Large Language Model Uncertainty

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

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

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

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

Uncertainty in large language model (LLM)-based systems is often studied at the level of a single model output, yet deployed LLM applications are compound systems in which uncertainty is transformed and reused across model internals, workflow stages, component boundaries, persistent state, and human or organisational processes. Without principled treatment of how uncertainty is carried and reused across these boundaries, early errors can propagate and compound in ways that are difficult to detect and govern. This paper develops a systems-level account of uncertainty propagation. It introduces a conceptual framing for characterising propagated uncertainty signals, presents a structured taxonomy spanning intra-model (P1), system-level (P2), and socio-technical (P3) propagation mechanisms, synthesises cross-cutting engineering insights, and identifies five open research challenges.

Diffusion language models expose an explicit denoising trajectory, making it possible to ask when different kinds of information become measurable during generation. We study three independent 32-step runs of LLaDA-8B-Base on masked WikiText-103 text, each with 1{,}000 probe-training sequences and 200 held-out evaluation sequences. From saved trajectories, we derive four temporal measurements: token commitment; linear recoverability of part-of-speech (POS), coarse semantic category, and token identity; confidence and entropy dynamics; and sensitivity under mid-trajectory re-masking. Across seeds, the same ordering recurs: content categories stabilize earlier than function-heavy categories, POS and coarse semantic labels remain substantially more linearly recoverable than exact lexical identity under our probe setup, uncertainty remains higher for tokens that ultimately resolve incorrectly even though late confidence becomes less calibrated, and perturbation sensitivity peaks in the middle of the trajectory. A direct/collateral decomposition shows that this peak is overwhelmingly local to the perturbed positions themselves. In this LLaDA+WikiText setting, denoising time is therefore a useful analysis axis: under our measurements, coarse labels are recovered earlier and more robustly than lexical identity, trajectory-level uncertainty tracks eventual correctness, and mid-trajectory states are the most intervention-sensitive.

Large Language Models (LLMs) are increasingly deployed to autonomously solve real-world tasks. A key ingredient for this is the LLM Function-Calling paradigm, a widely used approach for equipping LLMs with tool-use capabilities. However, an LLM calling functions incorrectly can have severe implications, especially when their effects are irreversible, e.g., transferring money or deleting data. Hence, it is of paramount importance to consider the LLM's confidence that a function call solves the task correctly prior to executing it. Uncertainty Quantification (UQ) methods can be used to quantify this confidence and prevent potentially incorrect function calls. In this work, we present what is, to our knowledge, the first evaluation of UQ methods for LLM Function-Calling (FC). While multi-sample UQ methods, such as Semantic Entropy, show strong performance for natural language Q&A tasks, we find that in the FC setting, it offers no clear advantage over simple single-sample UQ methods. Additionally, we find that the particularities of FC outputs can be leveraged to improve the performance of existing UQ methods in this setting. Specifically, multi-sample UQ methods benefit from clustering FC outputs based on their abstract syntax tree parsing, while single-sample UQ methods can be improved by selecting only semantically meaningful tokens when calculating logit-based uncertainty scores.

Large language models can detect their own errors and sometimes correct them without external feedback, but the underlying mechanisms remain unknown. We investigate this through the lens of second-order models of confidence from decision neuroscience. In a first-order system, confidence derives from the generation signal itself and is therefore maximal for the chosen response, precluding error detection. Second-order models posit a partially independent evaluative signal that can disagree with the committed response, providing the basis for error detection. Kumaran et al. (2026) showed that LLMs cache a confidence representation at a token immediately following the answer (i.e. post-answer newline: PANL) -- that causally drives verbal confidence and dissociates from log-probabilities. Here we test whether this PANL signal extends beyond confidence to support error detection and self-correction. Here we test whether this signal supports error detection and self-correction, deriving predictions from the second-order framework. Using a verify-then-correct paradigm, we show that: (i) verbal confidence predicts error detection far beyond token log-probabilities, ruling out a first-order account; (ii) PANL activations predict error detection beyond verbal confidence itself; and (iii) PANL predicts which errors the model can correct -- where all behavioural signals fail. Causal interventions confirm that PANL signals rescue error detection behavior when answer information is corrupted. All findings replicate across models (Gemma 3 27B and Qwen 2.5 7B) and tasks (TriviaQA and MNLI). These results reveal that LLMs naturally implement a second-order confidence architecture whose internal evaluative signal encodes not only whether an answer is likely wrong but whether the model has the knowledge to fix it.

