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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May 8, 2026cs.CL

Beyond Confidence: Rethinking Self-Assessments for Performance Prediction in LLMs

Large Language Models (LLMs) are increasingly used in settings where reliable self-assessment is critical. Assessing model reliability has evolved from using probabilistic correctness estimates to, more recently, eliciting verbalized confidence. Confidence, however, has been shown to be an inconsistent and overoptimistic predictor of model correctness. Drawing on cognitive appraisal theory, a framework from human psychology that decomposes self-evaluation into multiple components, we propose a multidimensional perspective on model self-assessment. We elicit six appraisal-based dimensions of self-assessment, alongside confidence, and evaluate their utility for predicting model failure across 12 LLMs and 38 tasks spanning eight domains. We find that competence-related appraisal dimensions, particularly effort and ability, consistently match or outperform confidence across most settings. Effort additionally yields less overoptimistic estimates that remain stable across model sizes. In contrast, affective dimensions provide marginally predictive signals. Furthermore, the most informative dimension varies systematically with task characteristics: effort is most predictive for reasoning-intensive tasks, while ability and confidence dominate on retrieval-oriented tasks. Broadly, our findings indicate that structured multidimensional self-assessment is a promising approach to improving the reliability and safety of language model deployment across diverse real-world settings.

Sree Bhattacharyya, Samarth Khanna, Leona Chen +3

Department of Informatics and Intelligent Systems, College of Information Sciences, The Pennsylvania State University. · Department of Computer Science and Engineering, College of Engineering, The Pennsylvania State University.

LLM Evaluation Confidence Estimation in Language Models Language Model Self-Assessment Language Model Calibration LLM Reliability LLM Uncertainty Estimation

May 8, 2026cs.LG

Tracing Uncertainty in Language Model "Reasoning"

Language model (LM) "reasoning", commonly described as Chain-of-Thought or test-time scaling, often improves benchmark performance, but the dynamics underlying this process remain poorly understood. We study these dynamics through the lens of uncertainty quantification by treating the "reasoning" traces, the intermediate token sequences generated by LMs, as evolving model states. We summarize each trace by an uncertainty trace profile: a small set of features describing the shape of the uncertainty signal over its trace, such as its slope and linearity. We find that across five LMs evaluated on GSM8K and ProntoQA, these profiles predict whether a trace yields a correct final answer with AUROC up to 0.807, improving markedly on recent related work. We reach AUROC 0.801 using only the first few hundred tokens of full traces, suggesting that errors can be detected early in the generation. A detailed comparison of correct and incorrect traces further reveals qualitatively distinct uncertainty profiles, with correct traces showing a steeper and less linear decline in uncertainty. Together, the results suggest that our method, grounded in decision-making under uncertainty, provides a principled lens for studying the generative process underlying LM "reasoning".

Nils Grünefeld, Bertram Højer, Philipp Mondorf +5

Data Science Section, IT University of Copenhagen · Pioneer Centre for Artificial Intelligence · MaiNLP, Center for Information and Language Processing, LMU Munich +2

LLM Evaluation CoT Reasoning LLM Uncertainty Estimation Reasoning Trace Analysis

May 8, 2026cs.LG

POETS: Uncertainty-Aware LLM Optimization via Compute-Efficient Policy Ensembles

Balancing exploration and exploitation is a core challenge in sequential decision-making and black-box optimization. We introduce POETS (

\textbf{Po}

licy

\textbf{E}

nsembles for

\textbf{T}

hompson

\textbf{S}

ampling), a novel framework that bridges uncertainty quantification and policy optimization. Our approach is grounded in the insight that policies trained with Kullback-Leibler (KL) regularization implicitly encode an underlying reward function. Building on this, POETS bypasses the complex, nested process of training an uncertainty-aware reward model and separately fitting a policy to this model. Instead, we directly train a policy ensemble to capture epistemic uncertainty by matching implicitly encoded reward functions to online, bootstrapped data. To overcome the prohibitive compute and memory constraints of ensembling Large Language Models (LLMs), POETS utilizes an efficient architecture: the ensemble shares a pre-trained backbone while maintaining diversity through independent Low-Rank Adaptation (LoRA) branches. Theoretically, we prove that POETS implicitly conducts KL-regularized Thompson sampling and thus inherits strong cumulative regret bounds of

{\mathcal O}(\sqrt{T γ_T})

. Empirically, we demonstrate that POETS achieves state-of-the-art sample efficiency across diverse scientific discovery domains, including protein search and quantum circuit design. Furthermore, it improves the optimization trajectories of reinforcement learning, proving particularly robust in off-policy settings with experience replay or in small dataset regimes.

Nicolas Menet, Andreas Krause, Abbas Rahimi

IBM Research – Zurich · Department of Computer Science, ETH Zürich

Thompson Sampling Black-Box Optimization Large Language Model-Guided Optimization LLM Uncertainty Estimation Language Model Ensembles Large Language Model-Guided Scientific Discovery

May 8, 2026cs.AI

Confidence-Aware Alignment Makes Reasoning LLMs More Reliable

Large reasoning models often reach correct answers through flawed intermediate steps, creating a gap between final accuracy and reasoning reliability. Existing alignment strategies address this with external verifiers or massive sampling, limiting scalability. In this work, we introduce CASPO (Confidence-Aware Step-wise Preference Optimization), a framework that aligns token-level confidence with step-wise logical correctness through iterative Direct Preference Optimization, without training a separate reward model. During inference, we propose Confidence-aware Thought (CaT), which leverages this calibrated confidence to dynamically prune uncertain reasoning branches with negligible O(V) latency. Experiments across ten benchmarks and multiple model families show that CASPO consistently improves reasoning reliability and inference efficiency. CASPO scales to Qwen3-8B-Base and surpasses tree-search baselines on AIME'24 and AIME'25 without using reward-model data. We also release a step-wise dataset with confidence annotations to support fine-grained analysis of reasoning reliability. Code is available at https://github.com/Thecommonirin/CASPO.

