Large Language Model Uncertainty

LLMs are increasingly deployed as Artificial Moral Advisors (AMA) in a variety of contexts: what kind of conversational patterns should they display? In this paper, we study how AMA can help their interlocutors "stay with the uncertainty". We propose three modes of uncertainty (Perspective-Multiplying, Tension-Preserving, Process-Reflecting) and compare them against three control conditions (Baseline, Persuasive, Sycophantic). A user-agent LLM engages in a dialogue on an ethical dilemma with an AMA following a specific uncertainty strategy, and completes pre- and post-conversation questionnaires. We further examine the effect of two persona prompt formats (Declarative and Narrative). We found that (1) no single model dominates as a simulated user agent, with open models aligning with human ambiguity through between-persona divergence and closed models through within-persona hedging; (2) declarative personas better capture initial stance diversity while narrative personas show more realistic belief revision; (3) all six AMA strategies produce distinguishable conversational patterns; and (4) uncertainty strategies differ not in how much stance revision they produce, but in the quality of engagement they sustain.

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

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

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

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

Existing hallucination taxonomies classify LLM errors by what is wrong with the output -- memorised misconceptions, reasoning failures, fluent fabrications. These taxonomies are useful for diagnosis but cannot answer a different question: which uncertainty scorer would have caught this error? We propose a complementary taxonomy that classifies errors by their detectability signature -- the signal a scorer family would read. The DECK taxonomy is a 2x2 partition along inter-sample consistency and token-level confidence into four behavioural regimes (Drift, Entrenched, Confabulation, Knotted), each mapping to a specific scorer family (or families) that can detect it: black-box consistency scorers have signal in D and C, white-box token-probability scorers have signal in K and C, and only an LLM-as-a-Judge with independent pretraining can detect E. Cell membership is operationalised by a Youden's J optimal split on each scorer axis. Across three models and four datasets we validate the taxonomy two ways: by analysing scorer-pair disagreement, and by checking that external labels (SelfAware unanswerable, HaluEval adversarial, PopQA entity popularity) land in the predicted DECK cells, with model-scale and content-specific secondary-cell refinements. We further identify a universal blind spot of output-level UQ: on knowledge-gap inputs where the generator emits confident, repeatable fabrications, every output-level family collapses by construction. A linear probe on Llama-3-8B's hidden states also collapses to chance, giving preliminary evidence that the failure may persist at the activation level; richer internal-state methods (UQ heads, information-theoretic estimators) remain to be tested.

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

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

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

Large language models (LLMs) are increasingly used as heuristic advisors for black-box optimization, yet their suggestions and self-reported confidence are not necessarily calibrated to downstream objective values. This issue becomes more pronounced in multi-objective Bayesian optimization, where different objectives may require different expert knowledge and where an LLM expert can be useful for one objective but misleading for another. We study how to use LLM-generated expert priors in discrete multi-objective Bayesian optimization without blindly trusting them. We propose an objective-wise reputation-market mechanism that treats each expert-objective pair as a falsifiable prior source. Expert weights are updated online from observed objective feedback, discounted over time, and gated by market-level trust. We then introduce a decoupled counterfactual gate that can use the LLM prior without confidence, use it with confidence, or abstain from the LLM prior entirely. Across controlled synthetic stress tests and three molecule optimization benchmarks with \qwenflash{}-generated expert priors, we find that dynamic objective-wise calibration improves robustness over fixed LLM priors. However, raw LLM confidence is not reliably beneficial: on ESOL, confidence is positively correlated with prediction error; on FreeSolv, confidence can help; and on Lipophilicity, ignoring confidence remains strongest. Our fixed three-arm counterfactual gate improves over the first counterfactual variant on ESOL and FreeSolv, while an attempted margin portfolio exposes a useful negative result: margin selection should be acquisition-aware rather than based only on one-step prior error.

Order-agnostic language models (OALMs), including discrete diffusion language models (dLLMs), are trained to predict masked tokens under arbitrary conditioning sets, allowing sequences to be generated or scored under arbitrary reveal orders at inference time. In LLaDA-2.1, we report three findings. First, the learned conditionals are not exact factorizations of a coherent joint distribution: changing only the reveal order shifts target log-likelihood by up to 0.49 nats/token, so likelihood alone mixes content difficulty with path-dependent artifacts. Second, although confidence-first (CF) decoding is order-agnostic, its reveal orders are close to left-to-right (L2R) on content tokens. Third, we propose a complementary diagnostic based on the shape of the confidence trace. A uniform-spreading theorem shows that, at fixed total likelihood, target recoverability is maximized when per-step confidence is spread uniformly; the resulting deviation motivates $\mathrm{Var}(\log q_t)$ as a diagnostic for comparing decoding paths. Across C4 and four downstream benchmarks, low variance separates structured paths from random ordering, and variance is consistently associated with downstream correctness. These results support reporting mean confidence and confidence variance jointly when comparing OALM decoding paths.

The prevailing paradigm in large language model (LLM) alignment operates via erasure, filtering unsafe data or training models to strictly refuse harmful prompts. While effective at reducing immediate toxicity, this approach fundamentally constricts the model's epistemological scope, resulting in over-cautious systems that output uninformative blanket refusals to sensitive yet benign queries. In this work, we challenge the orthodoxy that unsafe data must be discarded. We propose a dialectical approach to alignment, positing that unsafe data encodes rich, domain specific knowledge critical for nuanced, safe, and informative generation. To operationalize this, we introduce SafeMoE, a Mixture-of-Experts (MoE) framework that isolates unsafe knowledge into domain-specific Low-Rank Adapters (LoRA experts) trained exclusively on harmful corpora. To synthesize safety from these unsafe primitives, we train a lightweight gating network using a minimal, highly curated set of safe-informative responses. During inference, this router dynamically orchestrates the unsafe experts, effectively steering the generation trajectory to harness their deep domain knowledge while strictly enforcing safety constraints. Extensive empirical evaluations across stringent safety benchmarks demonstrate that SafeMoE is not only safer, achieving over a 20% relative improvement in safe response rate (more than a 15% absolute gain), but also produces more informative responses when safety and harmfulness are of paramount concern. Furthermore, the routing mechanism exhibits strong zero-shot generalization to unseen domains and broader safety tasks without domain-specific supervision. Our findings suggest a paradigm shift in alignment: true safety requires not the masking of unsafe knowledge, but its controlled integration.