Large language models can be uncertain yet correct, or confident yet wrong, raising the question of whether their output-level uncertainty and their actual correctness are driven by the same internal mechanisms or by distinct feature populations. We introduce a 2x2 framework that partitions model predictions along correctness and confidence axes, and uses sparse autoencoders to identify features associated with each dimension independently. Applying this to Llama-3.1-8B and Gemma-2-9B, we identify three feature populations that play fundamentally different functional roles. Pure uncertainty features are functionally essential: suppressing them severely degrades accuracy. Pure incorrectness features are functionally inert: despite showing statistically significant activation differences between correct and incorrect predictions, the majority produce near-zero change in accuracy when suppressed. Confounded features that encode both signals are detrimental to output quality, and targeted suppression of them yields a 1.1% accuracy improvement and a 75% entropy reduction, with effects transferring across the ARC-Challenge and RACE benchmarks. The feature categories are also informationally distinct: the activations of just 3 confounded features from a single mid-network layer predict model correctness (AUROC ~0.79), enabling selective abstention that raises accuracy from 62% to 81% at 53% coverage. The results demonstrate that uncertainty and correctness are distinct internal phenomena, with implications for interpretability and targeted inference-time intervention.

This paper studies uncertainty quantification for large language models (LLMs) under black-box access, where only a small number of responses can be sampled for each query. In this setting, estimating the effective semantic alphabet size--that is, the number of distinct meanings expressed in the sampled responses--provides a useful proxy for downstream risk. However, frequency-based estimators tend to undercount rare semantic modes when the sample size is small, while graph-spectral quantities alone are not designed to estimate semantic occupancy accurately. To address this issue, we propose SHADE (Soft-Hybrid Alphabet Dynamic Estimator), a simple and interpretable estimator that combines Generalized Good-Turing coverage with a heat-kernel trace of the normalized Laplacian constructed from an entailment-weighted graph over sampled responses. The estimated coverage adaptively determines the fusion rule: under high coverage, SHADE uses a convex combination of the two signals, while under low coverage it applies a LogSumExp fusion to emphasize missing or weakly observed semantic modes. A finite-sample correction is then introduced to stabilize the resulting cardinality estimate before converting it into a coverage-adjusted semantic entropy score. Experiments on pooled semantic alphabet-size estimation against large-sample references and on QA incorrectness detection show that SHADE achieves the strongest improvements in the most sample-limited regime, while the performance gap narrows as the number of samples increases. These results suggest that hybrid semantic occupancy estimation is particularly beneficial when black-box uncertainty quantification must operate under tight sampling budgets.

The validity screen (Cacioli, 2026d, 2026e) classifies LLM confidence signals as Valid, Indeterminate, or Invalid. We test whether these classifications predict selective prediction performance. Twenty frontier LLMs from seven families were evaluated on 524 items across six cognitive tracks. Valid models show mean Type 2 AUROC = .624 (SD = .048). Invalid models show mean AUROC = .357 (SD = .231). Cohen's d = 2.81, p = .002. The tiers order monotonically: Invalid (.357) < Indeterminate (.554) < Valid (.624). Split-half cross-validation yields median d = 1.77, P(d > 0) = 1.0 across 1,000 splits. The three-tier classification accounts for 47% of the variance in AUROC. DeepSeek-R1 drops from 85.3% accuracy at full coverage to 11.3% at 10% coverage. The screen predicts the criterion. For selective prediction, the screen matters.

LLM confidence signals are used for abstention, routing, and safety-critical decisions. No standard practice exists for checking whether a confidence signal carries item-level information before building on it. We transfer the validity screening principle from clinical personality assessment (PAI, MMPI-3) as a portable protocol for benchmark-based LLM confidence data. The protocol specifies three core indices (L, Fp, RBS), a structural indicator (TRIN), and an item-sensitivity statistic, computed from a single 2x2 contingency table. A three-tier classification system (Invalid, Indeterminate, Valid) draws on four clinical traditions. Validated on 20 frontier LLMs across 524 items, four models are classified Invalid, two Indeterminate. Valid-profile models show mean r = .18 (15/16 significant). Invalid-profile models show mean r = -.20 (d = 2.48). Cross-benchmark validation on 18 models using MMLU with verbalized confidence and on external data from Yang et al. (2024) confirms the screen transfers across benchmarks and probe formats. All data and code: https://github.com/synthiumjp/validity-scaling-llm

Multi-agent systems built on large language models (LLMs) are difficult to reason about. Coordination errors such as deadlocks or type-mismatched messages are often hard to detect through testing. We introduce a domain-specific language for specifying agent coordination based on message sequence charts (MSCs). The language separates message-passing structure from LLM calls, tool calls, and human control points, whose outcomes remain unpredictable. We define the syntax and semantics of the language and present a syntax-directed projection that generates deadlock-free local agent programs from global coordination specifications. We illustrate the approach with a diagnosis consensus protocol and show how coordination properties can be established independently of LLM nondeterminism. We also describe a runtime planning extension in which an LLM dynamically generates a coordination workflow for which the same structural guarantees apply. An open-source Python implementation of our framework is available as ZipperGen.