Kejia Chen, Jiawen Zhang, Yihong Wu +5

Zhejiang University · Université de Montréal · Sun Yat-sen University +1

LLM Alignment Direct Preference Optimization Efficient Language Model Reasoning Language Model Calibration LLM Reliability LLM Uncertainty Estimation+2

May 7, 2026cs.LG

Bias and Uncertainty in LLM-as-a-Judge Estimation

LLM-as-a-Judge evaluation has become a standard tool for assessing base model performance. However, characterizing performance via the naive estimator, i.e., raw judge outputs, is systematically biased. Recent work has proposed estimators to correct this bias, but their reliability depends critically on judge quality and, for model comparisons, on calibration stability. Sharing calibration across compared models is practically attractive but can introduce severe bias, including cases where the comparison estimate points in the wrong direction with high apparent confidence. We study these failure modes through analytical results, simulations over judge quality (

J

) and cross-model calibration instability (

ΔJ

), and a real-data MMLU-Pro case study with sign reversal. We propose

J

and

ΔJ

as diagnostics for when corrected estimates, especially shared-calibration comparisons, are likely unreliable, and provide reporting guidance for LaaJ evaluation.

James Fiedler

Indeed Inc.

LLM Evaluation LLM-as-a-Judge Language Model Calibration LLM Uncertainty Estimation Bias in LLM-as-a-Judge

May 7, 2026cs.CL

Can LLMs Take Retrieved Information with a Grain of Salt?

Large language models have demonstrated impressive retrieval-augmented capabilities. However, a crucial area remains underexplored: their ability to appropriately adapt responses to the certainty of the retrieved information. It is a limitation with real consequences in high-stakes domains like medicine and finance. We evaluate eight LLMs on their context-certainty obedience, measuring how well they adjust responses to match expressed context certainty. Our analysis reveals systematic limitations: LLMs struggle to recall prior knowledge after observing an uncertain context, misinterpret expressed certainties, and overtrust complex contexts. To address these, we propose an interaction strategy combining prior reminders, certainty recalibration, and context simplification. This approach reduces obedience errors by 25% on average, without modifying model weights, demonstrating the efficacy of interaction design in enhancing LLM reliability. Our contributions include a principled evaluation metric, empirical insights into LLMs' uncertainty handling, and a portable strategy to improve context-certainty obedience across diverse LLMs.

Behzad Shayegh, Mohamed Osama Ahmed, Fred Tung +1

RBC Borealis

Retrieval-Augmented Generation LLM Evaluation LLM Uncertainty Estimation Language Model Robustness LLM Context Management

May 7, 2026cs.LG

LLMs are not (consistently) Bayesian: Quantifying internal (in)consistencies of LLMs' probabilistic beliefs

Modern AI systems are being deployed in complex domains such as medicine, science, and law, where it is important that they not only produce correct answers, but also represent and update uncertain beliefs about the world as new evidence arrives. We introduce the novel technique of studying LLMs as information processing rules and utilize the information processing gap to study the internal (in)consistencies of how LLMs update their probabilistic beliefs from evidence. Our extensive experiments evaluate multiple approaches in which LLMs can incorporate evidence into their beliefs. Some of these approaches produce (nearly) Bayesian updates; others seem to use a learned heuristic. Surprisingly, the non-Bayesian heuristic updates often outperform exact Bayesian computation in terms of downstream task performance -- indicating the LLMs' probabilistic models of the world are misspecified. Lastly, we show how our measure can provide diagnostics to identify issues with LLM-powered inferential systems.

Chacha Chen, Matthew Jörke, Adam Goliński +4

1Apple · 2Stanford University · †Work done while an intern at Apple. +1

Belief Revision LLM Auditing Bayesian Inference LLM Uncertainty Estimation Belief Updating in LLMs

May 7, 2026cs.AI

Rethinking Vacuity for OOD Detection in Evidential Deep Learning

Vacuity, or Uncertainty Mass (UM), is commonly used as a metric to evaluate Out-of-Distribution (OOD) detection in Evidential Deep Learning (EDL). It generally involves dividing the number of classes (

K

) by the total strength of belief (

S

) of the model's predictions, where

S

is derived from summing the Dirichlet parameters. As such, UM is sensitive to the cardinality of

K

. In particular, it is unlikely in practice that there is a linear relationship between

K

and

S

as

K

and

S

increase due to the nature of EDL (suppressing incorrectly assigned evidence). As a result, when comparing In Distribution (ID) and OOD results, it is important that

K_{\mathrm{ID}}

and

K_{\mathrm{OOD}}

are equal; something that is not always ensured in practice. We provide an empirical demonstration of how results for AUROC and AUPR can substantially differ when class cardinality between ID and OOD differs by 1, with AUROC differing by as much as 0.318 and AUPR by 0.613 for standard EDL, and AUROC by 0.360 and AUPR by 0.683 for IB-EDL. More concretely, our findings isolate an evaluation artefact: when K differs between ID and OOD, AUROC/AUPR can be artificially inflated without any change in model predictions. We further discuss the evaluation of EDL over causal language models using Multiple-Choice Question-Answer (MCQA) datasets and argue for clearer definitions of ID and OOD in this context. Our primary contribution is an empirical and theoretical demonstration that vacuity-based OOD detection in EDL-fine-tuned LLMs is highly sensitive to uncontrolled differences in evaluated class cardinality.

