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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Aug 8, 2026cs.LG

From token probabilities to calibrated confidence: An empirical study of mathematical question answering

Confidence estimation for large language models (LLMs) aims to estimate the probability that a generated answer is correct, while calibration aligns these estimates with empirical accuracy. Prior work has shown that token probabilities are often overconfident, we investigate whether these readily available signals can nevertheless provide well-calibrated confidence estimation for mathematical question answering. We compare single-pass estimators, which reuse token probabilities from the original generation, with multi-pass estimators, which obtain additional confidence signals through verification or stochastic forward passes. While individual token probabilities can be highly saturated, we find that aggregating token probabilities over the full sequence captures small but consistent differences between correct and incorrect generations, yielding more informative confidence estimates. Multi-pass methods can yield calibrated confidence estimates. We study two such approaches: self-verification through re-prompting, including a lower-cost in-situ variant, and Monte Carlo Dropout, which derives confidence from variation across stochastic forward passes. We further evaluate two post-hoc calibration methods, Platt scaling and isotonic regression, both of which substantially reduce in-domain calibration error. However, their data efficiency varies with dataset difficulty, and the calibration mappings often transfer asymmetrically across datasets and models.

Avery Ma, Lorne Schell, Vin Bhaskara +1

RBC Borealis

LLM Answer Verification Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation LLM Mathematical Reasoning

Aug 5, 2026cs.CL

Provable Limits and Certified Deferral for Verbalized Uncertainty in Small Language Models

Small open-weight language models increasingly run in private, offline, and cost-sensitive settings, where the key deployment question is not only what a model answers but when it should defer to a human. We study whether verbalized confidence can support risk-controlled deferral, evaluating eleven instruction-tuned models from three families, 0.5B to 14B parameters, on ARC-Challenge and TruthfulQA with 25,168 local predictions. Three theoretical results delimit what calibration can provide: strictly monotone calibration preserves the risk-coverage frontier and error-detection AUROC; temperature scaling cannot calibrate models whose confidence stays above one half while accuracy falls below it; and a Clopper-Pearson procedure converts a 200-question calibration set into a finite-sample risk certificate under an i.i.d. deployment assumption. Empirically, eight of 22 model-task pairs hit the temperature-scaling infeasibility floor within one percentage point of the predicted bound. Platt scaling reduces ECE to as low as 0.02, yet certified autonomy at a 20% risk budget is granted to only three model-task pairs and to none at 10%. We also identify and repair an answer-ordering artifact in the multiple-choice form of TruthfulQA. Calibration gives confidence semantics; certified deferral determines when small models are safe to use.

Jianru Shen

University of Montana, Missoula, MT 59812, USA

Selective Prediction Confidence Estimation in Language Models Small Language Models Language Model Calibration LLM Uncertainty Estimation

Aug 5, 2026cs.CL

Evaluation Pitfalls and Sparsity Limitations in LLM-based Confidence Estimates for Classification

Confidence estimation is essential when LLMs are used for classification, indicating when predictions can be trusted. However, common approaches such as verbalization produce extremely sparse outputs. For instance, Qwen3-32B verbalizes only eight unique confidence values on SST-2, with over half being exactly 95%, a pattern we observe consistently across four datasets and two LLMs. Besides limiting practical utility, we show that this sparsity critically affects evaluation: the choice of interpolation in area under the accuracy-rejection curve (AUARC) dramatically alters rankings, with consistency sampling dropping from best to worst under stepwise versus linear interpolation. We advocate for standardizing stepwise interpolation for a fairer comparison. Under such a fair evaluation, we find that weighting verbalized digits by token probabilities, a method we term verbalization logprobs, addresses sparsity and achieves the best AUARC (+2.3 points over vanilla verbalization) without incurring additional inference cost.

Elena Merdjanovska, Omar Zaidan, Andreas Rücklé

Humboldt-Universität zu Berlin Science of Intelligence · Amazon

LLM Evaluation Selective Prediction Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation

Aug 5, 2026cs.LG

PPDL: LLM-Based Flows as Probabilistic Programs

Building reliable applications that leverage large language models (LLMs) remains a significant challenge. While LLMs offer impressive capabilities across diverse tasks, their outputs often lack accuracy and provide no clear measure of confidence. This uncertainty compounds in flows of multiple calls to LLMs and other tools, making it difficult for developers and end-users to trust the results. This paper introduces a probabilistic language for programming LLM-based flows. It enables developers to quantify and propagate uncertainty throughout the application's flow, and experiment with different inference scaling techniques without adding a single line of code beyond the flow's logic. We present an experimental study to demonstrate this capability, and a case study building a theorem proving agent for the Rocq theorem prover.

Louis Mandel, Guillaume Baudart, Mandana Vaziri +1

IBM, New York, USA · Université Paris Cité, Inria, CNRS, IRIF, France

LLM Inference LLM Reliability LLM Uncertainty Estimation Probabilistic Programming Uncertainty Propagation

Aug 4, 2026cs.CL

DUD: Decoupled Update Dynamics for Reliable Uncertainty Quantification in Large Language Models

Accurate Uncertainty Quantification (UQ) is critical for reliable deployment of Large Language Models (LLMs), yet traditional probability-based metrics often fail to capture the model's true epistemic state. While recent mechanistic approaches leverage hidden state dynamics, they typically aggregate residual stream updates, conflating the distinct roles of parametric memory (Feed-Forward Networks) and contextual processing (Attention). We argue that this aggregation obscures fine-grained mechanistic conflicts, such as memory-context misalignment, that are fundamental indicators of uncertainty. To address this, we introduce \textbf{D}ecoupled \textbf{U}pdate \textbf{D}ynamics \textbf{(DUD)}, a framework that explicitly decouples FFN and Attention contributions via noise-induced causal interventions. By quantifying the independent restoration capabilities of each module, we construct a dual-stream dynamic profile that captures the model's internal fragility. Extensive experiments demonstrate that DUD significantly outperforms state-of-the-art baselines in both uncertainty estimation and calibration, while exhibiting superior cross-dataset generalization, validating decoupled dynamics as a robust proxy for model faithfulness.