Reliable Large Language Models (LLMs) should abstain when confidence is insufficient. However, prior studies often treat refusal as a generic "I don't know'', failing to distinguish input-level ambiguity (data uncertainty) from capability limitations (model uncertainty). This lack of distinction limits downstream action decisions like requesting clarification or invoking external tools. In this work, we introduce UA-Bench, a benchmark of over 3,500 questions drawn from six datasets spanning knowledge-intensive and reasoning-intensive tasks, designed to evaluate explicit uncertainty attribution. An evaluation of 18 frontier LLMs shows that even state-of-the-art models struggle to reliably discriminate between data uncertainty and model uncertainty, and that high answer accuracy does not necessarily imply strong uncertainty attribution ability. To narrow this gap, we propose a lightweight data synthesis and reinforcement learning strategy. Experiments on both Qwen3-4B-Instruct-2507 and Qwen3-8B in thinking mode show that the proposed method improves uncertainty attribution while preserving answer accuracy. Our code and data are publicly available now.

Large language models (LLMs) often produce confident yet incorrect responses, and uncertainty quantification is one potential solution to more robust usage. Recent works routinely rely on self-consistency to estimate aleatoric uncertainty (AU), yet this proxy collapses when models are overconfident and produce the same incorrect answer across samples. We analyze this regime and show that cross-model semantic disagreement is higher on incorrect answers precisely when AU is low. Motivated by this, we introduce an epistemic uncertainty (EU) term that operates in the black-box access setting: EU uses only generated text from a small, scale-matched ensemble and is computed as the gap between inter-model and intra-model sequence-semantic similarity. We then define total uncertainty (TU) as the sum of AU and EU. In a comprehensive study across five 7-9B instruction-tuned models and ten long-form tasks, TU improves ranking calibration and selective abstention relative to AU, and EU reliably flags confident failures where AU is low. We further characterize when EU is most useful via agreement and complementarity diagnostics.

Large language models are increasingly deployed in settings where reliability matters, yet output-level uncertainty signals such as token probabilities, entropy, and self-consistency can become brittle under calibration--deployment mismatch. Conformal prediction provides finite-sample validity under exchangeability, but its practical usefulness depends on the quality of the nonconformity score. We propose a conformal framework for LLM question answering that uses internal representations rather than output-facing statistics: specifically, we introduce Layer-Wise Information (LI) scores, which measure how conditioning on the input reshapes predictive entropy across model depth, and use them as nonconformity scores within a standard split conformal pipeline. Across closed-ended and open-domain QA benchmarks, with the clearest gains under cross-domain shift, our method achieves a better validity--efficiency trade-off than strong text-level baselines while maintaining competitive in-domain reliability at the same nominal risk level. These results suggest that internal representations can provide more informative conformal scores when surface-level uncertainty is unstable under distribution shift.

Uncertainty estimation is a promising approach to detect hallucinations in large language models (LLMs). Recent approaches commonly depend on model internal states to estimate uncertainty. However, they suffer from strict assumptions on how hidden states should evolve across layers, and from information loss by solely focusing on last or mean tokens. To address these issues, we present Sequential Internal Variance Representation (SIVR), a supervised hallucination detection framework that leverages token-wise, layer-wise features derived from hidden states. SIVR adopts a more basic assumption that uncertainty manifests in the degree of dispersion or variance of internal representations across layers, rather than relying on specific assumptions, which makes the method model and task agnostic. It additionally aggregates the full sequence of per-token variance features, learning temporal patterns indicative of factual errors and thereby preventing information loss. Experimental results demonstrate SIVR consistently outperforms strong baselines. Most importantly, SIVR enjoys stronger generalisation and avoids relying on large training sets, highlighting the potential for practical deployment. Our code repository is available online at https://github.com/ponhvoan/internal-variance.

Despite the rapid advancement of Large Language Models (LLMs), uncertainty quantification in LLM generation is a persistent challenge. Although recent approaches have achieved strong performance by restricting LLMs to produce short or constrained answer sets, many real-world applications require long-form and free-form text generation. A key difficulty in this setting is that LLMs often produce responses that are semantically coherent yet factually inaccurate, while the underlying semantics are multifaceted and the linguistic structure is complex. To tackle this challenge, this paper introduces Interrogative Uncertainty Quantification (IUQ), a novel framework that leverages inter-sample consistency and intra-sample faithfulness to quantify the uncertainty in long-form LLM outputs. By utilizing an interrogate-then-respond paradigm, our method provides reliable measures of claim-level uncertainty and the model's faithfulness. Experimental results across diverse model families and model sizes demonstrate the superior performance of IUQ over two widely used long-form generation datasets. The code is available at https://github.com/louisfanhz/IUQ.

