Semantic Entropy

Audio-language models can produce confident answers unsupported by the audio, motivating uncertainty estimates that identify unreliable responses. We compare probability-based, sampling-based, self-verification, evidential, and contrastive measures across four open-weight models and five audio QA benchmarks. In multiple-choice evaluation, first-token measures are strongest overall, with top-1 probability achieving a mean AUROC of .740, compared with .708 for ten-sample discrete semantic entropy, while requiring no additional model calls. Across four benchmarks, shifting from multiple-choice to open-ended evaluation lowers mean accuracy from 57.6% to 36.6%, yet uncertainty remains predictive of errors: semantic entropy, maximum token entropy, and semantic agreement achieve mean AUROCs of .697, .694, and .693, respectively. To test whether uncertainty reflects the evidence available to answer the question, we perform input ablations that remove either the audio or the question. Across top-1 confidence, entropy, and sampling-based measures, removing audio reduces error-detection AUROC by .101 on average, compared with .010 when removing the question. Together, these results establish efficient uncertainty baselines and show that uncertainty in audio-language models depends substantially more on available audio evidence than on question text.

Dynamic facial expression recognition (DFER) benchmarks such as DFEW provide multiple annotator votes per clip, yet most models collapse them to a majority label and cannot represent human disagreement at inference time. We propose a disagreement-aware DFER framework that trains directly on the raw annotator count vector using a Dirichlet-Multinomial likelihood. Unlike mean-only soft-label objectives, the proposed likelihood provides scale-sensitive supervision for the Dirichlet concentration while preserving the predictive mean. A separate ambiguity head predicts annotation entropy for unseen clips, and a monotone Chow-style reject rule combines predicted ambiguity, vacuity, temporal instability, and input quality for selective prediction. On DFEW, the method preserves recognition accuracy while reducing ECE by 30% and AURC by 15%, and predicted ambiguity reaches a Spearman correlation of 0.52 with the annotation entropy of test clips. The calibration and selective-prediction gains transfer to FERV39k and remain under identity- and movie-disjoint DFEW splits.

Predictive-distribution entropy makes a strong selection rule in retrieval-augmented question answering: across five QA benchmarks, keeping the candidate answer that a frozen respondent LLM produces with the lowest answer-token entropy lifts mean answer $F_1$ from 0.4769 to 0.5148 over the retriever's top-ranked passage, with no gold answers. Yet this lowest-entropy rule, which prior entropy-based selectors adopt, fails in a specific and consequential way: a misleading passage makes the respondent confidently wrong, driving its entropy down precisely where the signal looks most trustworthy. We show that the failure comes from the passage the respondent reads -- and the context that passage is read in is an input we can intervene on. We introduce LODESTAR, to our knowledge the first method to score a text intervention by the uncertainty it induces in a third-party frozen respondent, compared across one question's candidates. LODESTAR uses reinforcement learning to train, once and offline, a polarizer -- a short fixed natural-language string inserted into the respondent's prompt and never into its weights; its training labels are built offline from gold answers and two LLM judges, and inference reads neither. Evaluating every competing selector under the same frozen respondent and the same candidate pools on 5,008 questions, LODESTAR attains the highest mean $F_1$ of any inference-ready selector (0.5148 to 0.5339), the highest exact match (0.4136), and the highest GPT-4o judge score of the frozen-respondent configurations judged (0.6435); its three-seed mean wins all 70 method-by-dataset $F_1$ cells against fourteen published configurations while remaining paired-significant against every one. The gain holds both in-domain and out-of-domain, and ablating the polarizer shows it is what makes the respondent read a misleading passage less often (26.0% against 30.3%).

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

Although reinforcement learning with verifiable rewards (RLVR) has improved the performance of large language models (LLMs) across a variety of reasoning tasks, there is significant debate as to whether RLVR expands the reasoning capability boundary, or just improves sampling efficiency. In this paper, we investigate the nature of test-time exploration in RLVR-trained LLMs by employing controlled maze-solving experiments and extracting a tree structure from mathematical reasoning traces (BODHI-Trees) based on semantic equivalence. This helps us delineate between entropy arising from stylistic variations and genuine inferential branching. Our findings demonstrate that the policy entropy collapse observed in RLVR models is not merely syntactic, and is accompanied by a significant reduction in semantic branching entropy. While RLVR improves adherence to environmental constraints and backtracking capabilities, it constricts the space of continuations; we provide evidence suggesting that this might be responsible for the sample efficiency gains of RLVR, albeit at the cost of genuine rollout diversity.