Hallucination remains one of the key challenges undermining the reliability of Large Vision-Language Models (LVLMs). But what makes an LVLM hallucinate less? Many existing efforts focus on improving internal components of the model. We argue that hallucination fundamentally stems from how the model architecture is designed. To investigate this, we factor the architecture design into three dimensions: Linguistic Foundation (LF), Visual Representation (VR), and Semantic Alignment (SA), and categorize hallucinations into Co-occurrence, Similarity, and previously overlooked Uncertainty types. Building on this formulation, we propose CoSimUE, a benchmark that creates fine-grained hallucination scenarios through controlled textual perturbations and random perturbations, enabling mapping between design choices and hallucination behaviors. Experiments across 7 design aspects show that: 1) the widely emphasized scaling of model parameters has only limited impact on reducing all three types of hallucinations; 2) larger and better-trained language foundations can reduce co-occurrence hallucinations; 3) stronger visual encoders and higher resolutions mitigate similarity errors; 4) effective alignment strategies alleviate uncertainty hallucinations. 5) Furthermore, cross-dimensional analysis reveals that jointly enhancing visual fidelity and alignment quality yields the most comprehensive improvements. This study provides the first systematic exploration linking architecture-level design to hallucination robustness, offering practical guidance for developing reliable and efficient LVLMs.

Fine-tuning is often believed to reduce uncertainty and diversity in large language models, but existing analyses overlook output length, a key confounder, and therefore fail to capture how uncertainty is distributed across an entire generation rollout. To address this, we propose Canopy Entropy ($\mathrm{CE}^\star$), a measure that views language generation from a tree perspective, where ``canopy'' represents the space of all possible rollouts, making $\mathrm{CE}^\star$ naturally quantify the effective size of the generation space. $\mathrm{CE}^\star$ jointly captures uncertainty in both the output length $N$ and the generated sequence $Y_{1:N}$ -- indeed, we show that it equals to total Shannon entropy $H(N, Y_{1:N}\mid X)$, where $X$ denotes the prompt. This formulation yields interpretable metrics, including a length-entropy correlation term $ρ(N, r_N)$, where $r_N$ is the entropy rate, quantifying information conveyance efficiency by indicating whether longer outputs are more or less informative per token. Empirically, across tasks and model families, we find that fine-tuned models consistently exhibit stronger positive correlation $ρ(N, r_N)$, even when total entropy decreases. Furthermore, after controlling for model family, task, prompt, and output-length effects, we find that fine-tuning nearly triples the correlation strength between entropy rate and semantic diversity, suggesting that aligned models convert token uncertainty into semantic diversity more efficiently. Overall, these results demonstrate that fine-tuning does not simply reduce uncertainty, but fundamentally reorganizes it into more informative and semantically meaningful generations. Our code is available at https://github.com/WeiyiTian/canopy-entropy.

Uncertainty Quantification is a large and growing subfield of large language model behavioral analysis. Primarily to recognize and combat hallucination, the field has largely focused on measuring and improving calibration, the accuracy of uncertainty judgments to task efficacy. In this work, we investigate the relatively underexplored question of how similar large language model uncertainty is to human uncertainty. We investigate the presence and strength of human-similar uncertainty signals, deemed uncertainty alignment, in large language model overt behavior and internal activation patterns. We identify whether the models show evidence of simultaneous alignment and calibration on a variety of datasets covering both multiple choice and open ended factual recall. And we characterize the effect of instruct fine-tuning on each of these facets.

Conformal prediction (CP) and its extension, conformal risk control (CRC), are established frameworks for quantifying uncertainty in supervised machine learning through formal guarantees. However, recent breakthroughs in artificial intelligence (AI) have been driven by unsupervised generative models, such as large language models (LLMs) and image generators, which are not directly compatible with CP or CRC. In this work we introduce conformal generation (Conf-Gen), a general framework adapting CRC to generative tasks while relaxing its theoretical assumptions. Conf-Gen unifies and generalizes previous attempts to apply CP to LLMs, and extends conformal methodology to entirely new domains. We demonstrate the flexibility of Conf-Gen through some novel applications, including obtaining conformal guarantees on: image generators producing non-memorized images, conversational AI systems having asked enough clarifying questions, and the output of AI agents being correct.

LLMs' linguistically expressed confidence should faithfully reflect their intrinsic uncertainty. While recent work shows LLMs struggle to use epistemic markers (e.g., "it is likely...") in a human-aligned fashion, it remains unclear whether models can apply their own linguistic confidence framework to associate markers with specific confidence levels in a stable and generalizable way, and how contextual features impact this ability. We conduct the first systematic study of this question, formalizing marker internal confidence (MIC) as the estimated intrinsic confidence a model associates with a specific epistemic marker in a given task domain. We present 7 metrics to evaluate the stability of MICs within and across distributions. Applying our analysis framework to diverse models and tasks, we find that LLMs remain faithfully miscalibrated even under model-centric interpretation of marker meanings, struggling to differentiate markers by internal confidence across distributions despite preserving a somewhat consistent ranking order across tasks. This supplies critical, complementary evidence to existing work toward a holistic understanding of faithful calibration in LLMs, emphasizing the need for more aligned and stable marker use to improve trustworthiness and reliability.

As large language models are increasingly deployed for clinical text, ensuring they can reliably signal their own uncertainty becomes critical. Most existing uncertainty quantification (UQ) methods are designed for open-domain generation and cannot localize uncertainty at the token or span level in long clinical text. We propose Reverse Probing, the first UQ framework specialized for clinical summarization, which estimates token-level uncertainty directly from pre-existing labeled summaries. Rather than sampling new outputs, Reverse Probing treats the text as a probe into the model's internal state, extracting uncertainty signals from four categories of internal activations. We evaluate on two expert-annotated clinical datasets and outperform eight adapted baselines on all metrics, achieving up to 4 times higher AUPRC while reducing inference time and computational costs. Feature analysis reveals that delta energy and neighborhood context are the most consistent predictors across all models. This study offers interpretable insights into how models internally respond to unsupported clinical content.