Clinical language models (LMs) are increasingly applied to support clinical risk prediction from free-text notes, yet their uncertainty estimates often remain poorly calibrated and clinically unreliable. In this work, we propose Clinical Uncertainty Risk Alignment (CURA), a framework that aligns clinical LM-based risk estimates and uncertainty with both individual error likelihoods and cohort-level ambiguities. CURA first fine-tunes domain-specific clinical LMs to obtain task-adapted patient embeddings, and then performs uncertainty fine-tuning of a multi-head classifier using a bi-level uncertainty objective. Specifically, an individual-level calibration term aligns predictive uncertainty with each patient's likelihood of error, while a cohort-aware regularizer pulls risk estimates toward event rates in their local neighborhoods in the embedding space and places extra weight on ambiguous cohorts near the decision boundary. We further show that this cohort-aware term can be interpreted as a cross-entropy loss with neighborhood-informed soft labels, providing a label-smoothing view of our method. Extensive experiments on MIMIC-IV clinical risk prediction tasks across various clinical LMs show that CURA consistently improves calibration metrics without substantially compromising discrimination. Further analysis illustrates that CURA reduces overconfident false reassurance and yields more trustworthy uncertainty estimates for downstream clinical decision support.

Recent work has shown that the hidden states of large language models contain signals useful for uncertainty estimation, motivating a growing interest in efficient probe-based approaches. Yet it remains unclear how robust existing methods are, with prior work reporting conflicting conclusions under substantially different evaluation settings. We address this by introducing ProbeDrift, a systematic evaluation framework for supervised uncertainty probes covering a wide range of OOD settings across models, tasks, and distributional shifts. Using ProbeDrift, we train over 2,000 probes to disentangle the effect of key design choices, showing poor robustness of current methods beyond near-OOD settings. We find that robustness is driven by design decisions that have a largely invisible effect in-distribution, including the choice of feature type, aggregation strategy, and training signal. We argue that robust uncertainty estimation requires robust evaluation. To support this, we release ProbeDrift as a lightweight Python library that contains the train and test splits underpinning our extensive evaluation. We also show how insights from our evaluation can directly lead to more robust methods through a simple Hybrid Back-Off (HBO) strategy.

A robust decision-making process must take into account uncertainty, especially when the choice involves inherent risks. Because artificial intelligence (AI) systems are increasingly integrated into decision-making workflows, managing uncertainty relies more and more on the metacognitive capabilities of these systems; i.e, their ability to assess the reliability of and regulate their own decisions. Hence, it is crucial to employ robust methods to measure the metacognitive abilities of AI. This paper is primarily a methodological contribution arguing for the adoption of the meta-d' framework as the gold standard for assessing the metacognitive sensitivity of AIs--the ability to generate confidence ratings that distinguish correct from incorrect responses. Moreover, we propose to leverage signal detection theory (SDT) to measure the ability of AIs to spontaneously regulate their decisions based on uncertainty and risk. To demonstrate the practical utility of these psychophysical frameworks, we conduct two series of experiments on three large language models (LLMs)--GPT-5, DeepSeek-V3.2-Exp, and Mistral-Medium-2508.

Existing methods for quantifying predictive uncertainty in neural networks are either computationally intractable for large language models or require access to training data that is typically unavailable. We derive a lightweight alternative through two approximations: a first-order Taylor expansion that expresses uncertainty in terms of the gradient of the prediction and the parameter covariance, and an isotropy assumption on the parameter covariance. Together, these yield epistemic uncertainty as the squared gradient norm and aleatoric uncertainty as the Bernoulli variance of the point prediction, from a single forward-backward pass through an unmodified pretrained model. We justify the isotropy assumption by showing that covariance estimates built from non-training data introduce structured distortions that isotropic covariance avoids, and that theoretical results on the spectral properties of large networks support the approximation at scale. Validation against reference Markov Chain Monte Carlo estimates on synthetic problems shows strong correspondence that improves with model size. We then use the estimates to investigate when each uncertainty type carries useful signal for predicting answer correctness in question answering with large language models, revealing a benchmark-dependent divergence: the combined estimate achieves the highest mean AUROC on TruthfulQA, where questions involve genuine conflict between plausible answers, but falls to near chance on TriviaQA's factual recall, suggesting that parameter-level uncertainty captures a fundamentally different signal than self-assessment methods.