Score Entropy Discrete Diffusion (SEDD) parameterizes discrete reverse processes with unconstrained positive score ratios. While positivity guarantees nonnegative reverse jump rates, it does not ensure Bayes realizability: ratios at a noisy state need not be jointly induced by any clean-token posterior under the forward kernel. The score-entropy loss has the correct population optimum but does not enforce this constraint away from it. In a trained pure-uniform SEDD checkpoint, roughly one quarter of complete score vectors violate the coordinate box, while more than half lie inside it yet remain materially incompatible with any valid posterior. Such violations can produce negative pre-normalization weights in finite-step sampling. Projecting raw scores onto the bridge polytope removes all observed negative weights and improves external generative PPL from $203.6$ to $175.1$ without changing the sampler. We introduce \emph{mean-to-score} (M2S), which predicts a clean-token posterior mean and converts it to the score through an exact kernel-dependent linear map. The construction applies to any known coordinate-wise continuous-time Markov chain (CTMC) satisfying a mild support condition. For uniform corruption, it maps the probability simplex onto the bridge polytope; for absorbing-mask corruption, the resulting objective recovers MD4 exactly. In a controlled 28.4M-parameter CIFAR-10 comparison, M2S lowers test BPD from $3.173$ to $3.129$ and FID-50k from $\CifarSEDDFID$ to $\CifarMtwoSFID$. A 170M-parameter M2S model trained on about 262B OpenWebText token slots outperforms the evaluated pure-uniform SEDD, GIDD, and Neural CTMC checkpoints at every tested sampling budget, reaching generative PPL $143.3$ at 128 steps versus $183.6$ for the strongest pure-uniform baseline.

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

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

Vision-language models can exhibit visual concept-conditioned divergence: given images containing demographic features, corporate logos, or ideological symbols, some models produce unusually uniform responses that differ from what peer models say about the same input. These behaviors evade text-only audits because visual concepts cannot be isolated or substituted the way text tokens can. We present VISTA (Visual Inconsistency Screening Through Analysis), a black-box cross-model audit that couples semantic entropy with distribution-based divergence to flag model-specific anomalies. In a controlled study, we implant concept-conditioned stances in three VLMs via fine-tuning on small biased datasets and confirm that VISTA detects them. Auditing six VLMs across 19 topics, VISTA surfaces 142 high-suspicion cases (1.2%) and identifies selective refusal as a previously unreported divergence pattern, where models refuse demographic queries at rates varying from 0 to 65% across groups.

Chain-of-thought (CoT) reasoning has emerged as an effective approach for activating latent reasoning capabilities in large language models. However, most existing CoT methods use reasoning chains mainly as inference-time prompts, while the generated reasoning traces are rarely reused as semi-supervised learning signals. In this report, we define \textbf{Semi-supervised Chain-of-Thought Learning} and propose \textbf{Semi-CoT}, a simple framework that uses unlabeled questions to construct pseudo reasoning supervision. Semi-CoT samples multiple pseudo-CoTs for each unlabeled question, estimates answer-level semantic entropy, and selects low-entropy reasoning chains as reliable pseudo-CoT demonstrations. This extends the self-training view of CoT from inference-time refinement to semi-supervised pseudo-supervision. Pilot experiments on AQuA, SVAMP, GSM8K, and MultiArith show that the entropy gate selects high-precision pseudo-CoTs, with pseudo-answer precision ranging from $91.36\%$ to $100\%$. Semi-CoT also gives small gains on SVAMP and GSM8K, while AQuA shows negative transfer and MultiArith reaches a ceiling. These results suggest that unlabeled questions can provide reliable pseudo reasoning signals, but their effective use still requires stronger demonstration selection or student training.

Vision-language models can produce confident answers on visually ambiguous inputs, resulting in biased predictions. Common entropy-based methods, such as Semantic Entropy (SE), rely on output diversity. Yet our analysis shows that overconfident visual embeddings suppress output diversity under stochastic decoding, causing SE to underestimate uncertainty in such cases. Recent methods instead probe output diversity through input perturbations, including textual paraphrasing or joint text-image perturbations, and show improved performance. We study these approaches and reveals that the resulting variability is often dominated by textual changes rather than visual evidence, causing uncertainty estimates to reflect prompt sensitivity rather than visual ambiguity. We therefore propose Visual Semantic Entropy (VSE), which perturbs only the image to probe nearby visual variations while keeping the text query fixed. VSE measures uncertainty by clustering generated answers into semantic prototypes and computing the mass-weighted dispersion among them. Extensive evaluation across five modern vision-language models and five diverse VQA benchmarks demonstrates that VSE effectively captures visual ambiguity, establishing a new state-of-the-art for VLM uncertainty estimation.