Yixin Bu, Runze Xia, Guanyun Zou +3

College of Artificial Intelligence, Nanjing University of Aeronautics and Astronautics, China · 2The Key Laboratory of Brain-Machine Intelligence Technology, Ministry of Education, Nanjing, China · 3Researcher

LLM Uncertainty Estimation Uncertainty Calibration

Aug 2, 2026cs.SE

When Policies Change Probabilities: Modular Decision-Making for LLM Code Review

LLM code reviewers often estimate patch risk and make approval decisions in one prompt. A probability should depend on evidence; costs should determine the action taken from it. We test whether four deployed reviewer interfaces preserve this separation using 15,792 responses on 720 candidate patches, with one that passed and one that failed an archived test harness for each of 360 repository issues. In matched calls with the patch and monitor evidence fixed, replacing an equal-cost policy with a 10:1 false-accept policy changes reported failure probabilities by 13.6 to 16.9 percentage points on average. For every reviewer, the actions returned under the high-cost prompt are worse than rejecting all patches. Applying the same high-cost rule to probabilities elicited under equal costs reduces loss for all four systems, showing that probability elicitation itself contributes to the excess loss. We also evaluate a modular pipeline that elicits risk without policy information, combines an independent monitor score, and applies costs in code. Relative to calibrated reviewer-only scores, the pipeline improves average probability accuracy and, at equal costs, reduces mean loss by .073 per issue while accepting 58 to 68% of patches. At 10:1, it accepts none and matches reject-all. Downstream policy can therefore change the probability it is meant to use, motivating separate evaluation of risk, outside evidence, and action.

Rasvik Kudum, Max Corbett, Hitansh Paliwal +3

LLM Evaluation LLM Decision-Making LLM Uncertainty Estimation Automated Code Review

Aug 2, 2026cs.LG

Conformalized Large Language Models under Configuration Shift

Conformal prediction (CP) is a distribution-free framework for uncertainty quantification that has recently been adapted to large language models (LLMs), providing prediction sets with finite-sample coverage guarantees under exchangeability. Yet for LLMs, nonconformity scores are often induced by an inference pipeline, not just a fixed model, making them depend not only on the data distribution but also on configurable factors such as the prompt template, decoding parameters, and deployment setting. Since such configurations are routinely modified in practice but rarely treated as a source of shift, their impact on CP validity remains poorly understood. We call this \emph{configuration shift} and study it systematically along three axes: prompt template, decoding temperature, and weight quantization. In a broad empirical study spanning

9

LLMs,

4

datasets, and

4

nonconformity scores, we find that configuration shift consistently erodes CP validity, often driving empirical coverage below the target. By contrast, efficiency is largely preserved: valid prediction sets remain close in size to the i.i.d. baseline. We derive coverage lower bounds that attribute this loss to a discrepancy between calibration and test score distributions, and use their finite-sample plug-in versions as empirical diagnostics of shift severity. We further show that these findings lead to practical mitigations: bound-inspired recalibration is effective with limited test examples, while fragility-aware calibration ensembling recovers much of the lost coverage without test data.

Yuqicheng Zhu, Jialin Yu, Lin Li +7

University of Stuttgart · Robert Bosch GmbH · University of Oxford +4

Conformal Prediction Language Model Calibration LLM Uncertainty Estimation

Aug 1, 2026cs.AI

TrAC: Trace-Conditioned Answer Consistency for Efficient Uncertainty Quantification in LLMs

Large language models (LLMs) can generate fluent reasoning traces that nevertheless lead to incorrect answers, making response-level uncertainty estimation important for abstention, human review, and adaptive compute allocation. Existing approaches generally fall into three categories: passive single-trace methods use token-level confidence signals, sampling-based methods compare multiple complete traces at higher generation cost, and active prefix-based methods probe partial traces to study answer stabilization or preference transitions. However, none actively re-elicits an answer from a completed reasoning trace to measure its consistency with and support for the original answer. To address this gap, we introduce Trace-Conditioned Answer Consistency (TrAC), a correctness-supervised uncertainty quantification framework that combines active and passive signals anchored to one completed reasoning trace. Its active component, Prefix-Conditioned Elicitation (PCE), re-elicits a short answer conditioned on the completed trace and represents both its consistency with the original answer and its token-level probabilistic support. Its passive component, Trace Uncertainty Profile (TUP), summarizes how token-level uncertainty evolves throughout the original generation without additional decoding. A lightweight head then integrates the two representations into a response-correctness score. Across five mathematical reasoning benchmarks and three LLM families, TrAC improves macro AUROC by 1.8% and reduces AURC by 3.4% relative to eight-sample self-consistency, while using one complete reasoning trace and a short cached answer probe. When eight samples are already available, augmenting sample consensus with re-elicitation further improves macro AUROC by 4.3% and reduces AURC by 8.3%, without additional full-trace generation.