Standard evaluation of LLM confidence relies on calibration metrics (ECE, Brier score) that conflate how much a model knows (Type-1 accuracy) with how well its confidence signal tracks that knowledge (Type-2 metacognitive sensitivity). We apply Signal Detection Theory (SDT) to decompose these capacities, treating token-level normalised log-probability as a graded confidence variable and answer correctness as the state to be discriminated. We characterise the Type-2 ROC of this signal, including its unequal-variance structure via z-ROC analysis, and -- because the meta-d' efficiency ratio is not well defined for open-ended QA, which lacks a two-alternative Type-1 decision -- quantify metacognitive efficiency with a model-free information measure, normalised metacognitive information (meta-I_2r). Applied to four LLMs (Llama-3-8B-Instruct, Mistral-7B-Instruct-v0.3, Llama-3-8B-Base, Gemma-2-9B-Instruct) across 224,000 factual QA trials, we find: (1) metacognitive information varies more than two-fold across models and co-varies inversely with accuracy -- the least accurate model has the most informative confidence -- though with four models this ordering cannot be separated from an error-difficulty confound, so we report it as coupling, not decoupling; (2) the confidence signal has model-specific unequal-variance structure (z-ROC slopes 0.81 to 1.18) invisible to calibration metrics; (3) metacognitive information is domain-specific, strongest in Arts & Literature for every model; (4) temperature dissociates Type-1 accuracy from metacognitive information, which stays stable while accuracy shifts. All estimates carry permutation nulls and bootstrap confidence intervals. Pre-registered; code and data public.

Understanding why a large language model (LLM) is uncertain about the response is important for their reliable deployment. Current approaches, which either provide a single uncertainty score or rely on the classical aleatoric-epistemic dichotomy, fail to offer actionable insights for improving the generative model. Recent studies have also shown that such methods are not enough for understanding uncertainty in LLMs. In this work, we advocate for an uncertainty decomposition framework that dissects LLM uncertainty into three distinct semantic components: (i) input ambiguity, arising from ambiguous prompts; (ii) knowledge gaps, caused by insufficient parametric evidence; and (iii) decoding randomness, stemming from stochastic sampling. Through a series of experiments we demonstrate that the dominance of these components can shift across model size and task. Our framework provides a better understanding to audit LLM reliability and detect hallucinations, paving the way for targeted interventions and more trustworthy systems.

While retrieval-augmented generation (RAG) enhances LLM performance, it does not eliminate hallucinations, making accurate detection essential. Uncertainty-based methods are attractive for this purpose because they can be integrated into real-world pipelines with little overhead. One of the most widely used uncertainty signals is predictive entropy. We show, however, that entropy can be unreliable in RAG settings and trace this limitation to two opposing internal effects. Induction heads, which copy patterns from earlier context, causally support correct responses and lower predictive entropy, but they also appear to co-activate entropy neurons that push it back up. As a result, correct, context-grounded responses can still receive high uncertainty scores. To address this, we propose INTRYGUE (Induction-Aware Entropy Gating for Uncertainty Estimation), a training-free, mechanistically grounded method that gates predictive entropy by an attention-based estimate of induction-head activity. Evaluated across four RAG-style benchmarks and six open-source LLMs (4B to 13B parameters), INTRYGUE performs competitively against a wide range of baselines, matching or exceeding the strongest of them in most settings. Our findings suggest that hallucination detection in RAG benefits from combining predictive uncertainty with interpretable internal signals of context utilization.

Uncertainty quantification has emerged as an effective approach to closed-book hallucination detection for LLMs, but existing methods are largely designed for short-form outputs and do not generalize well to long-form generation. We introduce a taxonomy for fine-grained uncertainty quantification in long-form LLM outputs that distinguishes methods by design choices at three stages: response decomposition, unit-level scoring, and response-level aggregation. We formalize several families of consistency-based black-box scorers, providing generalizations and extensions of existing methods. We also introduce FactScore-STEM-Geo, a new 400-question long-form QA dataset spanning four categories across STEM and Geography. In our experiments across multiple LLMs and datasets, we find 1) claim-response entailment consistently performs better or on par with more complex claim-level scorers, 2) claim-level scoring generally yields better results than sentence-level scoring, and 3) uncertainty-aware decoding is highly effective for improving the factuality of long-form outputs. Our framework clarifies relationships between prior methods, enables apples-to-apples comparisons, and provides practical guidance for selecting components for fine-grained UQ.

Running the same LLM agent on identical inputs yields 2.3-4.2 distinct action sequences per 10 runs; this behavioral variance constitutes a training-free, black-box uncertainty signal that instantiates selective classification and distribution-free calibration for agentic systems. Across 8,000 runs of four models on 200 HotpotQA questions, consistent tasks (at most 2 unique paths) achieve 82-87% accuracy while inconsistent tasks (4 or more paths) achieve 41-65%, a gap that survives controls for task difficulty. Divergence concentrates at step 2 (50.5% of Llama tasks), and consistency metrics detect failures with AUROC 0.62-0.78. Exploiting this signal, selective prediction (answering only when k=3 runs agree) achieves 87-88% accuracy at 54-62% coverage, a 6-14pp gain over single-run baselines, and matches a split-conformal baseline without a held-out calibration set. A cross-benchmark validation on SWE-bench (50 tasks, 1,000 runs) preserves the consistency hierarchy while revealing an ~8x spread in mean trajectory length across models, and bootstrap analysis shows single-run evaluations misrank models 29.3% of the time.