As large language models (LLMs) are increasingly integrated into high-stakes decision-making, the ability to reliably quantify uncertainty has become a critical requirement for safety and trust. However, current uncertainty quantification methods primarily operate at the output level, often failing to distinguish whether uncertainty arises from the model's lack of knowledge or from ambiguity in the user's input. While input-centric uncertainty quantification has recently emerged as a promising direction, it remains relatively underexplored and typically relies on coarse, input-level information. Consequently, users are provided with scalar uncertainty scores that offer little actionable guidance on which parts of the input should be clarified to improve reliability. To address this limitation, we propose Shapley-based input uncertainty Quantification (ShaQ), a framework for span-level attribution of input-induced uncertainty. Our approach models ambiguous spans in the input as players in a cooperative game and quantifies their contributions using Shapley values, defined via the weighted average of marginal reductions in conditional entropy obtained by clarifying each span coalition. Unlike existing input-level approaches, our formulation captures complex interactions among spans and provides a principled decomposition in which individual attributions sum exactly to the total input-induced uncertainty. We evaluate ShaQ on the AmbigQA and AmbiEnt benchmarks, where it achieves state-of-the-art performance in ambiguity detection. We further demonstrate its utility on MediTOD, showing that ShaQ can localize under-specified clinical utterances and facilitate human-AI collaboration in high-stakes settings. Overall, ShaQ improves uncertainty estimation and provides actionable insights for targeted input clarification.

Prompt-based verification is widely used to mitigate hallucinations in large vision-language models (LVLMs), yet when it helps remains poorly understood. We systematically study verification prompting across two representative LVLM architectures and hallucination benchmarks, and find that it is a risk-bearing intervention: its corrections increase with input difficulty, while newly introduced errors persist across difficulty levels. As a result, always-on prompting helps on hard inputs but offers little benefit -- and can harm -- easier ones. Our analysis further shows that this behavior is associated with a conservative output shift. Verification prompts redistribute attention from visual tokens toward instruction tokens and induce a distinct middle-layer entropy pattern absent in a neutral-prompt control, suggesting instruction-conditioned attention redistribution rather than uniformly improved visual grounding. Motivated by this input-dependent risk, we propose Risk-aware Selective Prompting (RSP), a training-free approach that uses pre-generation uncertainty signals to trigger verification selectively. RSP mitigates the degradation of always-on prompting while preserving baseline performance, and reveals that effective selection signals vary across architectures.

Self-evolving large language models (LLMs) learn by generating their own training tasks and solutions, reducing reliance on human-curated supervision. However, in many reasoning domains, the model must also validate generated tasks and judge generated answers to obtain training signals. This creates a training-signal challenge: erroneous self-judgments become erroneous gradient updates. Existing approaches either rely on external verifiers, which limits generality, or treat noisy self-generated feedback as supervision. We propose COSE (Confidence-Orchestrated Self-Evolution), which uses the LLM's intrinsic confidence as a lightweight uncertainty signal to modulate learning. COSE introduces confidence-weighted PPO updates and confidence-prioritized replay. Across 19 held-out benchmarks and four Qwen/Llama backbones (0.6B--4B), COSE consistently improves over base models and achieves the best average performance in general reasoning and mathematics, while remaining competitive on code. Code and data are available at https://anonymous.4open.science/r/COSE_-B5C2.

LLM confidence calibration is often evaluated by comparing two signals: token-probability scores and verbalized confidence. These signals are sometimes treated as direct readouts of model uncertainty, but their comparison depends on measurement choices that are rarely made explicit. In the main analysis, we hold the verbalized-confidence elicitation fixed: a single prompt template, probability scale, and output format. We then vary the measurement axes that define the verbalized-vs-token comparison: which answer string receives the token-probability score, how that score is read from the answer tokens, and under which conditioning context it is measured. We evaluate this design on four QA benchmarks across three open 7--8B base/Instruct model families, with larger Qwen2.5 variants as same-family robustness checks. The resulting comparison is sensitive to these choices: conditioning context changes the sign or magnitude of the ECE gap across settings, token readout produces smaller but still sign-moving changes, and changing the ECE estimator has little effect. Under the default generated-answer, bare-context protocol, Instruct settings are close to parity rather than showing a large calibration gain for verbalized confidence. In a separate supplied-answer analysis, surface-plausible wrong answers receive nearly the same confidence as supplied gold answers, suggesting that verbalized confidence also reflects answer plausibility and provenance rather than correctness alone. We argue that both confidence signals should be treated as protocol-dependent behavioral measurements, and provide a reporting checklist covering elicitation provenance, scored answer, token-probability readout, and conditioning context.

Existing training approaches for large language models learn a single set of parameters, based on large volumes of data, which is typically heterogeneous, conflicting and often outright contradictory. As a result, the model is forced to compress conflicting goals, and inherent uncertainties into a single, averaged pattern of behaviour. We propose an $α$-Rényi variational framework for learning distributions over post-training parameters, offering an uncertainty-aware alternative to deep ensemble approaches. The resulting variational objective interpolates between classical variational Bayes and predictively oriented posterior learning, balancing between globally plausible individual models against systems of complementary specialists. We identify local stability criteria, demonstrating how model misspecification can make non-degenerate posterior spread locally favourable, manifesting contradictory or conflicting data as epistemic uncertainty. We apply our framework to LLM post-training, learning an ensemble of LoRA adapters attached to a shared, frozen base model, providing a scalable training procedure for both supervised fine-tuning and preference optimisation. Our approach enables training examples to be softly routed across ensemble members, promoting model specialisation and providing actionable uncertainty estimates across different tasks.