Dahai Yu, Lin Jiang, Rongchao Xu +1

Florida State University Tallahassee, Florida, USA

LLM Evaluation Reasoning Consistency in Language Models LLM Uncertainty Estimation Reasoning Trace Analysis

Aug 1, 2026cs.AI

SymboUQ: Symbolic Uncertainty Quantification for Spatial Reasoning in LLMs

Although large language models (LLMs) can produce fluent spatial reasoning traces, their intermediate relations may fail to support the final conclusion, making token-level confidence insufficient for final-answer reliability estimation. Existing formal verifiers provide stronger semantic evidence, but their applicability is partial: a parsed claim need not yield a definite semantic verdict. To address this issue, we introduce SymboUQ, a symbolic uncertainty quantification framework that estimates final-answer reliability from reasoning traces by distinguishing symbolizability, whether a claim can be represented in the verifier's formal language, from semantic determinacy, whether its execution yields an entailed or contradicted verdict rather than an unknown or not-evaluable outcome. SymboUQ comprises (i) a Layout Auditor that executes ordered spatial claims and extracts feasibility, conflict, and repair evidence; (ii) a label-free Determinacy Profile that characterizes effective executable coverage; and (iii) a Determinacy-Aware Reliability Composer that integrates constraint-based, representation-based, and decoding-based scores according to verifier applicability. Extensive experiments on five spatial reasoning benchmarks with four frozen LLM backbones show that SymboUQ achieves approximately an 8% relative improvement in AUROC and a 7% relative reduction in class-balanced Brier loss over the strongest baseline.

Dahai Yu, Lin Jiang, Rongchao Xu +1

Florida State University, Tallahassee, Florida

Uncertainty Quantification LLM Reliability LLM Uncertainty Estimation Spatial Reasoning

Jul 29, 2026stat.ML

Think Short, Defer Smart, Act, and Repeat: Calibrated Reasoning and Uncertainty-Aware Deferral for Edge LLM Agents

LLM agents following the ReAct paradigm are promising enablers of complex multi-step tasks, including multi-hop question answering, code generation, and control of physical AI systems. Yet, when deployed at the edge, they must tightly manage their reasoning budget while remaining reliable and deferring to a cloud-side model only when local uncertainty is too high to act safely. We propose Think Short, Defer Smart (TSDS), a framework that synergistically integrates a lightweight convergence probe, which halts on-device reasoning once the intended action has stabilized, with a perplexity-based deferral rule that escalates uncertain actions to a cloud-side model. Both mechanisms are jointly calibrated on end-to-end episode trajectories via a multi-objective Learn-Then-Test (LTT) procedure, providing simultaneous finite-sample guarantees on expected episode reward and cloud-call rate. We evaluate TSDS on four ReAct benchmarks spanning arithmetic reasoning (GSM8K), multi-hop question answering (HotpotQA), code generation (MBPP), and multi-step embodied planning (household robot), and compare against thought-calibration-only and calibrated-deferral-only standalone baselines. TSDS reduces per-episode thinking compute by 43%-73% over deferral-only baselines across HotpotQA, MBPP, and the household robot task, while maintaining certified reward and cloud-call rate guarantees.

Amirmohammad Farzaneh, Osvaldo Simeone

Institute for Intelligent Networked Systems (INSI) Northeastern University London London, UK

LLM Inference Efficiency AI Agent Reliability LLM Agents LLM Uncertainty Estimation LLM Agent Reliability

Jul 29, 2026cs.LG

Thinking Under Uncertainty: Evidence Use and Information-Seeking in Language Models

Inference-time thinking improves the performance of large language models, but aggregate outcomes do not reveal whether models use available evidence more effectively or seek information that could improve future decisions. We distinguish these responses by measuring action preference, thinking length, and reported confidence under matched uncertainty. Ten open-weight models completed matched horizon-style two-armed bandit trials in thinking and non-thinking modes. A cognitive model separated value-guided action and uncertainty-independent choice noise from two behavioral signatures of exploration: a UCB-like preference for the less-known arm and Thompson-like choice variability that increases with total uncertainty. On average, thinking strengthened value-guided action and reduced uncertainty-independent choice noise, without producing UCB-like exploration or strengthening Thompson-like exploration. Outside action, the information-imbalanced history condition, which also displayed more observations than the matched balanced condition, was associated with greater thinking length. Reported confidence became more sensitive to decision difficulty and more strongly associated with chosen task evidence. We interpret these thinking-length and reported-confidence patterns as consistent with metacognitive control and metacognitive monitoring, respectively, without establishing either process. Decoder sweeps, especially temperature, altered choice noise and thinking length but did not reproduce the joint cross-output pattern. In this controlled decision setting, thinking improved how models acted on current evidence, while neither measured signature supported a shift toward a more information-seeking policy.

Hua-Dong Xiong, Xinyuan Yan, Ji-An Li +3

School of Psychological and Brain Sciences, Georgia Tech · Department of Neurosurgery, Baylor College of Medicine · Department of Psychology, New York University +1

LLM Decision-Making LLM Uncertainty Estimation Metacognition in Language Models

Jul 28, 2026cs.SE

Model-Driven Requirements Configuration with Three-Valued Uncertainty Scoring

Context: Large Language Models (LLMs) offer natural-language flexibility for automated requirements elicitation but frequently generate structurally invalid requirements and logical inconsistencies, lacking formal correctness guarantees. Objectives: This study aims to eliminate logical inconsistencies and enforce structural conformance in LLM-generated requirements while quantifying the LLM's pre-validation decision uncertainty within a formal domain model. Methods: We present a neuro-symbolic multi-agent architecture that operationalizes the Object-Oriented Method for Requirements Authoring and Management (OOMRAM) lattice. The LLM acts as a non-deterministic heuristic for lattice traversal, while a deterministic symbolic validator enforces all structural constraints. We introduce a three-valued (T, I, F) -- Truth, Indeterminacy, Falsity -- framework to classify and score the LLM's requirement decisions before and after validation. Results: Evaluated across 37 natural-language project visions in eleven application families, the system completely eliminated structural inconsistencies in 35 out of 37 cases (94.6%), with the remaining two containing only 6 unresolved structural errors (0.39% of decisions) due to iteration limits. Three-valued analysis revealed that 24.7% of all decisions are indeterminate -- structurally valid but discretionary choices not explicitly mandated by the stakeholder. Conclusion: Offloading structural integrity to a deterministic symbolic layer successfully guarantees structural conformance, while the three-valued classification provides a formal way to measure neural uncertainty, facilitating safe LLM deployment in formal requirements engineering.