Large language models present challenges for principled uncertainty quantification, in part due to their complexity and the diversity of their outputs. Semantic dispersion, or the variance in the meaning of sampled answers, has been proposed as a useful proxy for model uncertainty, but the associated computational cost prohibits its use in latency-critical applications. We show that sampled semantic distributions can be distilled into lightweight student models which estimate a prompt-conditioned density before the language model generates an answer token. The student model predicts a semantic distribution over possible answers; the entropy of this distribution provides a prompt-level uncertainty signal, and the probability density allows answer-level reliability evaluation. Across experiments on TriviaQA and MMLU, we find our student models perform competitively relative to the teacher's sampled semantic dispersion on a hallucination prediction task, whilst offering additional uncertainty primitives for out-of-domain detection and multiple-choice answer selection. We term this technique Semantic Self-Distillation (SSD), which can serve as a general framework for distilling predictive uncertainty in complex output spaces beyond language.

LLM unlearning aims to remove the influence of undesirable knowledge from pretrained language models, which offers a practical mechanism for addressing safety and privacy concerns. Existing unlearning approaches, such as Gradient Ascent, are prone to catastrophic forgetting. Alignment-based approaches provide an alternative direction, yet their effectiveness is limited by the quality of the reference model. In realistic settings, both methods still require large retention datasets to preserve general knowledge. We propose a principled method that quantifies the target LLM's confidence in undesirable knowledge and uses it to calibrate the model's unlearning gradient updates more precisely. It enables fine-grained control over forgetting while better preserving model utility, thus reducing the dependence on retention data or prohibitive unlearning training data. Extensive evaluations on multiple benchmarks, including MUSE and WMDP, show that our method achieves effective unlearning and improves the trade-off between knowledge removal and utility preservation compared with state-of-the-art methods.

Large Vision-Language Models (LVLMs) often produce plausible but unreliable outputs, making robust uncertainty estimation essential. Recent work on semantic uncertainty estimates relies on external models to cluster multiple sampled responses and measure their semantic consistency. However, these clustering methods are often fragile, highly sensitive to minor phrasing variations, and can incorrectly group or separate semantically similar answers, leading to unreliable uncertainty estimates. We propose Semantic Gaussian Process Uncertainty (SGPU), a Bayesian framework that quantifies semantic uncertainty by analyzing the geometric structure of answer embeddings, avoiding brittle clustering. SGPU maps generated answers into a dense semantic space, computes the Gram matrix of their embeddings, and summarizes their semantic configuration via the eigenspectrum. This spectral representation is then fed into a Gaussian Process Classifier that learns to map patterns of semantic consistency to predictive uncertainty, and that can be applied in both black-box and white-box settings. Across six LLMs and LVLMs on eight datasets spanning VQA, image classification, and textual QA, SGPU consistently achieves state-of-the-art calibration (ECE) and discriminative (AUROC, AUARC) performance. We further show that SGPU transfers across models and modalities, indicating that its spectral representation captures general patterns of semantic uncertainty.

Confidence calibration, the alignment of a model's predicted confidence with its actual accuracy, is crucial for the reliable deployment of Large Language Models (LLMs). However, this critical property remains largely under-explored in multilingual contexts. In this work, we conduct the first large-scale, systematic studies of multilingual calibration across six model families and over 100 languages, revealing that non-English languages suffer from systematically worse calibration. To diagnose this, we investigate the model's internal representations and find that the final layer, biased by English-centric training, provides a poor signal for multilingual confidence. In contrast, our layer-wise analysis uncovers a key insight that late-intermediate layers consistently offer a more reliable and better-calibrated signal. Building on this, we introduce a suite of training-free methods, including Language-Aware Confidence Ensemble (LACE), which adaptively selects an optimal ensemble of layers for each specific language. Our study highlights the hidden costs of English-centric alignment and offer a new path toward building more globally equitable and trustworthy LLMs by looking beyond the final layer.

