Large Language Model Uncertainty

In high-stakes decision-making applications of large language models (LLMs), practitioners require not only accurate LLMs but also uncertainty estimates for their predictions. Existing approaches to uncertainty estimation for LLMs require access to log-probabilities output by the model or require fine-tuning access. However, many industrial LLM products use closed-source API models, and many such API models like GPT do not return log-probabilities and may not allow fine-tuning. We introduce Pinocchio, an external calibrator that estimates the correctness of responses from black-box API models. Trained jointly on responses from seven LLMs, it achieves 0.862 AUROC predicting the correctness of held-out responses from those same models, and shows zero-shot transfer to thirteen unseen models across eight organizations. Our model needs only a single forward pass to generate an uncertainty estimate and requires no access to the target model's logits, weights, or internal states. A lightweight text only 0.8B checkpoint matches our largest model's AUROC. We release code for adding uncertainty estimation to existing repos in only two additional lines of code.

Large Language Models (LLMs) frequently exhibit hallucinations, presenting a major barrier to reliability in complex reasoning tasks. While traditional detection methods rely on output-based confidence metrics, these logits are often miscalibrated by modern alignment techniques. In this paper, we investigate the temporal volatility of internal attention mechanisms as an alternative diagnostic signal for hallucination that does not depend on output calibration. By introducing an unsupervised metric for attention dispersion, we show that epistemic uncertainty leaves a measurable trace within intermediate layers, where spikes in attention entropy are associated with reasoning breakdowns. We evaluate our approach on mathematical reasoning benchmarks (GSM8K and MATH-500) using the Qwen2.5 model family (1.5B and 3B parameters), finding statistically significant AUC improvements of up to +0.076 over output-based baselines across all tested conditions. These findings suggest that attention dispersion is a promising complement to traditional hallucination detection methods, requiring further investigation across broader model families and task domains.

Multimodal large language models (MLLMs) have made strong progress on visual question answering and image captioning, yet they still produce fluent claims about objects, attributes, or relations that are not grounded in the image. Many remedies either modify decoding at test time, which adds latency, or fine tune with preferences such as DPO variants, which teach which answer is preferred but not when the model's own answer is unreliable. We argue that calibrated self assessment is the missing signal. We introduce Savor, a training framework that (i) augments the output schema with token and answer confidence, (ii) optimises the policy with a Group Relative Policy Optimisation (GRPO) objective that penalises calibration error and poor abstention decisions, and (iii) uses the learned confidence at inference time to revisit visual evidence only when the model is uncertain. Experiments on POPE, HallusionBench, AMBER and MMHal-Bench across two recent backbones (InternVL3-8B and Qwen3-VL-8B) show that Savor reduces hallucination while preserving general capability on MME and MMBench, with lower Expected Calibration Error than DPO and decoding baselines.

Vision-language models are increasingly explored for clinical prediction from electronic health records and medical images, where identifying unreliable predictions is important for safe deployment. Uncertainty estimation (UE) enables detecting such predictions, but its evaluation depends on a correctness criterion that determines whether each model output is correct. If this criterion disagrees with human judgement or distorts downstream UE performance, conclusions about model reliability can be misleading. We introduce a two-axis framework that evaluates correctness criteria by their agreement with human judgements and fidelity to human-referenced UE performance. We assess eight criteria across three clinical prediction tasks and three models using 450 predictions annotated by two reviewers. Across the audited tasks, canonical exact matching (EM) achieved the highest observed human agreement and lowest UE distortion, while the BERT-based matching (BEM) and LLM-judge also showed strong human agreement. Across four UE methods and 23,254 clinical predictions, criterion choice changed error-detection AUROC by up to 0.146 and reversed the relative ranking of UE methods. The LLM-judge also selectively accepted invalid or uncertain outputs, accepting 16 of 30 such human-identified errors. These results demonstrate that correctness assessment is an integral component of clinical UE evaluation and should be validated before UE methods are compared.

A key challenge in reliable LLM deployment is recognizing when uncertainty reflects irreducible variability in the task rather than limitations in the model's knowledge. In language tasks, a central source of such aleatoric uncertainty is input ambiguity or underspecification, where multiple interpretations remain plausible. Existing decomposition methods estimate aleatoric uncertainty by generating multiple clarifications of the input, querying the model for an answer under each clarification, and comparing the resulting answers. We argue that answers are not necessary for identifying ambiguity: they are often redundant, add avoidable cost, and can mislead through epistemic leakage. We support this claim theoretically, and propose a clarification-only approach that estimates this ambiguity-induced component directly from the space of plausible interpretations, without answers to the clarified inputs. Using ambiguity detection as an operational evaluation across three benchmarks, this direct approach improves AUROC (63.34 vs. 60.85), reduces computational cost by 4-26x in output tokens and 2.2-3.5x in API calls, and yields estimates with substantially lower correlation with epistemic uncertainty. Overall, our results suggest that ambiguity-induced aleatoric uncertainty is better estimated from the interpretation space than from the response space.

Reliable uncertainty estimation is a crucial requirement for deploying large language models (LLMs) and vision-language models (VLMs) in safety-critical settings, especially when the model parameters are not accessible (black-box). We propose BiG-SURE, an uncertainty estimator based on cross-temperature semantic agreement. The method samples low-temperature responses as stable semantic anchors and high-temperature responses as probes under meaning-preserving input transformations. It then constructs an anchor-probe Bipartite Graph (BiG) using NLI-based entailment scores and defines confidence through the normalized squared spectral energy of this matrix, with uncertainty given by its complement. This bipartite graph-based Semantic Uncertainty and Reliability Estimation (SURE) score measures whether high-temperature probes remain semantically aligned with the model's stable low-temperature belief or not. We evaluate BiG-SURE on text QA, multilingual QA, and multimodal QA tasks across multiple model families. In these experiments, BiG-SURE improves average abstention AUROC over prior black-box uncertainty estimators, while remaining simple, unsupervised, and applicable to black-box model settings.

LLM-based multi-agent systems (MAS) solve complex tasks through communication among role-specialized agents. However, inter-agent dependencies introduce reliability risks beyond isolated agent failures. For instance, errors in intermediate messages could be inherited and amplified by downstream agents. Existing uncertainty quantification (UQ) methods mainly target isolated responses or single-agent reasoning, and therefore fail to capture uncertainty propagation in MAS. To this end, we propose PropUQ-MAS, an error propagation-aware UQ framework that represents MAS execution as a communication-structured graph and estimates each step's reliability by combining local uncertainty with uncertainty inherited from upstream messages. Extensive experiments demonstrate that PropUQ-MAS consistently improves UQ in MAS, with average relative gains of +6.10% in AUROC and +47.58% in PRR.