Probabilistic forecasting estimates the likelihood of uncertain future events. To improve LLM forecasting, existing methods typically learn from binary outcomes to output verbalized forecasts. However, while aggregated human forecasts contain rich information in both the crowd probability estimate and the degree of agreement among forecasters, how to utilize these signals remains underexplored. To address this, we propose the Beta-Bernoulli Calibrator (BBC), which converts an initial point estimate forecast from any model into a distribution over event likelihood, using supervision from both binary outcomes and human forecasts. BBC models event likelihood $p \sim \text{Beta}(α, β)$ and outcome $y \sim \text{Bernoulli}(p)$, with the mean as the calibrated point forecast and the variance as the epistemic uncertainty. Our results show that BBC generally provides better calibrated and more accurate forecasts than both traditional post-hoc calibration methods and models fine-tuned specifically for forecasting, while remaining lightweight and having good generalization. We also show that the epistemic uncertainty captured by BBC is a more reliable predictor of forecasting error than verbalized confidence.

Large language models (LLMs) are known to abandon their initial stance to conform to user pushback. While prior research largely attributes this behavior to sycophancy learned during reinforcement learning from human feedback, we hypothesize that conformity is also driven by a model's epistemic uncertainty at inference time. In this paper, we introduce MUSE, a two-stage evaluation framework to disentangle the mechanisms driving LLM conformity. Specifically, MUSE maps a model's epistemic uncertainty in responding to a query against its likelihood to yield to user pushback in a subsequent turn. We demonstrate that the mechanisms driving conformity extend beyond sycophancy alone. Specifically, we characterize two distinct factors that jointly drive conformity: sycophantic conformity, where a model aligns with user pushback even with absolute certainty in its initial response, and uncertainty-driven conformity, where a model's likelihood for conformity increases alongside its uncertainty. Furthermore, we conduct ablation studies to demonstrate that both sycophantic conformity and uncertainty-driven conformity grow with 1) the LLM's perceived expertise of the user and 2) the plausibility of the user's suggestions. More broadly, MUSE informs more targeted intervention strategies by distinguishing alignment-induced sycophancy and training-corpora-driven uncertainty.

Uncertainty quantification (UQ) remains a critical challenge in Large Vision Language Models (LVLMs) for reliable predictions and real-world deployment. However, most existing methods are adapted from the LLM literature and primarily focus on the language modality, leaving the contribution of visual information to LVLM uncertainty largely underexplored. In this paper, we investigate how LVLMs process visual information and whether this process can be used to improve uncertainty estimation. By analyzing hidden representations after the integration of visual features during the generation process, we observe that high-confidence predictions rely more heavily on visual content than uncertain ones. Building on this insight, we propose Visual-Grounded Token UQ (VIG-TUQ), a training-free framework that explicitly incorporates visual grounding into uncertainty estimation by weighting token-level language uncertainty with visual grounding scores. We evaluate VIG-TUQ on multiple datasets and across diverse LVLM architectures, including early-fusion, late-fusion, and native-fusion models. Results indicate that our method often improves upon existing token-level uncertainty approaches. Code and data will be made available upon acceptance.

Large language models (LLMs) are prone to hallucinations, i.e., statements unsupported by the input or training data, hindering reliable deployment. In parallel, numerous uncertainty estimation (UE) methods have been proposed to quantify model confidence and are often implicitly treated as proxies for model failure. However, the relationship between uncertainty and hallucinations remains insufficiently characterized. We present a systematic empirical study of the association between uncertainty estimators and hallucinations in LLMs. Rather than assuming this association, we evaluate directly when and to what extent it holds. We consider a diverse set of uncertainty estimators, including information-theoretic, sampling-based, and reflexive estimators, and examine their behavior across hallucination settings. Our experiments cover both intrinsic hallucinations (violations of input faithfulness) and extrinsic hallucinations (unsupported claims relative to training data), using four complementary benchmarks, including RAGTruth and HalluLens. We find that the association is highly variable and often weak, depending on the hallucination type and the LLM under evaluation. These results challenge the use of uncertainty as a direct signal of hallucination and clarify when it provides actionable information.

Educational virtual laboratories can make experimental training more scala-ble, adaptive, and accessible, especially when students have limited access to physical laboratory facilities. However, authoring new simulated laboratory procedures remains costly: educators must describe new equipment, define how instruments and materials interact, and specify valid procedural flows that can be executed or assessed inside the virtual environment. Large lan-guage models can assist in this authoring process by generating detailed ex-perimental procedures, but their output should not be treated as directly exe-cutable plans. They may omit necessary actions, arrange steps in the wrong order, or produce instructions that are logically incorrect or incompatible with the laboratory equipment. This paper presents a prototype framework for managing uncertainty in LLM-generated procedural knowledge for virtu-al laboratory planning. The framework aims to reduce procedural uncertainty by using structured domain representations and uncertain LLM-generated state-transition samples to extract candidate procedural rules, transform them into explicit and inspectable constraints, and use them to repair uncertain procedural steps. Although the motivating domain refers to educational vir-tual laboratories, the underlying problem is more general: managing uncer-tain procedural knowledge for action planning in structured interactive envi-ronments. We illustrate the approach in a virtual laboratory domain involving laboratory instruments, containers, tools, and material-transfer actions.

Single-pass uncertainty quantification (UQ) methods for classification represent uncertainty by predicting a tractable distribution over the class probability vector. While existing approaches primarily focus on enhancing the expressiveness of this distribution, they often provide limited insight into how predictive uncertainty is structured and aggregated, resulting in weak interpretability. We introduce the courtroom analogy, which conceptualizes uncertainty-aware classification as a structured debate among class-specific advocates. Each advocate forms a probabilistic opinion, and a final verdict is reached by aggregating these opinions using input-dependent plausibility weights. In this framework, each advocate's opinion is modeled as a Dirichlet distribution whose concentration parameter is decomposed into shared evidence and class-specific advocacy. This yields a structured mixture of Dirichlet distributions with semantically interpretable parameters. To instantiate this formulation, we propose Mixture of Dirichlet EXperts (MoDEX), a single-pass neural architecture that predicts the courtroom parameters, enabling efficient and expressive UQ while explicitly modeling uncertainty aggregation. We demonstrate that MoDEX enjoys strong theoretical properties and achieves state-of-the-art UQ performance across diverse benchmarks, yielding interpretable uncertainty estimates with meaningful semantics.