Large language models are known to hallucinate, generating linguistically plausible but incorrect answers to questions. Uncertainty quantification has been proposed as a strategy to detect such behaviour, but existing methods lack a unified framework to assess reliability at both the prompt and answer level. We introduce a geometric framework which quantifies language model uncertainty at both levels by explicitly modelling a prompt-conditioned semantic distribution in answer embedding space. Our approach is black-box and sampling-based; we generate multiple answers per prompt, and use archetypal analysis to estimate a geometric support for the answer distribution. At the prompt level, we approximate the distribution entropy to quantify uncertainty; for each individual answer, we then use notions of atypicality to assess its reliability relative to the batch. We employ our framework to not only detect hallucinations but correct them, by selecting the batch example deemed most reliable. Experiments show that our framework performs comparably to or better than prior methods on short form question-answering datasets, and achieves superior results on medical datasets where hallucinations carry particularly critical risks. Beyond pure performance, we suggest the theoretical grounding of our work provides support for semantic distributions as useful objects of study for language model uncertainty.

Accurate uncertainty quantification remains a key challenge for standard LLMs, prompting the adoption of Bayesian and ensemble-based methods. However, such methods typically necessitate computationally expensive sampling, involving multiple forward passes to effectively estimate predictive uncertainty. In this paper, we introduce an approach enabling uncertainty estimation in LLMs without incurring the heavy inference latency typically associated with sampling methods. Specifically, we distill uncertainty-aware teachers - originally requiring multiple forward passes - into single-pass students, fine-tuned using LoRA. We compare two distinct distillation strategies: one in which the student employs traditional softmax-based outputs, and another in which the student leverages Dirichlet-distributed outputs to explicitly model epistemic uncertainty via evidential learning. Empirical evaluation on classification tasks demonstrate that such students can achieve comparable predictive and uncertainty quantification performance relative to their teachers, while requiring only a single forward pass.

Understanding how large language models (LLMs) internally represent and process their predictions is central to detecting uncertainty and preventing hallucinations. While several studies have shown that models encode uncertainty in their hidden states, it is underexplored how this affects the way they process such hidden states. In this work, we demonstrate that the dynamics of output token probabilities across layers for certain and uncertain outputs are largely aligned, revealing that uncertainty does not seem to affect inference dynamics. Specifically, we use the Tuned Lens, a variant of the Logit Lens, to analyze the layer-wise probability trajectories of final prediction tokens across 11 datasets and 5 models. Using incorrect predictions as those with higher epistemic uncertainty, our results show aligned trajectories for certain and uncertain predictions that both observe abrupt increases in confidence at similar layers. We balance this finding by showing evidence that more competent models may learn to process uncertainty differently. Our findings challenge the feasibility of leveraging simplistic methods for detecting uncertainty at inference. More broadly, our work demonstrates how interpretability methods may be used to investigate the way uncertainty affects inference.

Large language models (LLMs) often produce incorrect answers with high confidence, yet the factors associated with such overconfidence remain insufficiently understood. We study this problem through the lens of knowledge popularity. Using entity-centric factual QA derived from Wikidata triplets, we characterize popularity through question entity popularity, answer popularity, and question-answer co-occurrence. We find two consistent patterns. First, hallucinated answers are far from random: compared with ground-truth answers, they tend to be more popular or more frequently associated with the question entity. Second, confidence is strongly tied to the popularity of generated answers: even among incorrect predictions, more popular answers or those with higher question-answer co-occurrence receive higher confidence. Together, these findings suggest that popular but wrong alternatives may contribute to overconfidence. We further show that popularity-related signals can mitigate overconfidence and improve overall confidence estimation. Across six models and three datasets, incorporating knowledge popularity reduces average confidence on incorrect answers from 0.765 to 0.254 and overall ECE from 0.356 to 0.050, while improving Alignment from 77.08% to 83.72%.

Large Language Models (LLMs) demonstrate remarkable capabilities in generative tasks but pose potential risks due to their tendency to generate hallucinatory responses. Therefore, Uncertainty Quantification (UQ), which aims to distinguish the validity of answers, is crucial for ensuring the safety and robustness of AI systems. However, existing methods primarily rely on measuring the entropy of multiple stochastic samples to represent uncertainty, often overlooking the specific uncertainty information associated with the candidate answer under evaluation. This oversight can lead to biased classification outcomes. In this paper, we investigate the discrepancy between global entropy from multiple samples and local confidence of candidate answer, and propose a Label-Confidence-Aware Uncertainty Quantification (LCA-UQ) method based on Pointwise Kullback-Leibler (PKL) divergence. Our method effectively bridges the gap between the consistency of sampled outputs and the calibration of the candidate answer, thereby enhancing the reliability and stability of uncertainty assessments. Empirical evaluations across a range of popular LLMs and NLP datasets reveal that label sources significantly impact classification. Furthermore, our approach effectively captures the nuances between sampling results and label sources, demonstrating superior performance in uncertainty estimation.