Large language models (LLMs) may generate fluent but incorrect answers, making uncertainty quantification important for reliable question answering. However, heuristic uncertainty scores cannot perfectly distinguish correct predictions from incorrect ones, and directly applying a fixed uncertainty threshold provides no statistical control over the error rate among accepted answers. To address this limitation, we propose A-CRC-QA, a post-hoc calibration framework for uncertainty-aware selective question answering. The proposed method reformulates selection-conditioned error control as a linear expectation constraint and applies a monotonized empirical-risk calibration procedure inspired by conformal risk control. Since the resulting instance-wise loss is generally non-monotone with respect to the acceptance threshold, our framework targets asymptotic rather than finite-sample risk control. A-CRC-QA is model-agnostic, requires no additional training, and can be combined with different uncertainty estimators. Experiments on CoQA and MedMCQA demonstrate its applicability to both open-ended and closed-ended question answering, achieving a favorable trade-off between accepted-answer reliability and answer retention compared with uncalibrated and confidence-bound-based baselines.

In open-domain human-computer interaction scenarios, large language models (LLMs) frequently encounter user queries that are ambiguous or incomplete. In such cases, directly producing an answer often leads to overgeneralized, erroneous, or low-information responses. In contrast, asking clarifying questions can substantially improve interaction quality. However, existing approaches still rely heavily on manually annotated data or preference alignment to address two fundamental challenges: when clarification is necessary, and which aspect of the query should be clarified. This reliance incurs high annotation costs and limits generalization. To address these challenges, we propose CLAIM, an uncertainty-driven framework for active clarification learning in open-domain settings. CLAIM eliminates the need for explicit human preference annotations by quantifying query uncertainty through the entropy induced by answer disagreements across multiple models. This uncertainty signal is then used to construct high-quality synthetic data, enabling the training of a unified clarification decision model through a combination of supervised learning and reinforcement learning. Specifically, we propose an entropy-driven synthetic data generation pipeline that integrates entropy-based uncertainty estimation with semantic clustering and reasoning-based judgments, enabling reliable automatic annotation of clarification requirements. To train CLAIM, we formulate the clarification process as a structured decision generation problem and adopt a training paradigm that combines supervised fine-tuning (SFT) with group-relative policy optimization (GRPO). Experimental results demonstrate that CLAIM can learn stable and generalizable clarification strategies without relying on manually labeled data, offering a low-cost and robust solution for proactive understanding in real-world open-domain interactions with LLMs.

Uncertainty quantification (UQ) methods for language models are typically evaluated on single-turn outputs, where uncertainty is attached to one generated answer. For LLM agents, however, the unit of observation is an interactive trajectory, where the model can ask clarifying questions, call tools, update state, and make intermediate decisions whose errors propagate to the final outcome. We study whether three common families of single-turn UQ methods transfer to this setting. Across five LLMs and four multi-turn tool-use datasets from BFCL-v4 and $τ^2$-bench, we evaluate white-box scorers based on action-token probabilities, black-box consistency scorers based on resampled trajectories, and reflexive scorers based on model self-assessment of the trajectory. We find that transfer is often useful but uneven. Token-probability scores are highly sensitive to the choice of aggregator used across turns, reflexive scores provide the strongest low-cost baseline in most evaluated settings, and black-box self-consistency is often the strongest UQ family, with trajectory-equivalence and action-set consistency typically ranking highest among its variants. These results suggest that UQ methods developed for single generations should be revalidated at the trajectory level, with careful attention to the consistency measurement, aggregator choice, and computational budget.

We propose that a model's uncertainty about a token is reflected not only in the breadth of its output distribution but also in whether a confident prediction is \emph{fragile} under perturbation of its attention pathways. We instantiate this as ASMI (Attention-Subnetwork Mutual Information), a training-free estimator that masks attention heads and measures the BALD mutual information among the resulting subnetworks, with a semantic-agreement kernel to discount surface-form disagreement. The signal is not a restatement of output confidence: on grounded QA an out-of-fold test shows it adds error-predictive information beyond single-pass confidence and entropy, concentrated in \emph{confident-but-fragile} predictions, where acting on it roughly halves the retained error of a confidence filter. The distinctness is regime-graded, so ASMI predicts its own domain of applicability, strong where answers are routed through provided context and bounded by design where they are recalled from parametric knowledge. Sem-ASMI reads the signal from a single greedy response, without the stochastic generations the strongest baselines require, and ties or beats Semantic Entropy on ten of the twelve grounded benchmark-backbone settings. Across the same twelve settings, the best ASMI variant, typically the adaptive one reusing the ten samples already drawn for the baselines, ties or leads the strongest baseline in eight, significantly in three under a paired test. On parametric QA all variants revert to or below the zero-cost MSP baseline, exactly as predicted, and the estimates are near-deterministic across reruns. A head-level analysis shows that what tracks this boundary is not the presence of head-level fragility but whether that fragility couples to errors.

Recent research on Large Language Model (LLM) safety has widely adopted guardrails to identify unsafe LLM outputs. Existing guardrails typically formulate safety assessment as a deterministic classification task, mapping a discrete token sequence to a discrete safety label. However, this paradigm has two limitations: First, safety assessment is inherently an uncertain problem, particularly during the early generation state. Second, relying solely on discrete token sequences discards the rich probabilistic information embedded in the LLM output distribution. To address these limitations, we propose the first completely probabilistic architecture-agnostic guardrail \textsc{ProbGuard} to leverage the LLM early output distributional signals for estimating and calibrating the safety probability, thereby enabling early stopping of unsafe ongoing outputs. Specifically, given an LLM's generated prefix distribution, we formulate the safety risk as the unsafe probability of its continued generation dynamics and estimate this risk by Monte-Carlo sampling. Through post-training on the distributional signals and calibrated safety risk, \textsc{ProbGuard} achieves the best calibration performance across all nine model--dataset combination settings, reducing the average Brier score and ECE by 79.6% and 71.9%, respectively, over the best baseline. \textsc{ProbGuard} further limits the attack success rate to at most 1% across six representative jailbreak attacks after observing the LLM early output distributions from only the first ten decoding steps.