Quantifying how meaning propagates through communicative exchanges remains underdeveloped in computational linguistics. Here we introduce an information-theoretic framework that quantifies the directed flow of semantic content between interlocutors and decomposes multi-source contributions into redundant, unique, and synergistic components. Our approach leverages large language models as probabilistic estimators of natural language to compute two measures: semantic transfer entropy (STE), which captures directed predictive influence between speakers, and semantic partial information decomposition (SPID), which resolves how multiple sources jointly shape a target's language. Across four experiments we show that the framework detects reduced information flow in cognitively rigid dialogue, captures the dominant role of persuaders in shaping discourse, distinguishes high- from low-quality psychotherapy by the directionality of therapist-client information exchange, and reveals synergistic premise contributions in argumentative essays. This framework opens new avenues for studying information dynamics in digital discourse, pedagogical interactions, clinical dialogues, and any domain in which the structure of linguistic exchange is of research relevance.

Large language models (LLMs) are increasingly deployed in high-stakes domains, where free-text explanations such as chain-of-thought and post-hoc rationales are used to justify model outputs. Yet it remains unclear whether these explanations are sufficient, i.e., if they contain enough information to explain the model's output-generating process. We generalize classical sufficiency from feature attributions to arbitrary explanations and prove that explanation sufficiency can change depending on the input distribution, which must be explicitly defined for LLM explanations. We propose using the LLM itself to generate alternative inputs conditioned on an explanation, capturing its beliefs about possible inputs. We formalize self-consistent sufficiency as a goal for free-text explanations and introduce an information-theoretic metric, SCSuff, that enables evaluation of free-text explanations without relying on predefined biases or shortcuts. Our experiments show that SCSuff agrees with targeted perturbation tests where applicable and demonstrate that explanation sufficiency can vary with the input distribution. We find LLM explanations are generally insufficient and weakly correlated with model size, accuracy, or output entropy. Analysis of final-token hidden states shows that top and bottom SCSuff scores can be predicted from internal representations, suggesting that SCSuff can guide detection and improvement of sufficient LLM explanations. The code for this paper is available at https://github.com/rajesh-lab/self-consistent-sufficiency .

Large language models (LLMs) have achieved strong performance across a wide range of language-based tasks by leveraging both extensive parametric knowledge and in-context learning ability, enabling them to incorporate external information provided in the input prompt. However, the integration of external knowledge can introduce conflicts, not only between the model's internal parametric knowledge and the external information, but also among multiple pieces of external contexts. Existing approaches typically assume that either the model or the provided context is reliable, overlooking the possibility that both sources may contain errors, and avoid conflicts by privileging one source over the other, rather than actively resolving inconsistencies. To address these limitations, we propose a novel framework MACR for LLM knowledge conflict resolution that moves beyond the conventional binary choice paradigm and incorporates an explicit conflict-resolution mechanism based on a multi-agent reasoning approach. Specifically, we first propose an adaptive knowledge assessment and retrieval approach that employs a modified semantic entropy measure to quantify an LLM's confidence in its answer to a given query. Based on this confidence estimation, MACR either externalizes the model's internal knowledge as textual representations or retrieves relevant external knowledge when internal knowledge is insufficient, generating basic contexts for subsequent reasoning. Then we introduce an inductive multi-agent reasoning framework with three specialized agents that, respectively, induce explicit rules, analyze potential conflicts, and resolve inconsistencies across all available contexts. Empirical results demonstrate that MACR significantly outperforms state-of-the-art baselines across benchmarks, while also providing interpretable resolutions of explicit conflicts.

Recent advances in Large Language Models (LLMs) and multi-agent systems have driven the rise of Agentic AI, showing promise for medical reasoning. However, open-ended conversational agents remain prone to two critical failure modes: premature diagnostic handoff and silent clinical hallucinations that may go undetected before reaching the patient. In this work, we propose a multi-agent framework that addresses both issues by replacing ``LLM-as-a-judge'' routing with deterministic orchestration constraints. The framework incorporates two safety mechanisms. First, a neuro-symbolic state-tracking gate enforces completeness of the OLDCARTS clinical protocol (Onset, Location, Duration, Character, Aggravating/Alleviating factors, Radiation, Timing, and Severity) by blocking diagnostic transitions until all required dimensions are collected. Second, an epistemic uncertainty quantification (UQ) gate computes semantic entropy (H) across K=5 independent diagnostic samples to identify and intercept divergent outputs before delivery. We evaluate the system using simulated patient agents powered by the llama-3.1-70b-instruct model on 150 test cases. The full architecture achieves 49.3% diagnostic precision, representing an absolute improvement of 11.3 percentage points over an unconstrained baseline. Additionally, we observe a statistically significant negative correlation (r = -0.181, p < 0.05) between OLDCARTS completeness (σ) and semantic entropy (H), suggesting that structured information gathering is associated with reduced diagnostic uncertainty.