Claire McNamara

∗Accenture Labs · †Trinity College Dublin.

LLM Evaluation Evidential Deep Learning LLM Uncertainty Estimation OOD Detection

May 7, 2026cs.AI

Measuring Black-Box Confidence via Reasoning Trajectories: Geometry, Coverage, and Verbalization

Reliable confidence estimation enables safe deployment of chain-of-thought (CoT) reasoning through text-only APIs. Yet the dominant black-box baseline, self-consistency over K samples, is linearly expensive and ignores the geometry of the trace. We propose a black-box trajectory-confidence score: we embed a CoT as a sliding-window trajectory and measure its convergence to external answer anchors with a one-parameter softmax. The method needs no logits, hidden states, or supervised calibrators. Across six (benchmark, reasoner) settings on MedQA-USMLE, GPQA Diamond, and MMLU-Pro with Gemini 3.1 Pro and Claude Sonnet 4.6, fusing this score with coverage and verbalized-confidence channels at K=4 yields Pareto improvements over self-consistency at K=8 in 6/6 settings (median AUC 0.78 vs 0.71, deltaAUC=+0.075). A fixed-pick control (+0.060) and E5 cross-embedder replication rule out answer switching and single-vendor artifacts. Geometry peaks in the penultimate window across benchmarks and reasoners, and inverts at the terminal window on GPQA Diamond. Three unscaffolded regimes separate black-box confidence into a judge-mediated Coverage prior (C), within-trace Geometry (G), and a conditional Verbalization channel (V). Across 18 benchmark x reasoner x proposer settings, C and G provide independent signal in 18/18 and 16/18, while V contributes residual signal in 6/18. Swapping the judge from GPT-5-mini to Claude Sonnet 4.6 leaves G-only AUC unchanged (|delta|<=0.013) and shifts C-only AUC by at most +/-0.02 (kappa=0.82). Fusion beats the best single channel in 17/18 settings (median AUC 0.78, max 0.92).

Marc Boubnovski Martell, Josefa Lia Stoisser, Kaspar Märtens +4

1Novo Nordisk · University of Oxford

Confidence Estimation in Language Models CoT Reasoning LLM Uncertainty Estimation LLM Reasoning Reasoning Trace Analysis

May 7, 2026cs.LG

Towards Generation-Efficient Uncertainty Estimation in Large Language Models

Uncertainty estimation is important for deploying LLMs in high-stakes applications such as healthcare and finance, where hallucinations can appear fluent and plausible while being factually incorrect, making it difficult for users to judge whether an output should be trusted. Existing methods require one or more full autoregressive generations to estimate uncertainty, which introduces substantial inference cost and often delays uncertainty assessment. In this paper, we investigate whether effective uncertainty estimation can be achieved with partial generation or even input-only information. Specifically, we first develop a unified framework that formulates uncertainty estimation as an early estimation problem over the autoregressive generation process of LLMs. This framework organises existing and proposed estimators by the information they observe, ranging from multi-generation to input-only prediction, and clarifies the performance-cost trade-off underlying different uncertainty estimation methods. Building on this view, we study two largely underexplored low-cost settings: estimating uncertainty with part of the generation, and predicting uncertainty from the input prompt. We propose Logit Magnitude, which uses top-M logit evidence to estimate uncertainty from an early-stopped generation prefix, and MetaUE, which distils generation-based uncertainty into a lightweight input-only estimator trained with uncertainty scores. Extensive experiments on general and domain-specific benchmarks show that Logit Magnitude achieves strong performance, and partial generations of LLMs are often sufficient for effective uncertainty estimation. MetaUE further provides a competitive input-only approximation in several settings. These findings suggest that effective uncertainty estimation requires less generation than commonly assumed, enabling unreliable responses to be identified earlier.

Mingcheng Zhu, Yu Liu, Tingting Zhu

University of Oxford

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

May 7, 2026cs.CL

Estimating the Black-box LLM Uncertainty with Distribution-Aligned Adversarial Distillation

Large language models (LLMs) have progressed rapidly in complex reasoning and question answering, yet LLM hallucination remains a central bottleneck that hinders practical deployment, especially for commercial black-box LLMs accessible only via APIs. Existing uncertainty quantification methods typically depend on computationally expensive multiple sampling or internal parameters, which prevents real-time estimation and fails to capture information implicit in the black-box reasoning process. To address this issue, we propose Distribution-Aligned Adversarial Distillation (DisAAD), which introduces a generation-discrimination architecture to guide a lightweight proxy model to learn the high-quality regions of the output distribution of the black-box LLM, thus effectively endowing it with the ability to know whether the black-box LLM knows or not. Subsequently, we use the proxy model to reproduce the specific responses of the black-box LLM and estimate the corresponding uncertainty based on evidence learning. Extensive experiments have verified the effectiveness and promise of our proposed method, indicating that a proxy model even one that only accounts for 1% of the target LLM's size can achieve reliable uncertainty quantification.