Large language models often generate confident but incorrect answers rather than abstaining when uncertain. This problem is particularly acute for small language models (SLMs), where computational constraints and autonomous operation amplify the need for reliable uncertainty detection. We propose Second Guess, a lightweight, parameter-free prompting technique for abstention in multiple-choice question answering (MCQA) that is well-suited for SLMs. Our key empirical insight is that models which truly know an answer will select it consistently, while uncertain models exhibit unstable behavior when an ``I don't know'' option is added. Evaluated on four open models (2B-8B parameters) and four benchmarks, Second Guess achieves the highest composite risk improvement of 10.81%. Notably, it maintains an 8% composite risk improvement on fine-tuned models where entropy-based methods degrade, and improves most for lower-performing models. All code and results required to reproduce this work is available in https://github.com/Mystic-Slice/second-guess

Large Language Models (LLMs) and Multimodal LLMs (MLLMs) have demonstrated immense potential in autonomous driving (AD) by offering human-like reasoning and open-world generalization. However, the excessive computational overhead and high inference latency of these massive models severely hinder their deployment in resource-constrained AD systems. To address this challenge, we propose a novel decision-making framework utilizing a lightweight confidence-aware language model, which bridges the gap between complex multimodal intention reasoning and efficient inference. Specifically, we design a multi-agent collaborative workflow, comprising action voting, confidence assessment, and summarization agents, to generate high-quality, confidence-annotated decision demonstrations via explicit Chain-of-Thought (CoT) reasoning. These demonstrations are then distilled into a lightweight language model featuring a dual-head architecture, enabling the joint prediction of decision probabilities and the generation of textual rationales. The distillation is realized via a confidence-aware fine-tuning strategy coupled with Retrieval Augmented Generation (RAG) to enhance the model's adaptability and data efficiency. Comprehensive closed-loop experiments on the nuPlan benchmark demonstrate that our approach achieves state-of-the-art (SOTA) success rates in both regular and long-tail scenarios while maintaining low inference latency.

Safety alignment in large language models (LLMs) and multimodal large language models (MLLMs) is commonly assumed to operate as a near-binary threshold mechanism. We challenge this assumption by revealing that safety behavior is governed by an instability region where small perturbations induce stochastic refusal decisions rather than deterministic outcomes. We develop a multi-metric diagnostic framework combining external and internal signals to characterize this instability. Through systematic experiments, we identify a characteristic diagnostic signature: inputs in unstable regimes exhibit elevated output uncertainty yet decreased internal safety activation, a decoupling phenomenon that explains why detection-based defenses fail against sophisticated attacks. Building on this framework, we introduce Furina, a jailbreak attack that deliberately induces this signature through fragmented, scene-anchored prompts without model-specific optimization. Furina outperforms strong single-turn and multi-turn baselines on HarmBench and achieves competitive results on MM-SafetyBench, demonstrating that uncertainty amplification provides a principled and transferable mechanism for understanding safety vulnerabilities. Code is available at: https://github.com/0xCavaliers/Furina_Jailbreak.

Large Language Models (LLMs) are predominantly governed by probabilistic frameworks in which the sum of outcome probabilities is constrained to unity. This architectural limitation, often imposed by Softmax layers, leads to a collapse of uncertainty that makes it difficult to differentiate between epistemic uncertainty, paradox, and vagueness. We present an empirical investigation of the application of Neutrosophic Logic, a framework that treats Truth (T), Indeterminacy (I), and Falsity (F) as three independent dimensions, to model epistemic states in LLMs. We conducted experiments on a family of four OpenAI GPT models across five linguistic phenomena: logical paradoxes, epistemic ignorance, vagueness, ethical contradictions, and future contingencies, under three prompting strategies: neutrosophic, probabilistic, and entropy-derived. Our findings reveal that the neutrosophic approach, by allowing T+I+F > 1, a state we term hyper-truth, provides a richer representation of a model's internal state. In 35% of evaluations, hyper-truth emerged spontaneously, predominantly under ethical contradiction and logical paradox. We demonstrate that this approach preserves truth values in fuzzy contexts and offers a robust method for identifying and quantifying internal model conflict. We conclude that the integration of neutrosophic evaluation layers is a critical step toward more transparent, reliable, and ethically aware AI systems.

The maximum softmax probability (MSP) represents a default approach when evaluating uncertainty quantification for language model generation with structured output. Although cheap, it is often miscalibrated. Methods that probe the model's internal activations feed raw hidden states into opaque classifiers, reading activations as static snapshots and leaving implicit the layer-wise trajectory by which a representation is formed. Yet, similar endpoints can arise from very different paths, and how evidence accumulates, reinforces, or reverses across depth might reveal uncertainty that final probabilities obscure. We extract eleven scale-invariant geometric features, tracing the cumulative path of per-layer MLP updates, and feed them to a sparse linear probe. The probe outperforms MSP under selective abstention, with gains scaling with baseline miscalibration up to 21 AURC points. Because every feature has a closed-form geometric meaning, the probe's coefficients trace how and where along depth errors take shape -- which layers commit prematurely, which contradict the running state, where trajectories drift away from their endpoint.

Uncertainty Quantification (UQ) is widely regarded as the primary safeguard for deploying Large Language Models (LLMs) in high-stakes domains. However, we argue that the field suffers from a category error: mainstream UQ methods for LLMs are just unsupervised clustering algorithms. We demonstrate that most current approaches inherently quantify the internal consistency of the model's generations rather than their external correctness. Consequently, current methods are fundamentally blind to factual reality and fail to detect ``confident hallucinations,'' where models exhibit high confidence in stable but incorrect answers. Therefore, the current UQ methods may create a deceptive sense of safety when deploying the models with uncertainty. In detail, we identify three critical pathologies resulting from this dependence on internal state: a hyperparameter sensitivity crisis that renders deployment unsafe, an internal evaluation cycle that conflates stability with truth, and a fundamental lack of ground truth that forces reliance on unstable proxy metrics to evaluate uncertainty. To resolve this impasse, we advocate for a paradigm shift to UQ and outline a roadmap for the research community to adopt better evaluation metrics and settings, implement mechanism changes for native uncertainty, and anchor verification in objective truth, ensuring that model confidence serves as a reliable proxy for reality.