Evaluating multi-turn dialogue is challenging because quality emerges across turns rather than within individual responses. We focus on a key dimension of information-seeking dialogue: semantic progress, defined as the accumulation of new, question-relevant, and non-redundant information over the course of a conversation. We formalize semantic progress as question-conditioned uncertainty reduction and introduce an information-theoretic metric that approximates it in embedding space. Our main estimator uses a tractable Gaussian formulation with closed-form updates, while a complementary maximum-entropy argument shows why log-determinant structure arises more broadly when only second-order embedding information is retained. This formulation yields desirable theoretical properties, including monotonicity, additive decomposition of total information gain across turns, and diminishing returns for redundant evidence. Unlike LLM-as-a-judge approaches, our metric requires no autoregressive inference at evaluation time and is fully reproducible for a fixed embedding model. Experiments on MT-Bench, Chatbot Arena, and UltraFeedback show that the proposed metric achieves competitive agreement with human judgments despite targeting only semantic progress, with improved alignment on MT-Bench and UltraFeedback compared to several LLM-based judges. Notably, the method remains effective with lightweight embedding models under CPU-only execution, indicating that semantic progress can be captured without reliance on large model capacity.

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

Multi-agent code generation offers a promising paradigm for autonomous software development by simulating the human software engineering lifecycle. However, system reliability remains hindered by LLM hallucinations and error propagation across interacting agents. While semantic entropy provides a principled way to quantify uncertainty without ground-truth answers, current methods often rely on costly LLM-driven equivalence checks. In this work, we introduce Fast Adaptive Semantic Entropy (FASE), a novel metric that approximates functional correctness based on the minimum spanning tree of structural and semantic dissimilarity graphs. Evaluations on HumanEval and BigCodeBench demonstrate that FASE outperforms state-of-the-art semantic entropy by LLM entailment, achieving a 25% average improvement in Spearman correlation and a 19% increase in ROCAUC score against Pass@1 from ground-truth test cases when using the Qwen3-Embedding-8B model. Furthermore, by eliminating costly LLM-driven equivalence evaluation, FASE incurs negligible computational overhead, requiring only approximately 0.3% of the runtime cost of traditional semantic entropy approaches. These results position FASE as a practical, cost-effective solution for optimizing uncertainty quantification in real-world multi-agent workflows.

Majority voting is the default unsupervised aggregator for multi-sample LLM inference, but it discards two signals: within-group answer entropy and between-group reasoning geometry. We aggregate by delegation instead (Propagational Proxy Voting, PPV): each group of samples keeps weight on its own answer in proportion to its entropy-based confidence (When) and routes the rest to peers by reasoning-embedding similarity (Whom); the stationary distribution of the resulting delegation matrix picks the consensus answer. This requires neither gold labels nor training. On MMLU-Pro with 128 samples per question, delegation beats majority by +1.5 pp overall and +2.24 pp on non-trivial questions (McNemar p ~ 1.0e-14, n = 8,099), overturning wrong majorities whose answer cluster is geometrically incoherent while the correct minority is tight. We then characterize exactly when delegation overturns majority: a two-option model gives a closed-form flip condition on each option's confidence and the weight it routes to the other, with a do-no-harm corollary for near-unanimous questions. The condition calls the realized winner on 96.5% of non-trivial questions, and its predicted mass gap tracks the realized gap at r = 0.97. We did not find any other unsupervised ensemble methods that close the oracle gap.

Large language models have shown impressive capabilities in code generation, yet they often produce functionally incorrect code. Uncertainty quantification (UQ) methods have emerged as a promising approach for detecting hallucinations in natural language generation, but their effectiveness for code generation tasks remains underexplored. We systematically evaluate how UQ techniques transfer to code generation across three programming languages, five LLMs, and over 1,700 problems. We find that some token-probability-based methods generalize effectively without modification, while sampling-based methods relying on natural language inference (NLI) fail because NLI models cannot distinguish functionally different code, causing most responses to collapse into a single semantic cluster. To address this, we introduce functional equivalence methods, a family of code-specific methods that replace NLI-based semantic equivalence with an LLM-based functional equivalence assessment, including functional entropy, a code-specific analog of semantic entropy. Functional equivalence methods achieve top AUROC in 11 out of 15 model-benchmark combinations and the best calibration across most settings, consistently outperforming both NLI-based counterparts and all other methods evaluated.

