantization and pruning are widely used to reduce the deployment cost of large language models (LLMs), with existing evaluations focusing almost exclusively on accuracy preservation. However, in safety-critical applications, a model's ability to reliably quantify its own uncertainty is equally important. We ask: does compression preserve this ability? To answer this question, we benchmark 12 LLMs under various compression configurations across five NLP tasks, using conformal prediction to provide a rigorous, distribution-free measure of uncertainty. Our experiments reveal that: (I) compression frequently decouples accuracy from uncertainty; (II) larger models absorb compression-induced uncertainty far more effectively than smaller ones; and (III) uncertainty inflation is often threshold-like rather than gradual. These results suggest that accuracy-only evaluation is insufficient for assessing the deployment readiness of compressed LLMs, and that uncertainty-aware benchmarking should be a standard component of model compression pipelines.

Yujia Tong, Yuxi Wang, Yunyang Wan +3

Wuhan University of Technology · Nanyang Technological University

LLM Quantization LLM Evaluation LLM Pruning LLM Compression Confidence Estimation in Language Models LLM Reliability+1

May 31, 2026cs.AI

TriLens: Per-Layer Logit-Lens Entropy for White-Box Hallucination Detection

When a language model hallucinates, the final answer is wrong, but the mistake is not necessarily invisible inside the model. Different internal pathways may remain uncertain, disagree in how quickly they sharpen, or commit to competing continuations before the output is produced. We introduce TriLens, a white-box detector that turns this intuition into a compact representation: at every layer, it reads the multi-head self-attention output, the feed-forward output, and the residual stream through the model's own logit lens, then records only the entropy of each readout. The resulting 3L-dimensional trajectory describes how certainty forms across depth and across modules, without storing high-dimensional hidden states or sampling multiple generations. This simple signal yields a strong detector across instruction-tuned LLMs and QA benchmarks, and our analyses show that the three module-wise entropy trajectories provide complementary evidence. TriLens suggests that hallucination detection can benefit from tracking how internal computation settles, not only what the final layer predicts.

Bohan Yang, Yijun Gong, Zhi Zhang +3

Binjiang Institute of Zhejiang University · Beijing Normal-Hong Kong Baptist University · Great Bay University +1

Language Model Error Detection LLM Reliability LLM Hallucination Detection LLM Uncertainty Estimation

May 31, 2026cs.CL

HypothesisMed: Inference-Time Answer Fusion and Structured Hypothesis-Space Reporting for Biomedical Question Answering

Biomedical question answering with large language models is commonly evaluated using answer accuracy, but answer accuracy alone does not indicate whether a model can produce parseable outputs, follow structured reliability instructions, recognize weak answer spaces, or avoid confident incorrect commitments. This paper presents HypothesisMed, an inference-time reliability pipeline for biomedical multiple-choice question answering. It combines direct, chain-of-thought, HypothesisMed-v3 prompting, and answer fusion. The final answer is selected by fusion, while HypothesisMed-v3 supplies SPACE labels and confidence information. SPACE labels mark the answer space as VALID, INCOMPLETE, or CONTRADICTED. We evaluate Qwen2.5-7B, Phi-4-mini, DeepSeek-R1-32B, and BioMistral-7B on MedQA, MedMCQA, and PubMedQA using 1,000 examples per dataset. The pipeline improves weighted accuracy over each model's best direct or chain-of-thought baseline while increasing parse and SPACE coverage. We also scale evaluation to Qwen2.5-7B and Phi-4-mini using 10,183 examples per model. Fusion improves Phi-4-mini accuracy from 0.4296 to 0.5192, while Qwen2.5-7B chain-of-thought remains slightly higher in answer accuracy. However, Qwen2.5-7B fusion achieves complete parse and SPACE coverage with much lower false commitment. A 12,000-example SPACE stress test shows answer-space diagnosis remains difficult, with SPACE accuracy of 0.3074 for Qwen2.5-7B and 0.4168 for Phi-4-mini. These results show that answer accuracy, parseability, structured reliability reporting, calibration behavior, and false-commitment behavior are separable capabilities. The main contribution is not a universal state-of-the-art claim, but a reproducible inference-time framework for evaluating biomedical question answering models as auditable workflow components under structured reliability constraints.

Md Motaleb Hossen Manik, Ge Wang

Department of Computer Science Rensselaer Polytechnic Institute Troy, NY, USA · Department of Biomedical Engineering Rensselaer Polytechnic Institute Troy, NY, USA

Biomedical QA LLM Uncertainty Estimation Medical LLMs

May 30, 2026cs.LG

Sequential statistical inference for Large Language Models: Representation, validity, and monitoring

This discussion argues that sequential statistical inference can naturally contribute to LLM trustworthiness. In deployment, LLM systems are queried repeatedly, conditioned on evolving contexts, and incorporate user or tool feedback, and may exhibit behavioral shifts after model updates or distribution changes. The discussion is organized around three tasks: representation, modeling LLM interactions as dependent stochastic processes rather than isolated prompt--response pairs; validity, developing uncertainty guarantees that remain meaningful under dependence, repeated use, and adaptation; and monitoring, using sequential alarms and change-point detection to identify shifts in calibration, hallucination rates, refusal behavior, fairness, or other task-relevant properties. This perspective complements recent surveys by viewing trustworthy LLM deployment as a problem of statistical process control.

Yao Xie

H. Milton Stewart School of Industrial and Systems Engineering Georgia Institute of Technology

Language Model Calibration LLM Reliability LLM Uncertainty Estimation