Ahmed Ibrahim

aWestern University, London, Canada

Logical Reasoning Requirements Engineering LLM Uncertainty Estimation Neuro-Symbolic AI

Jul 28, 2026cs.LG

Spend Experts Where You Are Unsure: Confidence-Adaptive Routing for Mixture-of-Experts LoRA

Mixture-of-Experts (MoE) variants of Low-Rank Adaptation (LoRA) route every token to a fixed number of experts

k

. Tokens differ in how uncertain the model is about them, so a single k over-spends on easy tokens and under-serves hard ones. We observe that the router's output distribution is already a per-token uncertainty signal: peaked mass indicates confidence, while a flat distribution indicates ambiguity. We introduce CARE (Confidence-Adaptive Routing of Experts), which admits experts in a nucleus fashion. Experts are activated in decreasing router weight until their cumulative mass reaches a threshold, with a small extension when the admitted experts disagree. A budget thermostat calibrates the threshold so that the average number of active experts matches any target. CARE is a drop-in, single-forward-pass rule with no extra parameters. Across eight commonsense benchmarks on LLaMA-3.1-8B and Qwen2.5-7B, as well as math, code, and knowledge tasks, CARE improves over fixed top-k MoE-LoRA at matched compute and matches the fixed-k=4 baseline while activating fewer experts. The same confidence and disagreement signals also improve out-of-distribution detection over MSP, entropy, and multi-pass proxies. We support the design with nucleus fidelity, budget optimality, and an epistemic reading of disagreement, and we release code.

Tom Saliencro, Rohan Desai, Priya Nair +2

University of California, Irvine · University of Washington

Parameter-Free Mixture-of-Experts Routing LLM Inference Acceleration Expert Routing LLM Uncertainty Estimation Mixture-of-Experts Models

Jul 28, 2026cs.IR

Beyond Self-Knowledge: Propagating Uncertainty Across Reasoning and Retrieval in LLMs

Retrieval-augmented generation improves knowledge-intensive question answering, but indiscriminate retrieval can introduce irrelevant evidence and unnecessary computation. We investigate whether verbalized confidence from black-box language models can serve as an actionable signal for retrieval routing. Our method, BeyondUncertainty, first elicits a structured provisional answer and confidence estimate, then applies a model-specific threshold selected on held-out validation data and frozen before test evaluation. Low-confidence questions receive top-5 TF-IDF retrieval followed by a second answer call, whereas high-confidence questions return the provisional answer directly. We evaluate 27,000 policy instances across six QA benchmarks, three model families, and three retrieval policies. BeyondUncertainty achieves 0.483 mean token-level F1, compared with 0.467 for always retrieval and 0.401 for no retrieval, while reducing retrieved passages by 20.4% relative to always retrieval. When matched on the number of questions routed to retrieval within each dataset-model cell, it outperforms a post-hoc random allocation in 17 of 18 settings, with an average gain of 0.024 F1. Although poorly calibrated as an absolute probability, probe uncertainty modestly predicts question-level retrieval benefit (AUROC = 0.628). However, the additional probe increases total token usage by 28.2%, revealing a trade-off between more selective evidence acquisition and end-to-end token efficiency.

Chandan Kumar Sah, Li Zhang, Xiaoli Lian

Beihang University, Beijing, China

Retrieval-Augmented Generation Confidence Estimation in Language Models LLM Uncertainty Estimation RAG Evaluation Efficient Language Model Inference

Jul 28, 2026stat.AP

Laplace-PSN-IRT: Uncertainty Quantification for Neural Item Response Theory Models of LLM Benchmarks

Item Response Theory (IRT) has recently been proposed as a framework for evaluating large language model (LLM) benchmarks by separating a model's latent ability from the properties of individual benchmark items. Existing neural IRT approaches, including PSN-IRT, estimate these quantities using point estimates, limiting uncertainty quantification and downstream statistical inference. We introduce Laplace-PSN-IRT, a post-hoc last-layer Laplace approximation that augments a trained PSN-IRT model with approximate Bayesian posterior inference, recovering calibrated uncertainty over model ability and item difficulty without retraining. The resulting posterior enables credible intervals, probabilistic comparisons between models, and propagation of parameter uncertainty into Fisher-information-based item selection. We show that most pairwise comparisons among 12 models on a standard LLM benchmark leaderboard are not statistically distinguishable despite differing point-estimate ranks. We further show that point-estimate Fisher information can become nearly zero for many benchmark items because it is evaluated at a single reference ability, whereas posterior-expected Fisher information remains substantially more stable across the ability range. Finally, posterior-expected Fisher information more accurately recovers full-benchmark ability rankings from small benchmark subsets in most experimental settings while matching point-estimate performance for the smallest subsets. We validate the calibration of the approximate posterior using held-out predictive coverage and find that modeling item difficulty as random while treating item discrimination as fixed produces well-calibrated uncertainty in this architecture.