Large Language Models (LLMs) deployed as AI agents frequently exhibit user specification-grounding failures, executing hallucinated, undesired actions to force a resolution rather than expressing uncertainty. Existing detection methods fail to provide actionable, real-time correction as they either do not localize the hallucinations, or incur prohibitive inference latency. We introduce the Latent Critic, a lightweight low-rank adapter (LoRA) that operates concurrently with a frozen base LLM's generation to actively restructure the transformer's residual stream---amplifying latent grounding signals and translating them into localized, natural language feedback within a single sequence. By refining the base model's native uncertainty signals, this manipulation of the latent space enables reliable, granular detection without the overhead of secondary inference loops. Mechanistic analysis via activation patching and layer-wise probing shows that this rank-invariant behavior restructures pre-existing uncertainty geometry into a linearly separable representation that transfers more reliably than base model representations alone. Using tool-calling as an instantiation of granular hallucinations, we validate the detection and downstream improvements enabled by the Latent Critic architecture across Qwen and Llama-based models. Demonstrating superior real-time efficacy, our approach significantly outperforms equivalent-scale fine-tuned external detectors, semantic entropy baselines, and passive internal probes in isolating hallucinations, achieving 0.966 AUROC and >80% accuracy in localization (e.g., ungrounded: date). When deployed in a closed-loop ReAct environment, the Critic acts as a negligible latency guardrail, intercepting hallucinations before execution to prevent undesired actions while simultaneously leveraging this specific localized feedback to enable efficient agent self-correction.

Large Language Models (LLMs) have achieved strong performance in medical question answering and clinical reasoning tasks. However, their reliability under uncertainty remains poorly understood which raises critical concerns for deployment in high-stakes clinical settings. In such environments, incorrect predictions are inherently risky, but confident incorrect predictions can be particularly harmful as they may mislead clinical decision-making. In this paper, we conduct a systematic behavioral analysis of LLMs under clinical information uncertainty. We propose an evaluation framework based on the MedMCQA dataset consisting of two complementary uncertainty settings. First, we introduce linguistic uncertainty cues through prompt modifications to simulate ambiguous clinical contexts. Second, we construct an answer removal setting, wherein the correct option is deliberately excluded mandating the model to recognize insufficient information and abstain. We analyze both model accuracy and confidence behavior using multiple calibration metrics including calibration gap, Expected Calibration Error (ECE), and Unsafe Confident Error Rate (UCER) across 500 medical questions. Our results reveal a consistent failure mode, i.e., although accuracy degrades under increasing uncertainty, model confidence remains misaligned with accuracy. This leads to a substantial increase in unsafe confident errors, indicating that model confidence remains largely insensitive to clinically meaningful information loss. Furthermore, we observe significant variation across models in their ability to abstain when the correct answer is unavailable, with some models persistently producing high confidence hallucinated answers. These findings expose critical limitations in the epistemic reliability of current LLMs and highlight the need for uncertainty aware evaluation methods prior to their deployment in clinical workflows.

Preference alignment often makes large language models (LLMs) overconfident and poorly calibrated. Traditional post-hoc temperature scaling is inherently domain-dependent: a temperature fitted on one domain does not generalize across domains. This motivates us to modify model parameters during training to improve calibration. We propose maximizing the entropy of predictive distributions as the calibration objective, which directly targets overconfidence by discouraging overly concentrated predictions. Inspired by temperature scaling, we realize this through a bilevel optimization formulation, where the lower level trains the model under a parametric loss and the upper level selects loss hyperparameters to maximize entropy. To make the framework practical at LLM scale, we adopt an efficient first-order approximation that avoids explicit second-order computation. Across both multiple-choice and open-ended generative question answering, experiments demonstrate that our method yields well-calibrated LLMs with particular advantages in out-of-domain generalization.

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.

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.

Large vision--language models (LVLMs) demonstrate strong multimodal reasoning capabilities but remain prone to hallucination, where model predictions are not grounded in visual evidence. Existing black-box hallucination detection methods estimate uncertainty through a single consistency metric, implicitly assuming that model uncertainty can be adequately characterized by a single measure. However, hallucinations exhibit diverse manifestations of uncertainty across different behavioral probes, making a single measure insufficient to characterize their underlying behavior. We propose \emph{Unique Hallucination Pattern (UHP) Detection}, a fully black-box framework that models hallucination as a structured uncertainty pattern defined by two axes: perturbation modality (image vs.\ text) and logical polarity (a statement vs.\ its negation). Their intersection produces four complementary consistency groups that capture distinct manifestations of model uncertainty, from which both within-group and between-group features are extracted to train a lightweight classifier. Through comprehensive experiments on AMBER and PhD across three LVLMs, UHP Detection consistently outperforms prior black-box and white-box baselines, with improvements of up to $+18.72\%$ AUC-ROC and $+20.07\%$ AUC-PR over the strongest black-box methods. Extensive ablation studies demonstrate that each consistency group contributes complementary information and that their combination forms a structured hallucination pattern. Furthermore, cross-dataset evaluation shows that this learned pattern generalizes across benchmarks, indicating that hallucination behavior reflects a model-specific consistency pattern. \textbf{Code is publicly available at} https://github.com/amirezzati/uhpdet.

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.

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.

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.

Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities in multimodal understanding and generation. However, when textual inputs conflict with visual evidence, they still suffer from hallucinations and produce responses inconsistent with visual content. Existing approaches mainly rely on decoding strategies, additional training, verification methods, or prompting techniques, but often lack fine-grained conflict localization and conflict-aware generation. In this work, we propose CAER, a backbone-agnostic framework for visual-language conflict detection and conflict-aware generation. CAER introduces a span-grounded evidence router that transforms claim representations into soft textual queries and retrieves corresponding evidence from frozen visual tokens, enabling fine-grained conflict estimation. Furthermore, we design a dual-prefix expert routing mechanism that learns separate experts for visually supported and contradicted inputs, enabling conflict-aware generation through explicit expert selection. Experiments on the public MMMC benchmark and our newly curated AgriConflict dataset demonstrate that CAER effectively detects visual-language conflicts and improves the reliability of open-source MLLMs without updating their backbone parameters.

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.