Huizi Cui, Huan Ma, Qilin Wang +2

School of Computer Science and Technology, Tianjin University, China · School of Future Technology, Tianjin University, China · Georgia Tech Shenzhen Institute, Tianjin University, China +1

Language Model Distillation LLM Uncertainty Estimation Knowledge Distillation Adversarial Knowledge Distillation

May 6, 2026cs.CL

The First Token Knows: Single-Decode Confidence for Hallucination Detection

Self-consistency detects hallucinations by generating multiple sampled answers to a question and measuring agreement, but this requires repeated decoding and can be sensitive to lexical variation. Semantic self-consistency improves this by clustering sampled answers by meaning using natural language inference, but it adds both sampling cost and external inference overhead. We show that first-token confidence, phi_first, computed from the normalized entropy of the top-K logits at the first content-bearing answer token of a single greedy decode, matches or modestly exceeds semantic self-consistency on closed-book short-answer factual question answering. Across three 7-8B instruction-tuned models and two benchmarks, phi_first achieves a mean AUROC of 0.820, compared with 0.793 for semantic agreement and 0.791 for standard surface-form self-consistency. A subsumption test shows that phi_first is moderately to strongly correlated with semantic agreement, and combining the two signals yields only a small AUROC improvement over phi_first alone. These results suggest that much of the uncertainty information captured by multi-sample agreement is already available in the model's initial token distribution. We argue that phi_first should be reported as a default low-cost baseline before invoking sampling-based uncertainty estimation.

Mina Gabriel

Department of Computer and Information Sciences Temple University Philadelphia, PA 19122, USA

Uncertainty Quantification Self-Consistency Decoding Hallucination in Language Models LLM Hallucination Detection LLM Uncertainty Estimation

May 6, 2026cs.CL

Detecting Hallucinations in Large Language Models via Internal Attention Divergence Signals

We propose a lightweight and single-pass uncertainty quantification method for detecting hallucinations in Large Language Models. The method uses attention matrices to estimate uncertainty without requiring repeated sampling or external models. Specifically, we measure the Kullback-Leibler divergence between each attention head's distribution and a uniform reference distribution, and use these features in a logistic regression probe. Across multiple datasets, task types, and model families, attention divergence is highly predictive of answer correctness and performs competitively with existing uncertainty estimation methods. We find that this signal is concentrated in middle layers and on factual tokens such as named entities and numbers, suggesting that attention dynamics provides an efficient and interpretable white-box signal of model uncertainty.

Gijs van Dijk

Utrecht University

Language Model Error Detection Confidence Estimation in Language Models LLM Interpretability Hallucination in Language Models LLM Reliability LLM Hallucination Detection+1

May 6, 2026cs.LG

NoisyCoconut: Counterfactual Consensus via Latent Space Reasoning

This paper presents NoisyCoconut, a novel inference-time method that enhances large language model (LLM) reliability by manipulating internal representations. Unlike fine-tuning methods that require extensive retraining, NoisyCoconut operates directly on model representations during inference and requires no retraining. Rather than training models to reason in latent space, we inject controlled noise into latent trajectories to generate diverse reasoning paths. Agreement among these paths provides a confidence signal, enabling models to abstain when uncertain. We demonstrate that this approach achieves effective coverage-accuracy tradeoffs across multiple reasoning benchmarks without requiring access to training data or modification of model parameters. This approach provides a practical pathway to improving the reliability of LLM outputs while maintaining compatibility with existing models. Our experiments show that unanimous agreement among noise-perturbed paths reduces error rates from 40-70% to below 15%, enabling models to exceed 95% accuracy on mathematical reasoning tasks through selective abstention.

Michael Jerge, David Evans

University of Virginia

Selective Prediction LLM Inference LLM Reliability LLM Uncertainty Estimation

May 6, 2026cs.CL

Elicitation Matters: How Prompts and Query Protocols Shape LLM Surrogates under Sparse Observations

Large language models are increasingly used as surrogate models for low-data optimization, but their optimizer-facing prediction and its uncertainty remain poorly understood. We study the surrogate belief elicited from an LLM under sparse observations, showing that it depends strongly on prompt text and query protocol. We introduce an uncertainty-alignment criterion that measures whether model uncertainty tracks residual ambiguity among sample-consistent functions. Across controlled inference tasks and Bayesian optimization studies, we find that structural prompts act as effective priors, POINTWISE and JOINT querying induce different beliefs, and sequential evidence leads to non-monotonic, order-sensitive confidence updates. These effects change downstream acquisition decisions and regret, showing that elicitation protocol is part of the LLM surrogate specification, not a formatting detail.

Ge Lei, Samuel J. Cooper

Dyson School of Design Engineering Imperial College London Exhibition Road, London SW7 2AZ

Surrogate Modeling Bayesian Optimization LLM Prompting Large Language Model-Guided Optimization LLM Uncertainty Estimation

May 6, 2026cs.CL

Gradients with Respect to Semantics Preserving Embeddings Tell the Uncertainty of Large Language Models

Uncertainty quantification (UQ) is an important technique for ensuring the trustworthiness of LLMs, given their tendency to hallucinate. Existing state-of-the-art UQ approaches for free-form generation rely heavily on sampling, which incurs high computational cost and variance. In this work, we propose the first gradient-based UQ method for free-form generation, SemGrad, which is sampling-free and computationally efficient. Unlike prior gradient-based methods developed for classification tasks that operates in parameter space, we propose to consider gradients in semantic space. Our method builds on the key intuition that a confident LLM should maintain stable output distributions under semantically equivalent input perturbations. We interpret the stability as the gradients in semantic space and introduce a Semantic Preservation Score (SPS) to identify embeddings that best capture semantics, with respect to which gradients are computed. We further propose HybridGrad, which combines the strengths of SemGrad and parameter gradients. Experiments demonstrate that both of our methods provide efficient and effective uncertainty estimates, achieving superior performance than state-of-the-art methods, particularly in settings with multiple valid responses.