Large language models (LLMs) are widely used in decision-making across diverse domains. Ensuring the generation of safe and reliable responses is critical for the effective deployment of LLM-based applications, particularly in high-stakes domains such as healthcare and finance. Most of these applications typically use carefully crafted prompts to guide response generation; however, the relationship between prompts and the reliability of LLM-generated responses is not yet fully understood. To address this gap, we propose a novel prompt-response concept model that explains the relationship between the amount of task-relevant information (informativeness) provided in the prompt and the LLM-generated response uncertainty by identifying four sources of response uncertainty: prompt underspecification, model quality, task variability, and semantic redundancy. We prove that response uncertainty decreases as prompt informativeness or model quality increases, mirroring the behavior of epistemic uncertainty in probabilistic models. Our experimental results on real-world datasets further validate our proposed model and corroborate the theoretical results.

An LLM judge evaluates outputs at scale. Experts should label only where it is least sure. Its natural escalation signal conflates two uncertainties: aleatoric, real disagreement in the expert pool, which labels cannot reduce, and epistemic, the judge's ignorance, which labels do reduce. A small Bayesian model separates them: a regression on labels already collected learns how far to trust a black-box judge's prediction. Both components follow as simple formulas, with no sampling or further judge calls. The components isolate on a real LLM judge against exactly known truth, and stated confidence is no guide to its actual error. On real human disagreement (ChaosNLI) the epistemic ranking removes 83% more error than total uncertainty for the same expert labels, though simply escalating the least-labelled items does as well there. We demonstrate we can estimate where a judge is ignorant rather than where experts genuinely disagree, and propose using this to direct expert labelling. Code and data are available at https://github.com/composo-ai/judge-uncertainty-decomposition.

Verbalized confidence, in which LLMs report a numerical certainty score, is widely used to estimate uncertainty in black-box settings, yet the confidence scale itself (typically 0--100) is rarely examined. We show that this design choice is not neutral. Across six LLMs and three datasets, verbalized confidence is heavily discretized, with more than 78% of responses concentrating on just three round-number values. To investigate this phenomenon, we systematically manipulate confidence scales along three dimensions: granularity, boundary placement, and range regularity, and evaluate metacognitive sensitivity using $meta\text{-}d'$. We find that a 0--20 scale consistently improves metacognitive efficiency over the standard 0--100 format, while boundary compression degrades performance and round-number preferences persist even under irregular ranges. These results demonstrate that confidence scale design directly affects the quality of verbalized uncertainty and should be treated as a first-class experimental variable in LLM evaluation.

The possibility of LLM self-awareness and even sentience is gaining increasing public attention and has major safety and policy implications, but the science of measuring them is still in a nascent state. Here we introduce a novel methodology for quantitatively evaluating metacognitive abilities in LLMs. Taking inspiration from research on metacognition in nonhuman animals, our approach eschews model self-reports and instead tests to what degree models can strategically deploy knowledge of internal states. Using two experimental paradigms, we demonstrate that frontier LLMs introduced since early 2024 show increasingly strong evidence of certain metacognitive abilities, specifically the ability to assess and utilize their own confidence in their ability to answer factual and reasoning questions correctly and the ability to anticipate what answers they would give and utilize that information appropriately. We buttress these behavioral findings with an analysis of the token probabilities returned by the models, which suggests the presence of an upstream internal signal that could provide the basis for metacognition. We further find that these abilities 1) are limited in resolution, 2) emerge in context-dependent manners, and 3) seem to be qualitatively different from those of humans. We also report intriguing differences across models of similar capabilities, suggesting that LLM post-training may have a role in developing metacognitive abilities.

Practical uncertainty quantification (UQ) for large language models must decide, from a single generation, whether a specific answer should be trusted. Existing methods either sample multiple generations, read only output-token probabilities, or reduce the model's internal computation to a single hidden state. We introduce ActMap, a white-box representation that compresses the generation-time hidden-state trajectory (every layer, every generated token) into a fixed $12\times32\times128$ tensor of temporal-statistic channels that preserves structure across transformer depth and pooled hidden coordinates. The map is captured during the generation pass with no measurable overhead, has a fixed shape across model depths and hidden sizes, and occupies 96 KiB: a compact artifact that can be retained for audit-relevant generations and probed directly, with occlusion analysis localizing the classifier's signal to mid-depth regions of the map. A lightweight classifier, instantiated as a compact Vision Transformer, reads an estimated correctness probability from each map in a fraction of a millisecond; capacity-matched MLPs perform comparably, indicating the representation itself carries the result. Trained and evaluated in-domain on short-answer QA, direct-answer math, and summarization factuality with three instruction-tuned 7-8B models, ActMap consistently outperforms sampling, token-probability, attention, and embedding baselines, and matches ACT-ViT, a detector trained on dense activation tensors $67\times$ larger, at essentially the same mean AUROC with lower calibration error on ten of twelve pairs. The resulting score supports abstention, routing, and selective verification from a single generation, making it a practical primitive for scalable oversight of deployed models.