This paper investigates how multi-agent systems (MAS)-based on large language models (LLMs) can support actuarial risk modelling, with a particular focus on uncertainty quantification. Actuarial workflows represent a high-stakes decision-support setting where unreliable outputs may lead to incorrect risk assessment, unfair pricing, and regulatory non-compliance. To address uncertainty introduced by the probabilistic nature of LLMs and dependencies between agents, a multi-agent framework is proposed in which specialised agents perform data preparation, modelling, review, and explanation tasks under a central hub. The main contribution is a novel approach to uncertainty propagation using token-level log-probabilities and a Bayesian Network. Importantly, log probabilities are not treated as direct probabilities of correctness or task success. Instead, length-normalised log-probability summaries are transformed into calibrated task-level confidence estimates before incorporation into the Bayesian Network. Results show that the framework reproduces baseline actuarial performance while providing additional insight into workflow stability and runtime uncertainty propagation.

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.

Vision-language models (VLMs) are increasingly deployed on consumer hardware where input images are degraded by compression, camera shake, and poor lighting. In such settings, a reliable uncertainty signal matters more than raw accuracy, because it determines when a system should defer rather than answer. We evaluate two small open-weight VLMs -- Qwen2-VL-2B-Instruct and SmolVLM-Instruct -- across six realistic photographic degradations at three severity levels, comparing two confidence signals: the confidence the model states in natural language, and the model's own mean token probability over its generated answer. Across 3,800 predictions, we find a large and consistent gap. Verbalized confidence in Qwen2-VL is almost constant (mean 0.87-0.90 across all conditions) and detects its own errors at chance level (AUROC 0.39-0.75, typically ~0.50), while internal token probability from the same model separates correct from incorrect answers with AUROC 0.92-0.99. In SmolVLM, verbalized confidence proved largely unobtainable: across three prompt templates, only one of five pilot attempts produced a parseable confidence value, while internal probability again yielded above-chance error detection (AUROC 0.54-0.92). Both models fail in the same place: under severe underexposure, accuracy collapses (0.99->0.22 for Qwen2-VL, 0.97->0.42 for SmolVLM) while both confidence signals barely move, and internal error-detection falls to chance. We conclude that small VLMs encode usable self-knowledge that their verbalized output does not express, that internal probability is therefore the better deferral signal in constrained deployment, and that neither signal should be trusted under severe low-light conditions.

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.

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.

Existing hallucination detection methods are typically conducted at the inference stage, without making any modifications to the model itself. In this paper, we are interested in exploring fine-tuning strategies that enhance the detectability of hallucinations in the resulting model. Focusing on semantic-entropy-based detection, we observe that many erroneous outputs remain undetected because the model produces nearly identical incorrect answers across multiple runs. To address this, we propose diversity-oriented fine-tuning to encourage more varied generations. We introduce two specific strategies: one based on Supervised Fine-Tuning (SFT) and the other on Direct Preference Optimization (DPO). Extensive experiments are conducted to evaluate our approach and analyze the behavior of the models before and after fine-tuning. We find that after adopting our fine-tuning methods, the models become less likely to produce low semantic entropy responses for hallucinated answers, thereby improving the effectiveness of hallucination detection, eventually yielding results better than or comparable with state of the art methods. The code will be publicly released.

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.

Learning temporal logic specifications from system demonstrations is essential for tasks such as formal verification and controller synthesis, especially in safety-critical domains. Existing approaches typically assume demonstrations are correct or only affected by misclassification errors. In practice, however, system traces are often uncertain or incomplete due to sensor faults, measurement errors, or data loss. We present a framework for learning minimal Linear Temporal Logic (LTL) formulas from demonstrations with uncertainty. Our approach models uncertainty via Hamming distance to generate possible estimates around each observed trace, which are grouped with constraints requiring that at least one trace per group is consistent with the learned formula. Our problem is then reduced to an equivalent Pseudo-Boolean Optimization. We evaluate our method against state-of-the-art LTL learning approaches and show that it recovers specifications that more closely align with ground-truth formulas under uncertainty.

Retrieval-augmented generation grounds large language models in external evidence, but most pipelines still treat retrieved passages as deterministic and mutually consistent context. In open information environments, retrieved sources may disagree because of temporal drift, source error, ambiguity, or genuine uncertainty. This paper introduces ERAG, an uncertainty-aware RAG framework that converts retrieved chunks into probabilistic evidence before generation. A lightweight evaluator extracts candidate claims and maps chunk-level support to Dirichlet evidence. A conflict-preserving Dempster-Shafer fusion rule then transfers unresolved disagreement into epistemic uncertainty rather than normalizing it away. The generator is routed to direct answering, conflict-aware answering, or abstention according to the fused uncertainty score. Experiments on CRAG, ConflictQA, and MuSiQue show that ERAG remains competitive with the strongest matched baseline on standard question answering while improving behavior under conflict. On the CRAG ambiguous subset, hallucination decreases from 45.3% for Corrective RAG to a human-calibrated estimate of 34.8%, conflict resolution increases from 35.2% to 51.2%, and expected calibration error improves to 0.122. These results suggest that evidential modeling is a practical mechanism for trustworthy information processing in foundation-model-based retrieval systems.

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.

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.

Uncertainty estimation (UE) enables LLM-powered systems to recognize when to abstain, yet existing research has predominantly focused on English. We present the first large-scale evaluation of UE methods across 22 languages, spanning high-, mid-, and low-resource settings. Using two human-curated Q&A datasets, we compare open and closed box UE methods (nine in total) across different model sizes and architectures while eliciting long-form reasoning, avoiding LLM-as-a-judge and embedding-based scoring, which can introduce evaluation noise. We report three main actionable findings. First, we find that prompting models to reason in English while keeping questions in low-resource languages substantially improves UE performance, suggesting that comprehension of low-resource languages is largely intact, and that the reliability bottleneck lies in generation rather than understanding. Second, prompting models to reason in English closes the UE performance gap between low and high-resource languages, demonstrating that generation language matters more than the question language. Third, the choice of UE method should depend on model scale: at smaller scales, open-box probability-based methods outperform alternatives; at larger scales, closed-box self-verbalized uncertainty becomes superior. Finally, we provide an analysis of threshold selection for selective prediction, offering guidance on calibrating abstention in multilingual settings.