Any system that models the world under finite representational capacity must compress; any compression entails a prior; and the prior is the system's bias. What has not been established is whether uncertainty participates in the dynamics governing future behavior, or merely describes the output distribution without consequence. We introduce a structural distinction between descriptive uncertainty, which does not recursively modulate the system's policy, and regulatory uncertainty, which directly enters the optimization landscape and drives persistent adaptive restructuring. We prove formally that current transformer architectures are confined to descriptive uncertainty at inference. We ground this in thermodynamics via Landauer's principle: for uncertainty to be regulatory, epistemic error must cost real energy; in a decoupled system, hallucinations and correct derivations dissipate identical energy. We test this empirically across three locally-deployed language models (3B, 8B, 70B parameters). Token-level Shannon entropy is statistically invariant across tasks spanning pattern retrieval, causal operator application, and out-of-distribution causal generalization in all three models (all pairwise p >= 0.568; within-model ranges 0.011-0.028 nats), while task accuracy varies substantially across the same conditions (0%-100%). Entropy and accuracy are orthogonal. The decoupling is scale-invariant: larger models achieve higher accuracy but identical entropy flatness. This structural incapacity is not resolvable by additional parameters or training data. Genuine epistemic grounding requires physical coupling between thermodynamic substrate state and information processing cost.

Large language models (LLMs) generate not only reasoning text, but also token-level confidence trajectories that record how uncertainty evolves during inference. Whether these trajectories are relevant to reasoning correctness remains unclear. Here we show that confidence trajectories encode a content-agnostic confidence geometry associated with trace-level final-answer correctness. Using only token-level confidence values, without access to the input question, reasoning text, hidden states, or external verifiers, we find that low-dimensional representations of confidence trajectories separate correct from incorrect reasoning traces. Across GSM8K, MATH, and MMLU, this geometric separation is quantitatively linked to downstream predictability: stronger clustering of correct and incorrect traces, measured by the Davies--Bouldin index, consistently corresponds to higher correctness-discrimination AUC. We further show that correctness-related information is enriched in the tail of reasoning, suggesting that late-stage confidence dynamics carry key correctness signals. We propose NeuralConf, a lightweight estimator that learns from confidence trajectories for correctness evaluation. Under a fixed trace budget, NeuralConf-derived scores improve confidence-weighted answer aggregation over majority voting, tail confidence, and other static baselines. These results reveal that LLMs expose trace-intrinsic statistical signals of correctness through their own confidence dynamics, offering a route to improve inference using information already present within generation.

When Large Language Models produce structured outputs such as travel plans, code solutions, or multi-step proofs, individual reasoning steps may appear correct while the output as a whole violates budgets, fails test cases, or contradicts earlier deductions. We propose a decomposed energy function that combines a learned quality scorer with deterministic analytical constraint penalties for verifying structured LLM outputs. The quality scorer is a heterogeneous ensemble of low-rank adapters on a single frozen encoder (3% trainable parameters); the ensemble mean ranks candidates while the standard deviation quantifies epistemic uncertainty, driving a two-pass inference loop that triggers targeted regeneration or abstention. Across five benchmarks (GSM8K, MuSR, TravelPlanner, TACO, Knights & Knaves), our 149M-parameter verifier orchestrating a pool of 7-26B open generators outperforms single-shot Qwen-72B on every benchmark, matches Claude Sonnet 4.6 on MuSR (67.7% vs. 68.0%), and reduces constraint violations by 53% relative to Opus 4.6 on TravelPlanner (oracle 0.028, random 0.231). The two routes are complementary: structural verification wins when constraints are checkable (the verifier captures signal frontier models cannot self-detect), while pretraining-scale priors win where they are not (narrative inference, code semantics). A cross-dataset confounding analysis confirms genuine quality discrimination on four reasoning tasks and identifies a model-identity shortcut on code, mitigated via last-layer retraining. Scorers trained on difficult data transfer zero-shot: a MuSR-trained scorer achieves 93.9% on GSM8K without seeing a math problem.

As large language models (LLMs) are deployed in consequential settings such as medical question answering and legal reasoning, the ability to estimate when their outputs are likely to be correct is essential for safe and reliable use, requiring well-calibrated uncertainty. Standard reinforcement learning with verifiable rewards (RLVR) trains models with a binary correctness reward that is indifferent to confidence, providing no penalty for confident but wrong predictions and thereby degrading calibration. Recent work addresses this by training models to produce verbalized confidence scores alongside answers and rewarding agreement with correctness. However, verbalized confidence is calibrated at the token level and thus exhibits inconsistency across textual variations with same semantic meaning. We propose \textbf{Calibration with Semantic Reward (CSR)}, a framework that calibrates language models directly in semantic space without a verbalized confidence interface. CSR combines the correctness reward with a novel semantic calibration reward that encourages exploitation among correct rollouts by promoting semantic agreement, and exploration among incorrect ones by discouraging spurious consistency. Experiments across three model families on HotpotQA (in-distribution) and TriviaQA, MSMARCO, and NQ-Open (out-of-distribution) show that CSR consistently achieves lower ECE and higher AUROC than verbalized-confidence baselines across nearly all settings, reducing ECE by up to $40\%$ and improving AUROC by up to $31\%$ over verbalized-confidence baselines, with calibration behavior generalizing robustly across all four evaluation settings.