Mingda Li, Rundong Lv, Xinyu Li +2

Research Center for Social Computing and Interactive Robotics, Harbin Institute of Technology, Harbin, China · Suzhou Research Institute, Harbin Institute of Technology, Harbin, China

Uncertainty Quantification LLM Uncertainty Estimation

May 5, 2026cs.LG

LLMs Uncertainty Quantification via Adaptive Conformal Semantic Entropy

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.

Hamed Karimi, Vaishali Meyappan, Reza Samavi

Toronto Metropolitan University, Toronto, Ontario, Canada · Vector Institute, Toronto, Ontario, Canada

Selective Prediction Semantic Entropy LLM Uncertainty Estimation Uncertainty Calibration

May 4, 2026cs.CL

Geometric Deviation as an Unsupervised Pre-Generation Reliability Signal: Probing LLM Representations for Answerability

A reliable language model should be able to signal, prior to generation, when a query falls outside its knowledge. We investigate whether representation geometry can provide such a pre-generation signal by measuring the deviation of hidden states from an answerable reference set, requiring no labeled failure data and no access to model outputs. Across three instruction-tuned models (Llama 3.1-8B, Qwen 2.5-7B, and Mistral-7B-Instruct) and three prompt forms (Math, Fact, Code), we find that geometry primarily encodes task form. Within mathematical prompts, unanswerable inputs consistently deviate from the answerable centroid, yielding strong separation (ROC-AUC 0.78-0.84). This single-pass pre-generation signal outperforms a simple refusal baseline and compares favorably to self-consistency. It also captures cases where models do not explicitly refuse. In contrast, no reliable geometric signal emerges for factual prompts, indicating that the effect is form-conditional rather than universal. Code prompts show large effect sizes with higher variance, suggesting partial generalization beyond mathematical form. A layer-wise analysis reveals that the signal arises in early layers and gradually attenuates toward the output. These results suggest that answerability-related geometry is established before the final stages of generation. Together, these findings indicate that geometric deviation can serve as a lightweight pre-generation signal that is reliable in structured domains with formal answerability constraints, with clear boundaries on where it generalizes.

Yucheng Du

University of Southern California

Representation Geometry LLM Reliability LLM Uncertainty Estimation Representation Geometry in Language Models Language Model Probing

May 4, 2026cs.AI

Zero-Shot Confidence Estimation for Small LLMs: When Supervised Baselines Aren't Worth Training

How reliably can a small language model estimate its own correctness? The answer determines whether local-to-cloud routing-escalating queries a cheap local model cannot handle-can work without supervised training data. As inference costs dominate large language model (LLM) deployment budgets, routing most queries to a cheap local model while reserving expensive cloud calls for hard cases is an increasingly common cost-control strategy. We compare zero-shot confidence signals against RouteLLM-style supervised baselines across three 7-8B model families and two datasets (1,000 and 500 queries per model, respectively). Average token log-probability, which requires no training data, matches or exceeds supervised baselines in-distribution (Area Under the Receiver Operating Characteristic curve (AUROC) 0.650-0.714 vs. 0.644-0.676) and substantially outperforms them out-of-distribution (0.717-0.833 vs. 0.512-0.564), because it measures a property of the model's generation rather than the query distribution. This paper further proposes retrieval-conditional self-assessment, a pre-generation signal that selectively injects retrieved knowledge when similarity is high, improving over bare self-assessment by up to +0.069 AUROC at 3-10x lower latency than log-probability. A supervised baseline trained on 1,000 labeled examples never exceeds the zero-shot signal. We release all code, data, and experiment logs.

Luong N. Nguyen

Confidence Estimation in Language Models Language Model Self-Assessment LLM Reliability LLM Uncertainty Estimation LLM Routing

May 3, 2026cs.LG

Feature Rivalry in Sparse Autoencoder Representations: A Mechanistic Study of Uncertainty-Driven Feature Competition in LLMs

Sparse Autoencoders (SAEs) decompose large language model representations into interpretable features, but how these features interact under uncertainty remains poorly understood. We introduce Feature Rivalry -- negatively correlated SAE feature pairs -- and study whether rivalry serves as a mechanistic signature of model uncertainty in Gemma-2-2B using Gemma Scope SAEs. Through a controlled within-domain experiment on PopQA split by response entropy, we find that high-entropy questions produce significantly stronger feature rivalry at layers 0 and 12 relative to low-entropy questions (p=5.3x10^-26 and p=5.8x10^-5 respectively), localizing uncertainty to specific processing stages in the residual stream. We then test whether rivalry is causally upstream of model outputs via activation steering along rivalry axes -- finding that steering along the rivalry direction (vec_A - vec_B) causes more output changes than random directions at low steering multipliers across 15 of 20 rival feature pairs. Finally, a per-prompt rivalry score derived from pairwise cosine similarities of active SAE feature decoder vectors predicts answer correctness (AUROC=0.689), approaching but not matching softmax confidence (AUROC=0.808).