Juan Francisco, Mandujano Reyes

Independent Research

LLM Evaluation Language Model Calibration LLM Uncertainty Estimation Item Response Theory

Jul 27, 2026cs.SE

Beyond "What to Retrieve": Uncertainty in Retrieval-Augmented Code Generation

Repository-level code generation relies on heterogeneous evidence whose relevance, compatibility, and completeness are inherently uncertain. Similar-code examples, repository context, and project-specific APIs may provide complementary information, but can also introduce noisy, redundant, or conflicting signals. Existing retrieval-augmented approaches primarily optimize retrieval relevance without explicitly modeling how uncertainty in retrieved evidence affects downstream generation. We introduce OpenCoder, an uncertainty-aware framework that estimates source-specific uncertainty, uses it to filter and rank heterogeneous evidence, and guides generation, verification, and repair. A factorial analysis over API knowledge, repository context, and similar-code evidence reveals no universal additive source ranking; instead, significant cross-source interactions depend on the accompanying evidence and LLM backend. On an expanded 32-task RepoExec-inline evaluation, OpenCoder improves GPT selected-output correctness over Baseline RAG from 56.25% to 78.13%. However, it matches a verification-and-repair control, and the corresponding Gemini improvement is not statistically supported, indicating backend-dependent benefits. Target-aware API refinement also substantially improves API-set retrieval. These findings support treating uncertainty as an actionable control signal for repository-level retrieval, verification, and repair.

Chandan Kumar Sah, Li Zhang, Xiaoli Lian

Beihang University, Beijing, China

Retrieval-Augmented Generation LLM Uncertainty Estimation Repository-Level Code Generation

Jul 25, 2026cs.IR

Statistically Supported LLM Ingredient and Recipe Data Collection in Computational Nutrition

Computational nutrition needs precise ingredient data, but current databases are incomplete, inconsistent, and built for human reference rather than automated reasoning. LLMs could help fill these gaps, but single-pass outputs are unreliable and can introduce silent errors into downstream computation. We present a quality-controlled LLM pipeline for ingredient data acquisition that combines robust statistical estimation, domain-specific invariant checks, and a web-fetch fallback. An illustrative Heap's Law fit to 233 recipes suggests that unique-ingredient growth is sub-linear and front-loaded: the projected ratio of unique ingredients to recipes falls from 1.74 at 100 recipes to 0.19 at 5,000. For each ingredient attribute, repeated LLM queries are treated as samples from a model-induced answer distribution, and we apply robust point estimators and normalised confidence scores across numerical, Boolean, multiple-choice, open categorical, and optional integer types. An invariant guard layer enforces nutritional and logical self-consistency within each ingredient record. Minor numeric inconsistencies are reconciled via a linear program that minimises worst-case percentage deviation while preserving semantic zeros, and major violations are escalated to web-evidence-grounded repair, then human review only if that fails. On a curated 30-ingredient reference set, the pipeline achieves 98.4% exact match on nutrient flags and cuts median absolute percentage error on nutrient ratios from 31.9% for the median-aggregated baseline to 10.1%, a reduction of 21.8 percentage points, at an API cost of about $1 per ingredient. This frames LLM-assisted database construction as a controlled data-engineering workflow that makes uncertainty operational rather than discarding it.

James Izzard, Hassan Eshkiki, Fabio Caraffini

Swansea University, Department of Computer Science, Bay Campus, Swansea, SA1 8EN, Wales, UK

LLM Grounding Training Data Curation LLM Information Extraction LLM Uncertainty Estimation

Jul 21, 2026cs.AI

The Knowing-Saying Gap: When Probes See Errors that Confidence Misses

Linear probes detect corrupted context in language models with near-perfect accuracy, yet this does not translate into reliable failure prediction. The result is a dissociation with direct implications for deployment monitoring. Across multi-hop arithmetic chains, probes that detect corruption turn out to be uninformative about final answer correctness; models forced into structured confidence formats collapse to two values with indistinguishable error rates; and probe persistence across hops fails to separate correct from incorrect outcomes, refuting our pre-registered "persistence beats peak" hypothesis. This pattern of knowing but not saying generalises across model families including reasoning models. As a real-time monitor, probe-based interventions are sharply model and error-type dependent: branch-and-pick is net-positive across models and uniquely non-breaking on Llama-3.1-8B (4 rescued, 0 broken), while reprompt and replace-prior break correct traces at roughly the rate they rescue wrong ones. Probe-based monitoring is a necessary complement to verbalised confidence, but no single intervention dominates, and the deployable answer is model-aware, error-type-aware routing.

Jyotin Goel, Ipshita Bandyopadhyay, Justin Shenk

Language Model Error Detection Confidence Estimation in Language Models Language Model Self-Assessment LLM Reliability LLM Uncertainty Estimation Causal Interventions in Language Models+1

Jul 20, 2026stat.ME

Calibrating Semantic Uncertainty from Observable Language-Model Probabilities

As generative artificial intelligence enters scientific and professional work, its uncertainty must be defined on the states that matter for inference and decision-making. Language models assign probabilities to words, whereas applications require uncertainty over meaningful states such as diagnoses, hypotheses or operational conditions. We introduce a \emph{semantic map}: a prespecified, testable bridge from probabilities over verbal responses to a posterior over declared finite states. The language distribution remains unrestricted; held-out calibration connects it to a reference posterior. We derive posterior-error bounds and conditions for existence, conditional uniqueness, presentation stability and stable inverse recovery. This distinction matters because language probabilities depend on prompt wording, while the target posterior should not change under information-equivalent rewording. Experiments use professional market text compiled from Federal Reserve economic and financial series, together with controlled simulations having exact posteriors. Across two fitted language models, language-derived probabilities outperform printed numerical confidence, recover held-out posteriors with valid uncertainty coverage, remain largely stable under paraphrase and respond appropriately to altered evidence. \textbf{Prompt engineering optimises a wording-dependent response; robust scientific use requires validated stability of application-relevant meaning.} The proposed map turns semantic uncertainty in generative systems into an identifiable and testable statistical measurement problem and, when its acceptance conditions hold, yields an auditable posterior estimate.