Large Language Diffusion Models (LLDMs) are emerging as an alternative to autoregressive models, offering faster inference through higher parallelism. Similar to autoregressive LLMs, they remain prone to hallucinations, making reliable uncertainty quantification (UQ) crucial for safe deployment. However, existing UQ methods are fundamentally misaligned with this new paradigm: they assume autoregressive factorization or use expensive repeated sampling, negating the efficiency of LLDMs. In this work, we present the first systematic study of UQ for LLDMs and propose lightweight, zero-shot uncertainty signals derived from the iterative denoising process, leveraging intermediate generations, token remasking dynamics, and denoising complexity. We further adapt a state-of-the-art UQ method to LLDMs by combining masked diffusion likelihoods with trajectory-based semantic dissimilarity. We prove that expected trajectory dissimilarity lower bounds the masked diffusion training objective, which motivates its usage as an uncertainty score. Comprehensive experiments across three tasks, eight datasets, and two models show that our method achieves a great cost-performance trade-off: it approaches the strongest sampling-based baselines while incurring up to 100x lower computational overhead. Our work demonstrates that LLDMs can deliver both fast inference and reliable hallucination detection simultaneously.

In safety-critical applications, language models should be able to characterize their uncertainty with meaningful probabilities. Many uncertainty quantification approaches require supervised data; however, finding suitable unseen challenging data is increasingly difficult for large language models trained on vast amounts of scraped data. If the model is consistently (and correctly) confident in its predictions, the uncertainty quantification method may consistently overestimate confidence on new and unfamiliar data. Finding data which exhibits enough uncertainty to train supervised uncertainty quantification methods for high-performance models may therefore be challenging, and will increase in difficulty as LLMs saturate datasets. To address this issue, we first introduce the problem of inducing artificial uncertainty in language models, then investigate methods of inducing artificial uncertainty on trivially easy data in the absence of challenging data at training time. We use probes trained to recognize artificial uncertainty on the original model, and find that these probes trained on artificial uncertainty outperform probes trained without artificial uncertainty in recognizing real uncertainty, achieving notably higher calibration on hard data with minimal loss of performance on easy data.

Large language models (LLMs) are increasingly deployed in settings where the available context is incomplete or degraded. We argue that an LLM generating answers under incomplete context can be viewed as an implicit imputer, and evaluated against a criterion from the multiple imputation (MI) literature: uncertainty should scale with the amount of missing information. We assess this criterion on SQuAD, using a controlled framework in which context availability is varied across five levels. We evaluate two answer-level uncertainty measures that can be estimated from repeated sampling: sampling-based confidence (empirical mode frequency) and response entropy. Confidence fails to reflect increasing missingness: it remains high even as accuracy collapses. Entropy, by contrast, increases with context removal, consistent with the MI analogy, and explains substantially more variance in accuracy than confidence across all evidence levels (quadratic $R^2$ gap up to 0.057). We further introduce a black-box diagnostic $ρ_R(α)$ that estimates the proportion of baseline uncertainty resolved by context level $α$, requiring only repeated sampling with and without context. These results suggest that entropy is a more responsive black-box uncertainty measure than confidence under incomplete context.

Prediction sets provide a theoretically grounded framework for quantifying uncertainty in machine learning models. Adapting them to structured generation tasks, in particular, large language model (LLM) based code generation, remains a challenging problem. An existing attempt proposes PAC prediction sets but is limited by its strong monotonicity assumption on risk and single-label classification framework, which severely limits the space of candidate programs and cannot accommodate the multiple valid outputs inherent to code generation. To address these limitations, we propose an approach RisCoSet that leverages multiple hypothesis testing to construct risk-controlling predictions for LLM-based code generation. Given a trained code generation model, we produce a prediction set represented by a partial program, which is guaranteed to contain a correct solution with high confidence. Extensive experiments on three LLMs demonstrate the effectiveness of the proposed method. For instance, compared with the state-of-the-art, our method can significantly reduce the code removal by up to 24.5%, at the same level of risk.

Large language models (LLMs) are increasingly used in social science as scalable measurement tools for converting unstructured text into variables that can enter standard empirical designs. Measurement validity demands more than high average accuracy, which requires well calibrated confidence that faithfully reflects the empirical probability of each measurement being correct. This paper studies the model miscalibration in LLM-based social science measurement. We begin with a case study on FOMC and show that confidence based filtering can change downstream regression estimates when LLM confidence is miscalibrated. We then audit calibration across 14 social science constructs covering both proprietary models, including GPT-5-mini, DeepSeek-V3.2, and open source models. Across tasks and model families, reported confidence is poorly aligned with tolerance-based correctness. As a simple mitigation, we propose a soft label distillation pipeline for calibrating Bert with LLM. The method converts an LLM score and its verbalized confidence into a soft target distribution, then trains a smaller discriminative classifier on encoder models for these targets. Averaged across datasets, this approach reduces ECE by 43.2% and Brier by 34.0%. These results suggest that LLM-based social science pipelines should treat calibration as part of measurement validity, rather than as an optional post-processing concern.

Large vision-language models suffer from visual ungroundedness: they can produce a fluent, confident, and even correct response driven entirely by language priors, with the image contributing nothing to the prediction. Existing confidence estimation methods cannot detect this, as they observe model behavior under normal inference with no mechanism to determine whether a prediction was shaped by the image or by text alone. We introduce BICR (Blind-Image Contrastive Ranking), a model-agnostic confidence estimation framework that makes this contrast explicit during training by extracting hidden states from a frozen LVLM twice: once with the real image-question pair, and once with the image blacked out while the question is held fixed. A lightweight probe is trained on the real-image hidden state and regularized by a ranking loss that penalizes higher confidence on the blacked-out view, teaching it to treat visual grounding as a signal of reliability at zero additional inference cost. Evaluated across five modern LVLMs and seven baselines on a benchmark covering visual question answering, object hallucination detection, medical imaging, and financial document understanding, BICR achieves the best cross-LVLM average on both calibration and discrimination simultaneously, with statistically significant discrimination gains robust to cluster-aware analysis at 4-18x fewer parameters than the strongest probing baseline.