Harshavardhan

Independent Researcher

LLM Interpretability Sparse Autoencoders LLM Uncertainty Estimation

May 2, 2026cs.CL

Hallucinations Undermine Trust; Metacognition is a Way Forward

Despite significant strides in factual reliability, errors -- often termed hallucinations -- remain a major concern for generative AI, especially as LLMs are increasingly expected to be helpful in more complex or nuanced setups. Yet even in the simplest setting -- factoid question-answering with clear ground truth-frontier models without external tools continue to hallucinate. We argue that most factuality gains in this domain have come from expanding the model's knowledge boundary (encoding more facts) rather than improving awareness of that boundary (distinguishing known from unknown). We conjecture that the latter is inherently difficult: models may lack the discriminative power to perfectly separate truths from errors, creating an unavoidable tradeoff between eliminating hallucinations and preserving utility. This tradeoff dissolves under a different framing. If we understand hallucinations as confident errors -- incorrect information delivered without appropriate qualification -- a third path emerges beyond the answer-or-abstain dichotomy: expressing uncertainty. We propose faithful uncertainty: aligning linguistic uncertainty with intrinsic uncertainty. This is one facet of metacognition -- the ability to be aware of one's own uncertainty and to act on it. For direct interaction, acting on uncertainty means communicating it honestly; for agentic systems, it becomes the control layer governing when to search and what to trust. Metacognition is thus essential for LLMs to be both trustworthy and capable; we conclude by highlighting open problems for progress towards this objective.

Gal Yona, Mor Geva, Yossi Matias

Google Research · Tel Aviv University

LLM Hallucination Mitigation Hallucination in Language Models LLM Reliability LLM Uncertainty Estimation Trust in AI Metacognition in Language Models+1

May 1, 2026cs.CL

CLEAR: Revealing How Noise and Ambiguity Degrade Reliability in LLMs for Medicine

Medical large language model (LLM) evaluations rely on simplified, exam-style benchmarks that rarely reflect the ambiguity of real-world medical inquiries. We introduce the CLinical Evaluation of Ambiguity and Reliability (CLEAR) framework, which assesses how decision-space presentation, ambiguity, and uncertainty affect LLMs' reasoning on medical benchmarks. CLEAR systematically perturbs (1) the number of plausible answer options, (2) the presence of a ground truth or abstention option, and (3) the semantic framing of answer options. Applying CLEAR on three benchmarks evaluated across 17 LLMs reveals three notable limitations of existing evaluation methods. First, increasing the number of plausible answers degrades a model's ability to identify the correct answer and abstain against incorrect ones. Second, this lack of caution intensifies as the framing of abstention shifts from assertive rejection like "None of the Above" to uncertainty admission like "I don't know" (IDK). Notably, just including IDK in the answer space increases incorrect answer selections. Lastly, we formalize the performance gap between identifying the correct answer and abstaining from incorrect ones as the humility deficit, which worsens with model scale. Our findings reveal limitations in standard medical benchmarks and underscore that scaling alone does not resolve LLM reliability issues.

Kevin H. Guo, Chao Yan, Avinash Baidya +5

Department of Biomedical Informatics, Vanderbilt University Medical Center, Nashville, TN, USA · Intuit AI Research, Mountain View, CA, USA · Department of Electrical and Computer Engineering, Vanderbilt University, Nashville, TN, USA +2

Healthcare LLM Reliability LLM Uncertainty Estimation Clinical Language Model Evaluation Language Model Robustness Medical LLMs+1

May 1, 2026cs.IR

"I Don't Know" -- Towards Appropriate Trust with Certainty-Aware Retrieval Augmented Generation

Achieving the right amount of trust in AI systems is important, but challenging. The problem is exacerbated with the rise of Large Language Models (LLMs) as they provide human-level communication capabilities, but potentially hallucinate in the content that they generate. Moreover, they express over-confidence in their answers, making it difficult for users to judge their truthfulness. An important human value that users seek is benevolence, which can be met by LLM's self-reflection leading to reliable and honest answers. Accordingly, this paper proposes conveying appropriate levels of self-reflected certainty to build appropriate trust. Our contributions are twofold: 1) We develop CERTA (Certainty Enhanced RAG for Trustworthy Answers), a specialized Retrieval Augmented Generation (RAG) system that incorporates the relevance between question, context, and answer to reflect its uncertainty in answering questions; 2) We create the Certainty Benchmark with 90 question-context pairs of non-objective questions, divided over four categories (factuality, preference, sycophancy, morality) and three types of contexts (relevant, incomplete, irrelevant). We run experiments with a baseline RAG system and three CERTA settings using two LLMs. Our evaluations indicate that CERTA helps identify answers that are uncertain, decreases the cases of over-agreeing, and provides cautious behavior when prompted for moral judgments.