Multimodal large language models can emit localized predictions, bounding boxes for objects and temporal windows for video and audio events, but they hallucinate these regions prolifically. The model's own token log-probabilities are nearly uninformative: they conflate grounding quality with input ambiguity, and coordinate tokens become near-deterministic once the model commits. We propose Multi-Token Localized Attention (MTLA): a training-free, post-hoc score that measures how strongly a prediction's tokens attend to the region they claim. Prior attention-based detectors, which sum attention over the entire input modality and read a single response token, are weaker special cases; we show that summing only within the claimed region and aggregating across all prediction tokens recovers a stronger grounding signal. The same recipe applies almost trivially to other modalities and tasks: object detection in images and temporal localization in video and audio. Across multiple MLLM families and three modalities, MTLA improves hallucination AUROC by +7 to +38 over the best prior training-free baseline. Used as a confidence score for re-ranking, it nearly doubles the zero-shot COCO detection AP of an open-source 8B generalist (from 20.4 to 37.0), narrowing the gap to supervised detectors without any task-specific training.

Uncertainty estimation is essential not only for the trustworthy deployment of large language models (LLMs) but also as a foundation for self-refinement in LLM generation. However, existing approaches operate at suboptimal granularities: token-level scores lack semantic coherence, while sequence-level scores fail to localize errors. We formalize Span-Level Uncertainty Estimation (SLUE), a new task that targets the natural granularity for uncertainty: semantically coherent text spans, each conveying a single assessable unit of meaning. To address this task, we introduce SPANUQ, a lightweight probe that distills the uncertainty knowledge from expensive multi-sample inference into a single forward pass over LLM hidden states. SPANUQ employs a DETR-style span decoder to simultaneously detect spans and estimate their uncertainty via a Mixture of Beta distribution, trained with a principled combination of Beta NLL regression and contrastive ranking objectives. We construct SPANUQ-BENCH, the first span-level uncertainty benchmark comprising 20K prompts, 293K annotated spans, and continuous soft labels derived from multi-sample claim verification. Experiments on five LLM backbones show that SPANUQ consistently achieves the best span-level uncertainty quality, outperforming the strongest probe baseline and all sampling-based methods while being 10-20x faster. Its DETR-based span detector attains 0.910 F1, surpassing the best heuristic by 39.4%, enabling precise error localization that sequence-level methods cannot provide. The framework generalizes across five LLMs spanning two model families.

Large language models (LLMs) are increasingly deployed in question answering (QA) systems, yet they may generate hallucinated or misaligned responses without reliable confidence estimates. Uncertainty quantification (UQ) offers a natural basis for selective answering, where a system answers only when its prediction is deemed reliable and abstains otherwise. However, existing uncertainty scores for LLMs are often heuristic: a threshold chosen on such scores does not, by itself, provide statistical guarantees on the error rate among accepted answers. We propose CIC, a confidence-interval-based calibration framework that converts arbitrary uncertainty scores into risk-controlled selective answering rules. Given a held-out calibration set, CIC evaluates each generated response using an application-specific alignment criterion and associates it with an uncertainty score and a binary error label. For each candidate uncertainty threshold, CIC estimates the acceptance-conditioned error rate and constructs a high-probability upper confidence bound using either Hoeffding-style or Clopper-Pearson confidence intervals. It then selects the largest threshold whose upper bound is below a user-specified risk level $α$, thereby maximizing the answering rate subject to a finite-sample reliability constraint. Under exchangeability, CIC guarantees with probability at least $1-δ$ that the selected threshold, if non-null, controls the error rate among accepted answers at level $α$. We evaluate CIC on both closed-ended and open-ended QA benchmarks across seven LLMs and multiple uncertainty estimators. Experimental results show that CIC consistently achieves valid risk control while retaining strong answering efficiency, providing a practical and statistically grounded mechanism for deploying LLMs in reliability-sensitive QA workflows.

As LLMs generate increasingly long outputs, effective uncertainty estimation must identify errors at fine-grained levels rather than discard entire responses. While such methods exist, evaluating uncertainty at any resolution (token to an entire generation) is challenging and highly sensitive to label imperfections, making zero-noise benchmarks essential; yet, long-form generation benchmarks tend to rely on fallible labels rather than deterministic ground truth. We introduce Single-answer Atomic Long-form Target (SALT), a benchmark of six procedurally generated tasks with single deterministic long textual ground truths, enabling unit-level evaluation of correctness, calibration, and ranking without external judges. Equipped with SALT, our analysis of 50+ LLMs reveals key insights: We identify which confidence functions dominate each uncertainty aspect and show that confidence ranking largely breaks at atomic resolution, even when clearer separability emerges at coarser line-level units. SALT further enables controlled atom-level interventions throughout generation, revealing two separable drivers of future errors: propagation from corrupted prefixes, dominated by global context correctness, and bounded degradation from increasing answer-context length. Finally, we demonstrate that reasoning, via Chain-of-Thought prompting or internalized through training, introduces a trade-off, improving accuracy while degrading confidence ranking. These findings directly impact risk-critical applications requiring reliable error identification and mitigation.

Large language models (LLMs) exhibit remarkable reasoning capabilities, but their task-specific fine-tuning is notoriously plagued by overconfidence, severely hindering trustworthy deployment. We propose Data-Adaptive Lower-Rank Adaptation (DALorRA), a simple and effective variational Bayesian sparse framework that shifts the paradigm of uncertainty quantification from the dense parameter space to the lightweight rank level of low-rank adaptation (LoRA). With the insight that LoRA essentially aggregates multiple rank-one components that may provide superfluous model capacity, DALorRA imposes stochastic masking on rank dimensions, enabling Bayesian regularization of model capacity during training and ensemble-like calibration during inference. Extensive experiments demonstrate DALorRA's excellent calibration of LLMs without compromising reasoning accuracy.

Trustworthy deployment of Agentic Retrieval-Augmented Generation (RAG) systems requires mechanisms for estimating when multi-stage reasoning pipelines may fail. This paper presents an uncertainty-aware Agentic Retrieval-Augmented Generation (RAG) framework in which planner, evaluator and generator stages produce uncertainty signals derived from semantic divergence and generator self-evaluation. These signals are propagated through a Bayesian Network (BN) to estimate system-level uncertainty and provide node-level indicators of potential failure points across the workflow. The approach is evaluated on StrategyQA and HotpotQA using GPT-3.5-Turbo and GPT-4.1-Nano, with Area Under the Receiver Operating Characteristic Curve (AUROC), Area Under the Accuracy-Rejection Curve (AUARC), Expected Calibration Error (ECE), and Brier Score used to assess discrimination, selective prediction and calibration. Results show that Bayesian propagation is more effective on HotpotQA, where uncertainty accumulates across multi-hop reasoning stages, while StrategyQA exposes limitations caused by miscalibration and unreliable upstream signals. The study positions Bayesian uncertainty propagation as a promising but preliminary mechanism for monitoring Agentic RAG systems, with future validation required in industrial domains such as Offshore Wind (OSW) maintenance decision support.