Large language models for subjectivity analysis are typically trained with aggregated labels, which compress variations in human judgment into a single supervision signal. This paradigm overlooks the intrinsic uncertainty of low-agreement samples and often induces overconfident predictions, undermining reliability and generalization in complex subjective settings. In this work, we advocate uncertainty-aware subjectivity analysis, where models are expected to make predictions while expressing uncertainty that reflects human disagreement. To operationalize this perspective, we propose a two-phase Disagreement Perception and Uncertainty Alignment (DPUA) framework. Specifically, DPUA jointly models label prediction, rationale generation, and uncertainty expression under an uncertainty-aware setting. In the disagreement perception phase, adaptive decoupled learning enhances the model's sensitivity to disagreement-related cues while preserving task performance. In the uncertainty alignment phase, GRPO-based reward optimization further improves uncertainty-aware reasoning and aligns the model's confidence expression with the human disagreement distribution. Experiments on three subjectivity analysis tasks show that DPUA preserves task performance while better aligning model uncertainty with human disagreement, mitigating overconfidence on boundary samples, and improving out-of-distribution generalization.

Large Language Models are increasingly used as zero-shot classifiers in complex reasoning tasks. However, standard constrained decoding suffers from a phenomenon we define as Renormalization Bias. When a model is restricted to a small set of target labels, the standard softmax operation discards the probability mass assigned to semantic synonyms in the original distribution. This loss of information, which we call the Silent Vote, results in artificial overconfidence and poor calibration. We propose Semantic Softmax, an inference-time layer that recovers this lost information by aggregating the scores of the semantic neighborhood surrounding each target label. We evaluate this approach on Qwen-3 and Phi-4-mini models using GoEmotions and Civil Comments datasets. Our results demonstrate consistent improvements across all evaluation metrics: Semantic Softmax substantially reduces Expected Calibration Error (ECE) and Brier Score, while simultaneously enhancing discriminative performance in terms of AUROC and Macro-F1. By accounting for linguistic nuances, our method provides a more calibrated and accurate alternative for zero-shot classification.

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

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

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

Automated mental health prediction using textual data has shown promising results with deep learning and large language models. However, deploying these models in high-stakes real-world settings remains challenging, as existing approaches largely rely on semantic representations and often produce overconfident predictions under ambiguous, noisy, or shifted data. Moreover, most methods lack reliable uncertainty estimation, undermining trust in risk-sensitive mental health applications. To address these limitations, we formulate the task as a multi-view learning problem that integrates semantic information from encoder-only models with higher-level reasoning information from decoder-only models, where reasoning-aware representations and uncertainty modeling are obtained in a trustworthy manner. To ensure reliable fusion, we adopt an evidential learning framework based on Subjective Logic to explicitly model uncertainty and introduce an evidential fusion strategy that balances complementary views while discounting unreliable evidence. Benchmarking on three real-world datasets, Dreaddit, SDCNL, and DepSeverity, reports accuracies of 0.835, 0.731, and 0.751, respectively, demonstrating its potential for reliable mental health prediction. Additional experiments on robustness to noise and case studies for interpretability confirm that our proposed framework not only improves predictive performance but also provides trustworthy uncertainty estimates and human-understandable reasoning signals, making it suitable for risk-sensitive applications in mental health assessment.

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

Direct Preference Optimization (DPO) has proven to be an effective solution for mitigating hallucination in Multimodal Large Language Models (MLLMs) by learning from preference pairs. One of its key challenges lies in how to transfer the sequence-level preference into fine-grained supervision on visual fidelity. To safeguard vision-related tokens that are prone to hallucination, existing methods typically allocate training emphasis according to the model's self-assessed visual sensitivity signals. However, such sensitivity, estimated by a model still under training, introduces self-referential bias: reinforcing already well-learned visual cues while neglecting hard-to-perceive but critical details, thereby limiting deeper alignment. In this work, we propose an Uncertainty-aware Exploratory Direct Preference Optimization (UE-DPO) method for MLLMs, which enables the model to uncover its cognitive deficiencies and actively explore for self-correction, guided by token-level epistemic uncertainty. Specifically, we first quantify the uncertainty from the model's failure to ground token predictions in the given image. Then, based on an uncertainty-aware exploration intensity, we encourage more learning pressure on visually deficient tokens in preferred samples, and alleviate the over-penalization of beneficial knowledge in dispreferred samples. Further, we provide a theoretical justification for our method, and extensive experiments demonstrate its effectiveness and robustness.

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

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

LLMs' overconfidence, particularly when hallucinating, poses a significant challenge for the deployment of the models in safety-critical settings and makes a reliable estimation of uncertainty necessary. Existing approaches for uncertainty quantification typically prioritize lexical or probabilistic measures; however, these techniques often ignore the semantic variance of different responses with similar meaning. In this paper, we propose Adaptive Conformal Semantic Entropy (ACSE), a method for estimating prompt-level uncertainty by adaptively measuring semantic dispersion in LLMs outputs. Our uncertainty scoring function is based on clustering semantic entropy of multiple diverse responses to the same prompt. The function adaptively adjusts the uncertainty score based on semantic features of each cluster. To ensure statistical reliability of our score, we use conformal calibration to apply a decision rule to accept/abstain the prompts, providing a finite-sample, distribution-free guarantee such that the error rate among the accepted responses remains bounded by a user-specified tolerance. Our extensive experimental evaluations using different LLMs and datasets, demonstrate that our approach consistently outperforms state-of-the-art uncertainty quantification baselines using discriminative performance, conformal guarantees, and probabilistic calibration indicators. As a highlight, for TriviaQA dataset, AUROC of our approach is 0.88 compared to 0.65 produced by the token entropy approach.

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

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

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

When language models lack relevant knowledge for a given query, they frequently generate plausible responses that can be hallucinations, rather than admitting being agnostic about the answer. Retraining models to reward admitting ignorance can lead to overly conservative behaviors and poor generalization due to scarce evaluation benchmarks. We propose a post hoc framework, Conformal Abstention (CA), adapted from conformal prediction (CP) to determine whether to abstain from answering a query. CA provides finite-sample guarantees on both the probability of participation (i.e., not abstaining) and the probability that the generated response is correct. Importantly, the abstention decision relies on prediction confidence rather than the non-conformity scores used in CP, which are intractable for open-ended generation. To better align prediction confidence with the model's ignorance, we introduce a calibration strategy using representation geometry within the model to measure knowledge involvement in shaping the response. Experiments demonstrate that we improve selective answering significantly with 75 percent conditional correctness.