Matthew F. Dixon

Artificial Intelligence Finance Institute (AIFI), 69 Charlton St, New York, NY 10014, USA

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

Jul 18, 2026cs.AI

Beyond Semantic Equivalence: Logical Graphs for LLM Uncertainty Quantification

Large Language Models often produce confidently stated yet unreliable outputs, posing critical challenges for deployment in safety-sensitive applications. Existing uncertainty metrics such as semantic entropy capture agreement at the level of semantic equivalence, but largely ignore the logical relationships between distinct answers. As a result, they tend to overestimate uncertainty and falsely flag hallucinations in settings where generated responses are diverse in form yet logically compatible (e.g., differing only in granularity or specificity). We propose Logical Graph Uncertainty (LGU), a framework that explicitly models implication and incompatibility among answers. LGU aggregates probability mass along entailment chains onto the most specific hypotheses the answers support, measures the entropy of the resulting distribution, and penalizes mutual incompatibility among those hypotheses. Across multiple question-answering benchmarks and model families, LGU ranks first on average among existing uncertainty measures, with its largest gains---up to +7.1% AUROC and +3.5% AUARC over semantic entropy---on questions whose sampled answers are logically structured.

Yanni Dong, Minghua Liu, Meilin Zhu +2

Institute of Intelligent Software, Guangzhou, China · Institute of Software, Chinese Academy of Sciences, Beijing, China · University of Liverpool, Liverpool, UK

Reasoning Consistency in Language Models LLM Reliability LLM Uncertainty Estimation

Jul 15, 2026cs.CL

The Severance Problem: LLMs are Unaware of the Person Beyond the Prompt

Personal AI assistants have attracted significant interest for their potential to enhance everyday life by automating routine tasks, supporting consequential decisions, and assisting with everyday personal matters. Yet despite rapid recent technical advances, these assistants continue to exhibit undesirable behaviors, such as sycophancy, overconfidence, and hallucination. We argue that these failures stem from a fundamental limitation: language models lack an explicit representation of the person beyond the context they are given, which we term as the \textbf{Severance Problem}. Even with rich personal context and strong commonsense reasoning capabilities from the backbone model, current AI assistants fail to represent what remains unknown about the user. We propose a simple solution: incorporating structured ignorance into the language model context via the \textbf{Severance Schema}, which explicitly outlines dimensions along which the model lacks knowledge about the user, including physicality, temporality, consequences, continuity, multiplicity, and interiority. Empirically, across five model families, with the Severance Schema, the assistant consistently reduces sycophancy, harmful advice, and hallucination. Notably, models with the schema ask clarifying questions when information about the user is missing, rather than confidently extrapolating from incomplete user information.

Dor Litvak, Liu Leqi

The University of Texas at Austin

LLM Sycophancy LLM Hallucination Mitigation User Modeling LLM Uncertainty Estimation

Jul 14, 2026cs.CL

From Critic to Confidence: PPO for Language-Based Quantitative Prediction with Confidence Estimation

LLMs can perform language-based quantitative prediction from unstructured inputs, but remain susceptible to hallucinations and overconfident errors, making it critical to know not only what a model predicts, but when its predictions can be trusted. We introduce CARE-PPO, a reinforcement learning framework that establishes a connection between loss prediction for uncertainty estimation and actor-critic PPO fine-tuning, enabling joint learning of accurate numerical estimates and reliable confidence signals in language-based quantitative prediction. CARE-PPO uses a Confidence-Aligned Reward for Estimation, defined as a function of prediction error, to provide dense error-aware feedback to the actor while inducing the critic to learn a value function aligned with prediction quality. During inference, we repurpose the critic as a confidence estimator. Across two real-world tasks in healthcare and finance and two Qwen-3 model scales (4B and 8B), CARE-PPO achieves strong quantitative prediction performance, while producing significantly better-aligned confidence estimates through the critic than logit-based and verbalized baselines. These gains persist under realistic out-of-distribution settings across domains, spanning linguistic and domain shifts. Finally, CARE-PPO reduces task-specific overfitting on general instruction-following prompts, consistent with the broader generalization advantages of RL fine-tuning over supervised approaches.

Mehak Dhaliwal, Rasta Tadayon, Andong Hua +2

University of California, Santa Barbara

RL for Language Models Confidence Estimation in Language Models Language Model Calibration LLM Uncertainty Estimation Proximal Policy Optimization

Jul 14, 2026cs.LG

The Computational Basis of Confidence in Large Language Models

Reliable confidence -- the probability that a model's own answer is correct -- is essential for the trustworthy deployment of language models. Existing work has largely evaluated confidence by how well it predicts correctness and whether it is calibrated, leaving open a more fundamental question: what does the confidence signal itself represent? Answer logits may reflect a latent decision variable sufficient to compute normative confidence, or instead a heuristic preference signal that combines the available evidence in a non-Bayesian manner. We address this using statistical decision confidence (SDC), a normative framework from computational neuroscience. Treating the answer-logit difference (LD) as a candidate readout of the latent decision variable, we test the qualitative signatures predicted by SDC. Across three perceptual discrimination tasks and a memory-based decision task, spanning three multimodal non-reasoning models and one reasoning model, LD satisfied these signatures -- including the diagnostic correct/error folded-X pattern -- showing that, in these settings, answer logits behave as monotonic readouts of a latent decision variable rather than heuristic preference scores. In complex visual reasoning, LD continued to predict correctness beyond objective task difficulty, but the full geometric signatures of SDC were absent, illustrating the current boundary of the framework when explicit normative process models are unavailable. These results provide a computational account of confidence in multimodal language models, delineate when answer logits behave as readouts of a latent decision variable, and establish SDC as a unifying framework for studying confidence across biological and artificial intelligence.