Metacognition is a critical component of intelligence that describes the ability to monitor and regulate one's own cognitive processes. Yet LLMs exhibit systemic deficiencies in key metacognitive faculties: they hallucinate with high confidence, fail to recognize knowledge boundaries, and misrepresent their internal uncertainty--undermining trustworthiness and reliability. Since monitoring task performance and adapting behavior accordingly are central to metacognition, we posit that models capable of accurately judging their own performance are better positioned to improve it. We operationalize this idea via two novel mechanisms: reinforcement learning with metacognitive feedback (RLMF), a paradigm to refine completion rankings during preference optimization based on the quality of a model's self-judgments of performance, and metacognitive data selection, which uses similar self-judgments to identify high-value training examples, outperforming naive active learning. We apply these innovations to the problem of faithful calibration (FC), a task that is itself fundamentally metacognitive: the goal is to align expressed with intrinsic uncertainty, difficult even for frontier LLMs. We adopt a two-stage, decoupled approach, first using these methods to calibrate the faithfulness of models' self-reported confidence scores, then mapping to natural, context-adaptable linguistic uncertainty via targeted output editing. Extensive experiments show RLMF achieves generalizable, state-of-the-art FC on diverse tasks while preserving accuracy. Further, RLMF surpasses standard RL by up to 63% while enhancing models' ability to assess and express their own capability limits. This positions RLMF as a promising paradigm to enhance LLM metacognition toward improved abilities and alignment, and suggests metacognitive performance as an effective RL signal to overcome limits of prior intrinsic feedback methods.

Uncertainty estimation has been a long-standing challenge in AI models; it amounts to "knowing what you don't know," and metacognition is notoriously difficult even for humans (cf. the Dunning-Kruger effect). Although it is still far from solved even in simpler classification systems, tackling it in multimodal large language models (MLLMs) is becoming increasingly important. Within MLLMs, uncertainty can stem from any of the diverse sources as well as from their relationships, and further can stem from the unbounded answers in the open-ended setting. To tackle the issues, we propose CoMet, an MLLM uncertainty estimation method by decomposing uncertainty into a context-specific term and a multiplicity-specific term. The former captures ambiguity induced by the given context (e.g., task or prompt), while the latter captures how many plausible answers determined by the context remain compatible with the given input. We train a lightweight post-hoc uncertainty module to estimate these quantities, which enables efficient uncertainty estimation without autoregressive answer generation or repeated sampling. Experiments on various open-ended multimodal benchmarks, hallucination detection, and multiple-choice visual question answering benchmarks show that CoMet consistently improves uncertainty estimation over existing baselines while remaining efficient in practice. Code is available at https://github.com/princetonvisualai/comet_uncertainty

With rapidly improving capabilities, Large Language Models (LLMs) are increasingly used in many complex real-world tasks. Beyond requiring in-depth knowledge and reasoning skills, many of these tasks exhibit a high degree of subjectivity and require that the outputs of the model can be trusted. While a lot of progress has been made to train better models, decision-making algorithms have received less attention. In this work, we present and evaluate various uncertainty-aware decision-making algorithms based on Bayesian decision theory and risk-averse decision making on the tasks of tutoring and automatic peer reviewing. Concretely, we take uncertainty over tutoring strategies and review scores into account when generating a tutor response or review and use conformal prediction to provide guarantees over strategy and score. We find empirically that these algorithms can improve the utility of the generations but need to be carefully implemented when ambiguity is high. For example, risk-averse rules can degrade performance by optimizing for generic outputs, while Bayesian methods tend to perform better. Our work uses techniques from decision theory to improve LLM-based decision-making and outlines open challenges for the community.

Probe-based uncertainty estimation (UE) has emerged as a prominent approach to detect hallucinations in Large Language Models (LLMs) by learning uncertainty from internal model signals. Yet, recent methods vary simultaneously across feature design, training data construction, and evaluation setting, obscuring what actually drives performance. To address this issue, we propose a factorised study of probe-based UE under matched conditions. Our results show that raw hidden states and attention features are difficult to outperform in-domain. However, under distribution shift, structured and compressed features are more robust, suggesting that in-domain performance alone is insufficient to measure progress. Furthermore, prompting and label construction significantly affect probe behaviour. Building on these best-practice findings, we train benchmark-based pretrained probes that transfer reasonably well to open-ended factual generation, providing a stable off-the-shelf baseline. Our work encourages more deployment-oriented evaluation of probe-based uncertainty estimators. The code repository is available at https://github.com/ponhvoan/ProbeUE.

Reinforcement Learning (RL) has become a powerful paradigm for de novo molecular design, enabling Chemical Language Models (CLMs) to navigate and explore the chemical space while optimizing specific desired properties. However, the existing RL frameworks treat all scoring functions as deterministic oracles, neglecting the inherent uncertainty attached to the predictions of the different molecular properties. This can lead to the exploration of highly-uncertain regions of the chemical space, focusing on the generation of highly scored molecules which are poorly supported by the training data. This can destabilize the optimization process, yielding predictions that are far from their true values. We propose and compare two complementary ways of incorporating predictive uncertainty into RL. In the first one, uncertainty is treated as an additional optimization objective and incorporated along with the rest of the scoring functions, allowing the policy to trade off exploitation against reliability. Secondly, uncertainty is used to modulate policy updates, reducing the influence of molecules whose properties lie far outside the scoring function confidence domain. Both approaches were evaluated across three different settings: (i) a controlled model system, in which the prediction error is modeled as a Gaussian distribution, with a variance proportional to the distance to the training data; and two real-world tasks, making use of (ii) ChemProp models and (iii) a Conformal Prediction wrapper applied to a Random forest classifier. We show that uncertainty-aware RL enables CLMs to explore chemical space more robustly by favoring lower-uncertainty regions. This leads to more reliable hit discovery without compromising molecular score, increasing the true hit rate by 0.25 (from 0.5 to 0.75), and nearly doubling the total number of true hits.