Daan Di Scala, Maaike de Boer, Pınar Yolum

TNO Netherlands Organisation for Applied Scientific Research, Department Data Science · Utrecht University, Department of Information and Computing Sciences

Retrieval-Augmented Generation LLM Reliability LLM Uncertainty Estimation RAG Evaluation Trust in AI LLM Honesty

Apr 30, 2026cs.CL

Confidence Estimation in Automatic Short Answer Grading with LLMs

Automatic Short Answer Grading (ASAG) with generative large language models (LLMs) has recently demonstrated strong performance without task-specific fine-tuning, while also enabling the generation of synthetic feedback for educational assessment. Despite these advances, LLM-based grading remains imperfect, making reliable confidence estimates essential for safe and effective human-AI collaboration in educational decision-making. In this work, we investigate confidence estimation for ASAG with LLMs by jointly considering model-based confidence signals and dataset-derived uncertainty. We systematically compare three model-based confidence estimation strategies, namely verbalizing, latent, and consistency-based confidence estimation, and show that model-based confidence alone is insufficient to reliably capture uncertainty in ASAG. To address this limitation, we propose a hybrid confidence framework that integrates model-based confidence signals with an explicit estimate of dataset-derived aleatoric uncertainty. Aleatoric uncertainty is operationalized by clustering semantically embedded student responses and quantifying within-cluster heterogeneity. Our results demonstrate that the proposed hybrid confidence measure yields more reliable confidence estimates and improves selective grading performance compared to single-source approaches. Overall, this work advances confidence-aware LLM-based grading for human-in-the-loop assessment, supporting more trustworthy AI-assisted educational assessment systems.

Longwei Cong, Sonja Hahn, Sebastian Gombert +3

DIPF | Leibniz Institute for Research and Information in Education, 60323 Frankfurt am Main, Germany · Faculty of Computer Science, Goethe University Frankfurt, 60629 Frankfurt am Main, Germany · Chemnitz University of Technology, 09111 Chemnitz, Germany

Uncertainty Quantification Selective Prediction Generative AI in Education LLM Uncertainty Estimation Automated Grading

Apr 30, 2026cs.AI

Belief-Guided Inference Control for Large Language Model Services via Verifiable Observations

In black-box large language model (LLM) services, response reliability is often only partially observable at decision time, while stronger inference pathways incur substantial computational cost, inducing a budgeted sequential decision problem: for each request, the system should decide whether the default low-cost response is sufficiently reliable or whether additional computation should be allocated to improve response quality. In this paper, we propose \textbf{Ver}ifiable \textbf{O}bservations for Risk-aware \textbf{I}nference \textbf{C}ontrol (\textsc{Veroic}), a framework for adaptive inference control in black-box LLM settings, which formulates request-time control as a \textit{partially observable Markov decision process} to capture partial observability and sequential budget coupling. It constructs a lightweight verifiable observation channel from the input-output pair by aggregating heterogeneous quality signals into a belief state over latent response reliability, which is then used by a budget-aware policy to decide whether to return the default output or trigger a higher-cost inference pathway. Experiments on diverse tasks show that \textsc{Veroic} achieves improved quality-cost trade-offs, stronger risk estimation and calibration, and more robust long-horizon inference control than competitive baselines.

Wenhao Yuan, Chenchen Lin, Jian Chen +3

The University of Hong Kong · Sun Yat-sen University

LLM Inference Cost-Aware Inference LLM Reliability LLM Uncertainty Estimation

Apr 28, 2026cs.LG

Entropy Centroids as Intrinsic Rewards for Test-Time Scaling

An effective way to scale up test-time compute of large language models is to sample multiple responses and then select the best one, as in Grok Heavy and Gemini Deep Think. Existing selection methods often rely on external reward models, which requires training a strong reward model and introduces additional computation overhead. As an alternative, previous approaches have explored intrinsic signals, such as confidence and entropy, but these signals are noisy with naive aggregation. In this work, we observe that high-entropy tokens tend to cluster into consecutive groups during inference, providing a more stable notion of model uncertainty than individual tokens. Together, these clusters reveal temporal patterns of model uncertainty throughout the inference process. Motivated by this observation, we propose to use the temporal structure of uncertainty as an intrinsic reward. To this end, we first formalize the basic unit of segment-level uncertainty as the High Entropy Phase (HEP), a variable-length segment that begins at a high-entropy token and ends when consecutive low-entropy tokens appear. We then define the Entropy Centroid, inspired by the concept of the center of mass in physics, as the weighted average position of all HEPs along the trajectory. Intuitively, a lower centroid indicates early exploration followed by confident generation, which we find often corresponds to higher response quality. Based on this insight, we propose the Lowest Centroid method, which selects the response with the lowest entropy centroid among multiple candidates. Experiments on mathematics, code generation, logical reasoning, and agentic tasks, across model scales ranging from 14B to 480B, show that Lowest Centroid consistently outperforms existing baselines and delivers stable gains as model size increases. Code is available at https://github.com/hkust-nlp/entropy-centroid.

Wenshuo Zhao, Qi Zhu, Xingshan Zeng +4

May · HKUST · ZJU +1

LLM Inference Test-Time Scaling LLM Reranking LLM Uncertainty Estimation

Apr 28, 2026eess.AS

Walking Through Uncertainty: An Empirical Study of Uncertainty Estimation for Audio-Aware Large Language Models

Recent audio-aware large language models (ALLMs) have demonstrated strong capabilities across diverse audio understanding and reasoning tasks, but they still frequently produce hallucinated or overly confident outputs. While uncertainty estimation has been extensively studied in text-only LLMs, it remains largely unexplored for ALLMs, where audio-conditioned generation introduces additional challenges such as perceptual ambiguity and cross-modal grounding. In this work, we present the first systematic empirical study of uncertainty estimation in ALLMs. We benchmark five representative methods, including predictive entropy, length-normalized entropy, semantic entropy, discrete semantic entropy, and P(True), across multiple models and diverse evaluation settings spanning general audio understanding, reasoning, hallucination detection, and unanswerable question answering. Our results reveal two key findings. First, semantic-level and verification-based methods consistently outperform token-level baselines on general audio reasoning benchmarks. Second, on trustworthiness-oriented benchmarks, the relative effectiveness of uncertainty methods becomes notably more model- and benchmark-dependent, indicating that conclusions drawn from general reasoning settings do not straightforwardly transfer to hallucination and unanswerable-question scenarios. We further explore uncertainty-based adaptive inference as a potential downstream application. We hope this study provides a foundation for future research on reliable, uncertainty-aware audio-language systems.