Dharshan Kumaran, Viorica Patraucean, Maks Ovsanikov +2

Google DeepMind · Google DeepMind and École Polytechnique · École Polytechnique +1

Confidence Estimation in Language Models LLM Uncertainty Estimation

Jul 14, 2026cs.AI

Critic Experience Bank: Self-Evolving Step-Level Confidence Estimation for LLM Agents

LLM agents act in external environments where each action changes the state that later decisions condition on, and where a single wrong step can waste interaction budget or trigger irreversible side effects long before the final failure is observed. Reliable deployment therefore requires \emph{step-level confidence estimation}: a calibrated probability that each proposed action is productive, available \emph{before} the action is executed. Existing LLM confidence estimators are designed to score a response from the given prompt, but agent confidence also depends on execution consequences: whether similar actions in similar situations actually advanced the task after the environment responded. We introduce the \method (\methodshort), a self-evolving critic framework in which an LLM critic accumulates evidence from its own past judgments and their observed consequences. After each trajectory, a hindsight LLM that sees the full execution feedback votes on whether each step was productive. The resulting pseudo-labels populate a memory bank from which related productive and unproductive experiences are retrieved into the critic's prompt whenever a similar step recurs. \methodshort requires no training and uses no ground truth step labels. Across three agent benchmarks and three critic backbones, \methodshort attains the best calibration (ECE and Brier) and ranking (AUC) in every dataset--critic combination, reducing ECE by up to

54\%

relative to the strongest training-free baseline.

Yaopei Zeng, Congchao Wang, JianHang Chen +3

Pennsylvania State University · Virginia Tech · Purdue University +1

AI Agent Reliability LLM Agent Evaluation LLM Uncertainty Estimation LLM Agent Reliability Memory-Augmented Language Model Agents

Jul 14, 2026cs.SE

Code-MUE: Measuring Code LLMs' Uncertainty through Execution-based Semantic Interaction Graphs

As Code Large Language Models (LLMs) become central to modern software engineering, their inherent stochasticity poses significant real-world risks, where even minor errors can lead to severe functional, security, or safety consequences. Reliable automation, therefore, demands the ability to distinguish between confident, well-supported predictions and stochastic guessing. However, existing uncertainty estimation methods face a critical gap: white and grey-box techniques are often inapplicable to closed-source models, while standard "black-box" text metrics fail to capture the unique fragility of code, where syntactic variation does not always imply semantic divergence. To bridge this syntax-semantics gap, we introduce Code-MUE, a purely black-box framework that measures uncertainty through execution-based Semantic Interaction Graphs. Unlike prior approaches that rely on superficial textual similarity, Code-MUE grounds uncertainty in observable runtime behavior, calculating the Von Neumann entropy of the solution space to quantify global semantic diversity. A large-scale empirical study across eight state-of-the-art LLMs demonstrates that Code-MUE achieves a strong negative correlation with functional correctness (Spearman's correlation up to -0.98), significantly outperforming lexical and embedding-based baselines while enabling robust risk detection and selective prediction in practical workflows.

Xiaoning Ren, Yinxing Xue, Lei Ma +1

Xi’an Jiaotong University, China · Institute of AI for Industries, Chinese Academy of Sciences, China · The University of Tokyo, Japan +1

Uncertainty Quantification LLM Uncertainty Estimation Code Language Models

Jul 13, 2026cs.CL

Confidently Wrong: Detecting Hallucinations in Financial Question Answering from LLM Internal States

Large language models (LLMs) in financial applications fail most consequentially when they are confidently wrong. Hedged, uncertain answers invite scrutiny, whereas confident errors silently degrade downstream decisions without warning. We ask how reliably such confidently wrong answers, or confident hallucinations, can be detected from a model's internal activations, and whether those activations carry information beyond its observable outputs. We train linear probes on the residual stream and evaluate them on two established question-answering (QA) benchmarks built from real filings, FinQA and TAT-QA. Behavioral confidence is measured as the agreement among eight resampled answers to the same question, and probe effectiveness is compared against baselines, such as token log-probabilities and the model's own True/False self-assessment of its answer. Our findings show that among confident answers, those for which all eight resamples agree, 15-23% are wrong on FinQA. There the probes have a significant advantage over baseline methods in detecting hallucinations, holding 0.68-0.77 AUROC while the best baselines fall to 0.55-0.63, across Qwen3-8B, Llama-3.1-8B, and Gemma-2-9B. Our results suggest that probing can be a cost-effective triage mechanism for routing LLM answers to human review and quality control procedures in high-stakes financial applications.