In high-stakes document processing pipelines, including financial reconciliation, compliance verification, and procurement automation, an LLM extraction that is silently wrong is more dangerous than one that is visibly absent. The central challenge is not extraction accuracy alone but reliable confidence estimation: knowing, field by field, whether an extraction can be trusted for automation or deferred to human review. Token-level log-probabilities, verbalized confidence, and multi-sample self-consistency all collapse toward all-positive behaviour at practical thresholds, offering no reliable separation between trustworthy and untrustworthy extractions. We present ExtractConf, a cross-domain, field-agnostic confidence engine that grounds confidence estimation in two structurally different readings of the same document. A field-guided Hunter call extracts each field under schema-slot completion pressure; a document-guided Mapper call scans holistically and surfaces values grounded in document content. This asymmetry yields different failure modes: Hunter hallucinates values for absent fields, while Mapper misses visually non-salient ones. Their disagreement is independently informative. ExtractConf fuses cross-call disagreement, LLM-internal uncertainty, OCR, image quality, and spatial layout into a classifier requiring no domain-specific rules or retraining. On DocILE (55-field invoices, 26% failure rate), it achieves 0.928 ROC AUC and reduces selective prediction risk by 70% over logprob-mean. At 80% coverage, accuracy reaches 99.1%, enabling a practical human-in-the-loop workflow. Zero-shot transfer to CORD receipts achieves 0.858 AUC; lightweight Lasso recalibration reduces ECE by 89% and Brier by 43%, confirming the signals generalise across document domains.

Benchmark-based evaluation is the dominant paradigm for assessing large language model (LLM) capabilities, yet data contamination inflates reported performance and undermines fair comparison. Existing decontamination methods are evaluated solely through aggregate accuracy, which can obscure substantial differences in per-sample model behaviour, and many require access to an uncontaminated model. In this paper, we propose a sample-level evaluation framework for decontamination that complements accuracy-based assessment with distributional distance metrics, measuring how closely a decontaminated model recovers the output distribution of an uncontaminated model on each sample. Building on this framework, we introduce Uncertainty-Based Decontamination (UBD), a family of methods that leverage deep ensembles of the contaminated model to estimate per-sample memorization without requiring a uncontaminated model or knowledge of which samples are contaminated. UBD estimates a per-sample correction scalar from ensemble uncertainty, which is used to construct a debiased target distribution that suppresses the inflated probability mass on correct answers induced by contamination. This target is then used either as a post-hoc output correction (debiasing) or as a soft training signal for parameter update (unlearning). Experiments on MMLU-Pro and MATH-MCQA across multiple LLM backbones demonstrate that UBD produces per-sample output distributions substantially closer to those of an uncontaminated model than paraphrasing or choice-permutation baselines, while preserving model performance on uncontaminated data.

Recent advancements in Large Language Models (LLMs) have enabled sophisticated reasoning and content generation, yet their inherent stochasticity poses significant challenges for ensuring predictive credibility. While traditional uncertainty taxonomy paradigms, such as the dichotomy of aleatoric and epistemic uncertainties, provide conceptual foundations, they often fail to capture the multi-component and multi-stage nature of LLM generation and struggle to evaluate the effectiveness of various Uncertainty Quantification (UQ) methods. In this paper, we propose a granular uncertainty taxonomy that systematically attributes LLM uncertainty into input-level, parameter-level, token-level, and decoding-process sources. Correspondingly, we categorize existing UQ methods into Bayesian, ensemble, consensus-based, and single-pass approaches. Furthermore, we introduce a comprehensive evaluation framework covering diverse generation settings and metrics. We empirically evaluate 21 typical UQ methods across three prominent LLM families, including Qwen3, Llama 3.2, and DeepSeek-V3, on benchmarks such as TriviaQA, GSM8K, and HumanEval. Our experimental results demonstrate that (i) the effectiveness of UQ methods is sensitive to task types and generation settings; (ii) consensus-based methods, typed Deg and EigV, consistently outperform other UQ approaches; and (iii) larger model scales correlate with lower uncertainty estimates, suggesting an empirical scaling law for LLM uncertainty. This work bridges the gap between theoretical origins and practical deployment, providing a versatile diagnostic tool for systematically quantifying uncertainty in LLM applications.

Large language models (LLMs) frequently encounter inputs that disagree with their prior outputs, through user pushback, retrieved documents, or web search results. While the way they resolve such conflicts -- a process we frame as cognitive dissonance resolution -- has been characterized behaviorally, its connection to internal model uncertainty is not well understood. To study this systematically, we vary persuasion attempts along two dimensions, source authority and evidence quality, across 12 health-science claims of stratified epistemic status. Dissonance can be resolved through persuasion, backfire, or immunity. We introduce Trust Elasticity (TE), an econometrics-inspired measure of how readily a model is persuaded toward conflicting evidence. Across four LLMs, TE varies substantially, while clearly false claims elicit near-zero TE across all models. On two open-weight models, we further find that this variation is associated with two complementary internal uncertainty indicators, Confidence Miscalibration in Qwen and Internal Uncertainty Change in Llama. These results link cross-model behavioral variation to a measurable internal property and point to interventions targeting internal uncertainty as future work.

Large language models (LLMs) are increasingly deployed as black-box classifiers in pipelines that automate confident decisions and route uncertain ones to human review. Such selective prediction needs a confidence score that an operator can threshold at a chosen risk level. Prior work asks whether LLM confidence is well calibrated or well ranked; we ask a complementary, deployment-oriented question that has been largely overlooked: at what resolution can the score be thresholded? We call the answer the score granularity gap. Through a controlled comparison of seven ways to build a confidence score, from a single verbalized number, to token probabilities, to querying the model many times and combining the answers, across 25 model-dataset pairs (9 LLMs, 3 benchmarks), we find that single-shot verbalized confidence, once correctly converted to a class probability, ranks cases surprisingly well, yet takes only a handful of distinct values. It therefore offers an operator only a few coarse thresholds, no matter how well it ranks. We show which constructions widen this gap, at what inference cost, and with what effect on ranking, notably that multi-query aggregation helps weak models but can degrade already-strong ones. We translate these trade-offs into concrete deployment guidance.