Chun-Yi Kuan, Wei-Ping Huang, Hung-yi Lee

Graduate Institute of Communication Engineering, National Taiwan University, Taiwan · Artificial Intelligence Center of Research Excellence (AI-CoRE), National Taiwan University, Taiwan

Semantic Entropy Audio Understanding Audio-Language Models LLM Uncertainty Estimation

Apr 28, 2026cs.CL

Quantifying Aleatoric Uncertainty of In-Context Learning for Robust Measure of LLM Prediction Confidence

In-Context Learning (ICL) allows LLMs to adapt to new tasks from a few demonstrations, but its reliability remains a concern: predictions are highly sensitive to both prompt design and the model's ability to understand the context, obscuring whether failures arise from data properties or model limitations. Uncertainty decomposition-separating aleatoric from epistemic sources-is particularly crucial in this setting, yet existing methods, designed for standard generation tasks, fail to capture the unique dynamics of ICL. To address this, we introduce a concept of self-function vectors, built upon Bayesian views and the mechanistic interpretability of ICL. These vectors leverage internal model representations to model the latent concept learned during in-context prompting, thereby enabling a direct estimation of aleatoric uncertainty within a Bayesian framework and circumventing the reliance on brittle input or decoding manipulations. Given the lack of established benchmarks and suitable evaluation protocols, we also propose the first and rigorous evaluation protocol, in which data is manipulated in controlled ways so as to quantify aleatoric uncertainty precisely and separately from epistemic uncertainty. With this new evaluation framework, initially grounded in synthetic tasks for conceptual development and subsequently extended to real-world datasets, we show that our proposed methodology can measure uncertainty of LLM predictions made under ICL more reliably than existing alternative methods. Moreover, we show it can be used as a practical tool for trustworthy-related applications, such as hallucination detection. Our findings pave a new direction for connecting the quantitative view of uncertainty with the mechanistic understanding of model behavior.

Jinseok Chung, Minkyoung Song, Hyunji Jung +1

POSTECH

Uncertainty Quantification In-Context Learning LLM Uncertainty Estimation Aleatoric Uncertainty Uncertainty Decomposition

Apr 27, 2026cs.AI

Representational Curvature Modulates Behavioral Uncertainty in Large Language Models

In autoregressive large language models (LLMs), temporal straightening offers an account of how the next-token prediction objective shapes representations. Models learn to progressively straighten the representational trajectory of input sequences across layers, potentially facilitating next-token prediction via linear extrapolation. However, a direct link between this trajectory and token-level behavior has been missing. We provide such a link by relating contextual curvature-a geometric measure of how sharply the representational trajectory bends over recent context-to next-token entropy. Across two models (GPT-2 XL and Pythia-2.8B), contextual curvature is correlated with entropy, and this relationship emerges during training. Perturbation experiments reveal selective dependence: manipulating curvature through trajectory-aligned interventions reliably modulates entropy, while geometrically misaligned perturbations have no effect. Finally, regularizing representations to be straighter during training modestly reduces token-level entropy without degrading validation loss. These results identify trajectory curvature as a task-aligned representational feature that influences behavioral uncertainty in LLMs.

Jack King, Evelina Fedorenko, Eghbal A. Hosseini

Brain and Cognitive Sciences Massachusetts Institute of Technology Cambridge, MA 02139 · Google DeepMind

Neural Representation Geometry Autoregressive Language Modeling LLM Uncertainty Estimation Representation Geometry in Language Models

Apr 27, 2026cs.HC

What Did They Mean? How LLMs Resolve Ambiguous Social Situations across Perspectives and Roles

People increasingly turn to large language models (LLMs) to interpret ambiguous social situations: a delayed text reply, an unusually cold supervisor, a teacher's mixed signals, or a boundary-crossing friend. Yet in many such cases, no stable interpretation can be verified from the available evidence alone. We study how LLMs respond to these situations across four domains: early-stage romantic relationships, teacher--student dynamics, workplace hierarchies, and ambiguous friendships. Across 72 responses from GPT, Claude, and Gemini, only 9 (12.5%) genuinely preserved uncertainty. The remaining 87.5% produced interpretive closure through recurring pathways including narrative alignment, narrative reversal, normative advice under uncertainty, and hedged language that still supported a single conclusion. We further find that narrator perspective shapes the path to closure: first-person accounts more often elicited alignment, while third-person accounts invited more detached interpretation, even when the underlying situation remained comparable. Together, these findings show that LLMs do not simply assist interpersonal sensemaking; they tend to resolve ambiguity into coherent and actionable narratives. These results suggest that the central risk is not only that LLMs may misinterpret social situations, but that they may make unresolved situations feel prematurely settled. We frame this tendency as a design challenge for uncertainty-preserving social AI.

Qiming Yuan, Linyi Han, Nam Ling +1

Santa Clara University, USA

LLM Uncertainty Estimation Social Reasoning