Richard Zhe Wang

St. John Fisher University Rochester, NY, USA

Financial QA LLM Hallucination Detection LLM Uncertainty Estimation Language Model Probing Finance

Jul 12, 2026cs.LG

Reliability Scaling Laws for Quantized Large Language Models

Quantization is a powerful strategy to build capable and resource-efficient large language models (LLMs) by reducing the bitwidth of the parameters. While quantized LLMs achieve state-of-the-art performance on unperturbed inputs using standard predictive metrics, their performance on perturbed inputs, measured using reliability metrics, remains underexplored, despite its importance for reliable deployment. To address this gap, we first conduct a comprehensive reliability evaluation of quantized LLMs consisting of three key components: (1) Uncertainty: We assess the trustworthiness of LLMs quantized to 2, 3, 4, and 8 bits using six different quantization methods, employing established uncertainty metrics. (2) Calibration: We assess how well-calibrated the uncertainty estimates of quantized models are across model scales and bit precisions. (3) Robustness: We design character-level and word-level input perturbations to evaluate the reliability of quantized models under semantically-preserving variations in the inputs that arise in real-world applications. Second, we characterize how reliability scales with the total number of model bits. Our study reveals that while the performance scales monotonically with the total number of bits, the reliability scalings are nonlinear. A reliability peak occurs for 4-bit quantized models, indicating that quantizing moderately sized models offers the best reliability-efficiency trade-off. Additionally, our empirical findings reveal that quantization enhances the robustness of LLMs to natural input perturbations.

Sirine Ayadi, Sándor Daróczi, Stephan Günnemann +1

School of Computation, Information and Technology, Technical University of Munich Munich Data Science Institute · Pruna AI

LLM Quantization Language Model Calibration LLM Reliability LLM Uncertainty Estimation Language Model Robustness

Jul 11, 2026cs.CL

Hallucination Detection in Large Language Models Using Diversion Decoding

Large language models (LLMs) have emerged as a powerful tool for retrieving knowledge through seamless, human-like interactions. Despite their advanced text generation capabilities, LLMs exhibit hallucination tendencies, where they generate factually incorrect statements and fabricate knowledge, undermining their reliability and trustworthiness. Multiple studies have explored methods to evaluate LLM uncertainty and detect hallucinations. However, existing approaches are often probabilistic and computationally expensive, limiting their practical applicability. In this paper, we introduce diversion decoding, a novel method for developing an LLM uncertainty heuristic by actively challenging model-generated responses during the decoding phase. Through diversion decoding, we extract features that capture the LLM's resistance to produce alternative answers and utilize these features to train a machine-learning model to develop a heuristic measure of the LLM's uncertainty. Our experimental results demonstrate that diversion decoding outperforms existing methods with significantly lower computational complexity, making it an efficient and robust solution for evaluating hallucination detection.

Basel Abdeen, S M Tahmid Siddiqui, Meah Tahmeed Ahmed +4

The University of Texas at Dallas, Richardson, TX 75080, USA · National Institute of Standards and Technology, Gaithersburg, USA · Carnegie Mellon University, PA, USA

Hallucination in Language Models LLM Hallucination Detection LLM Uncertainty Estimation

Jul 9, 2026cs.CL

Two Axes of LLM Abstention: Answer Correctness and Question Answerability

A model should refuse two different things: answers it would get wrong, and questions it should not answer at all, such as unanswerable ones or ones resting on a false premise. The usual recipe thresholds a single confidence score, which cannot tell these apart. Across five instruction-tuned models from three families (2B to 14B), we find they are separate axes. Ordinary answer-confidence tracks whether an answer is right but is nearly blind to whether the question is answerable; a linear probe on hidden states does the reverse. The blind spot does not shrink with scale. It is worst on naturally occurring false-premise questions (CREPE). There, answer-confidence, P(IK), P(True), and even asking the model outright whether a premise is false all stay near chance, while a hidden-state probe reaches 0.69 to 0.77 AUROC: the model represents a problem it will not report. This turns out to be fixable. Instructing a model to check premises backfires, because it then disputes sound and false premises alike (57% false challenges), unable to tell them apart; routing the same instruction with the probe roughly triples challenge precision. We turn the two axes into a calibrated policy that answers only when an answerability score and a correctness score each clear a separately certifies behave differently: the unanswerable-answer rate is controllable at every scale, while the wrong-answer rate is capped by model accuracy, so the guarantee tightens as threshold policy certifies both budgets at 0.75 coverage of correct answers, against 0.31 for a single threshold; at 14B it is the only policy that certifies at all.

Benedikt J. Wagner

City St George’s, University of London

Selective Prediction Confidence Estimation in Language Models LLM Uncertainty Estimation Refusal Behavior in Language Models

Jul 9, 2026cs.LG

Eigenvalue Calibration for Semantic Embeddings of Large Language Models

Uncertainty quantification is central to the reliable deployment of large language models (LLMs), and eigenvalues of semantic embeddings have recently emerged as a key tool in state-of-the-art methods. However, conventional calibration results developed for classification probabilities cannot be directly transferred to eigenvalues. We address this gap by proposing a novel framework for calibrating the eigenvalues of semantic embeddings. We interpret LLMs combined with semantic embeddings of their generated answers as density matrix predictors, and we propose a novel approach to calibrate density matrix predictors by applying temperature scaling to their eigenvalues. We establish entropy-risk equivalence under calibration, derive a central calibration inequality specific to eigenvalues, and prove that temperature-scaled eigenvalues optimize calibration when minimizing proper score risks. Experiments on a variety of real-world settings show that current LLMs are systematically overconfident, and validate our theoretical findings. Together, these results advance the foundations and practice of uncertainty quantification for semantic embeddings.

Sebastian G. Gruber, Nassim Walha, Francis Bach +1

1ESAT-PSI, KU Leuven, Belgium · 2German Cancer Research Center (DKFZ), Heidelberg, Germany · 3German Cancer Consortium (DKTK), Germany +3

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