Although large language models (LLMs) have shown strong capabilities across a wide range of tasks, their outputs often remain unreliable and may contain hallucinations, making uncertainty estimation (UE) essential for building trustworthy LLMs. In practice, many mainstream LLMs are only accessible through restricted APIs, where internal signals such as logits and hidden states are unavailable, making black-box UE especially important. However, existing work on black-box UE for LLMs remains fragmented in methodology and lacks a unified empirical comparison. To address this gap, we present a systematic review of black-box UE methods and organize them into five categories: verbalization-based, sampling-based, explanation-based, multi-agent, and hybrid methods. We further build a unified evaluation framework and benchmark 24 representative methods across 4 models and 4 dataset settings. Our results show that no single method consistently dominates across all settings. Nevertheless, methods that reason over and compare candidates in the answer space are generally effective, and hybrid methods that combine multiple uncertainty signals perform well under most conditions. By releasing the benchmark data and a unified evaluation framework, we aim to facilitate reproducible comparisons and support future research, while our empirical findings provide practical guidance for developing future black-box UE methods for LLMs.

Recent position papers argue that the classical aleatoric/epistemic uncertainty framework is insufficient for interactive large language model (LLM) agents and call for underspecification-aware, decomposed, and communicable uncertainty representations that can unlock new agent capabilities such as proactive clarification seeking and shared mental-model building. Practical deployment constraints -- black-box APIs, interactive latency budgets, and the absence of labeled trajectories -- rule out logprob-based, multi-sampling, and training-based methods, leaving prompt-based estimation as the most viable family for surfacing such signals at deployment time. We answer this call with a simple prompt-based decomposition that separates action confidence from request uncertainty (u), enabling the agent to ask for clarification when the task specification is ambiguous. To evaluate it, we introduce two clarification-augmented benchmarks (WebShop-Clarification and ALFWorld-Clarification) in which 50% of tasks are deliberately underspecified, and systematically compare the proposed decomposition against ReAct+UE and Uncertainty-Aware Memory (UAM) across five LLM backbones (GPT-5.1, DeepSeek-v3.2-exp, GLM-4.7, Qwen3.5-35B, GPT-OSS-120B) on these variants together with the standard WebShop, ALFWorld, and REAL benchmarks for fault detection. Averaged across the five backbones, the proposed decomposition improves clarification F1 on ALFWorld-Clarification by 73% over ReAct+UE and by 36% over UAM, and leads clarification F1 on every backbone on WebShop-Clarification and on four of five backbones on ALFWorld-Clarification, indicating that the gains generalize beyond a single LLM.

Large language models (LLMs) are increasingly used for clinical text tasks such as summarization and revision. While most studies evaluate the fluency and coherence of LLM-generated text, whether LLMs correctly preserve diagnostic uncertainty remains underexplored. In clinical practice, phrases such as ``possible pneumonia'' communicate the strength of available evidence and directly guide decisions about follow-up testing and treatment. Altering these uncertainty expressions can change the clinical meaning entirely. In this paper, we systematically evaluated this problem in two steps. First, we constructed a benchmark of 1,200 clinical documents with 9,184 uncertainty annotations across five levels. Second, we evaluated three LLMs on this benchmark. Our results show that (1) LLMs preserve the original uncertainty cues poorly, often less than half the time; (2) LLMs struggle with nuanced distinctions between adjacent levels. This work reveals a failure mode not captured by standard evaluation metrics and provides implications for the safe deployment of LLMs in clinical workflows.

We investigate whether language models internally track the value of their current trajectory, defined as the likelihood that their ongoing strategy will achieve their goals. Using synthetic, in-context reinforcement learning data, we construct a "value" axis for Qwen3-8B. We find that activations along this axis distinguish between high vs. low verbalized confidence, rollouts without and with backtracking, and correct vs. corrupted code. Steering towards high value causally suppresses self-correction and reduces explanatory verbosity, while steering towards low value induces backtracking and exploration. We demonstrate that direct preference optimization (DPO) can increase the internal value of rewarded behaviors (e.g. use a certain word), causing the model to act more confidently after exhibiting them. Finally, we apply the value axis to study in-the-wild settings. For example, we find that Qwen assigns low value to politically sensitive chat queries after post-training and that supervised fine-tuning increases internal confidence within the training domain. Our results suggest that language models linearly encode an estimate of expected goal success that modulates their confidence in pursuing a direction.

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

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

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

While large language models (LLMs) offer promising reasoning capabilities, their integration into safety-critical driving systems is hindered by limited reasoning diversity, high computational overhead, and static learning paradigms. To address these challenges, we propose LUNA-AD, a lightweight uncertainty-aware language model with lifelong learning for autonomous driving (AD). LUNA-AD features a tri-system architecture that reconciles complex multimodal behavioral reasoning, efficient deployment, and continual refinement. We design a multi-agent analytical system to generate uncertainty-aware decision-making demonstrations through diverse hypothesis exploration. A dual-head lightweight heuristic model is distilled to unify the inference of decision distributions and textual explanations while enabling efficient deployment. Furthermore, a reflection-driven lifelong learning mechanism operates on multimodal decision outputs and preserves strategic diversity, allowing for the refinement of candidate decisions and rationales via closed-loop feedback to enhance driving robustness. Extensive experiments on nuPlan benchmarks demonstrate that LUNA-AD achieves state-of-the-art success rates under both non-reactive and reactive modes, with drastically reduced inference latency compared to existing knowledge-driven AD frameworks.

Proactive robot assistance in household environments requires accurate prediction of human activities and object usage under dynamic and noisy conditions. Existing approaches often rely on complex spatio-temporal models, which can be computationally expensive and sensitive to environmental variability. In this paper, we propose GLOBE, a lightweight framework that combines n-gram Markov models for capturing temporal behavioral patterns with uncertainty-guided large language model (LLM) reasoning. The framework performs sequential prediction efficiently while selectively invoking LLM reasoning only when the model confidence is low. To evaluate performance under realistic conditions, we introduce HOMER-Noise, a noisy extension of the HOMER+ dataset that simulates structured disturbances such as object movements caused by humans, pets, and toddlers. Experimental results show that GLOBE achieves competitive performance with state-of-the-art methods while improving robustness and computational efficiency across both clean and noisy settings. The framework is further validated through a proof-of-concept integration with a Stretch 3 mobile manipulator, demonstrating its potential application in real-world human-robot interaction scenarios.