How much meaning does a text carry? Shannon's theory measures uncertainty over symbols and is intentionally indifferent to meaning, while pairwise metrics such as BERTScore compare two texts rather than characterizing one. We develop a geometric framework that measures semantic content from the structure of a text's sentence embeddings. The framework has three parts. First, within a fixed embedding and baseline, six natural axioms uniquely determine a scalar measure up to scale, a frame-conditional uniqueness theorem. The resulting scalar is empirically too coarse, motivating a richer representation. Second, we propose a three-coordinate semantic profile capturing novelty (displacement from generic discourse), breadth (diversity of distinct ideas), and integration (connectedness among them), together with a discrete minimal unit (the semantic quantum) whose resolution is fixed by a clustering threshold $τ$. Third, we prove a no-go theorem: no scalar summary of the profile can simultaneously satisfy analytic stability under paraphrase and concatenation, ordinal robustness across text scales, and cross-representation comparability. We exhibit two practical scalars, $S_{\mathrm{minmax}}$ and $S_{\mathrm{rank}}$, each occupying a distinct corner of this trade-off triangle. Validation across 23 synthetic categories, 5 Project Gutenberg novels, and 3 embedding models confirms the trade-off. The recommended rank-normalized configuration passes 25 of 28 ordinal checks as point estimates (21 of 28 after Benjamini-Hochberg correction), outperforming seven baselines including unigram entropy and a BERTScore-based novelty signal. A separate variational result connects the breadth coordinate to the log-determinant of a determinantal point process (Spearman $ρ= 0.985$ over 507 Gutenberg chapters), giving an optimization-theoretic foundation for breadth.

Post-training has become central to improving reasoning and alignment in large language models, where critic-free models enable scalable learning from model-generated outputs but lack principled mechanisms to distinguish informative from noisy signals. Recent approaches leverage response-level measures as uncertainty signals to regulate group-based optimization methods such as GRPO. Yet their empirical success remains unstable and unclear in how they influence optimization dynamics. In this paper, we provide, to our knowledge, the first principled formulation that interprets uncertainty signals as mechanisms for characterizing and regulating gradient variance and learning signal quality. Based on both empirical and theoretical analysis, we identify two critical gaps of current entropy-based estimators: The anisotropic gap and The calibration gap. Motivated by this analysis, we propose Geometric-aware Calibrated Policy Optimization (GCPO), a novel framework integrating geometry-aware measures to capture semantic disagreement with reward-based calibration to align uncertainty with learning signal strength. Experiments on multiple benchmarks show that our approach more faithfully tracks gradient variability and consistently improves post-training performance. Our results highlight the importance of designing uncertainty signals that are aligned with optimization dynamics, offering a principled perspective for robust post-training.

While medical Multimodal Large Language Models (MLLMs) have shown promise in assisting diagnosis, they still frequently generate hallucinated responses that appear linguistically plausible but lack visual evidence. Such hallucinations pose risks to clinical decision-making and necessitate effective detection. Existing introspective detection methods primarily perform uncertainty estimation or logical verification by analyzing model responses conditioned on original or perturbed inputs. However, such external perturbations are often heuristic and context-agnostic, which overlooks the internal cross-modal dependency between generated tokens and related visual tokens during decoding. To address this issue, we propose VIHD, a Visual Intervention-based Hallucination Detection method that leverages targeted visual token masking to calibrate semantic entropy for more effective hallucination detection. VIHD locates visually dominant decoder layers via Visual Dependency Probing (VDP), executes Visual Intervention Decoding (VID) via token masking to calibrate the semantic distribution, and quantifies the resulting Calibrated Semantic Entropy (CSE) as a reliable hallucination signal. Extensive experiments on three medical VQA benchmarks with two medical MLLMs demonstrate that VIHD consistently outperforms state-of-the-art methods, underscoring the importance of fine-grained visual dependency for hallucination detection. The code will be available at https://github.com/Jiayi-Chen-AU/VIHD

In the transductive setting, where the full graph is observed but node labels are only partially available, progress in semi-supervised node classification has largely focused on architectural innovation. In this paper, we revisit an orthogonal axis: the training objective. We start from a simple observation: transductive models produce predictions for every node during training, including nodes without labels. These unlabeled-node predictions may contain useful training signal, but standard supervised objectives discard them because no ground-truth labels are available. Inspired by the decomposition of cross-entropy into a label-dependent alignment term and a label-independent entropy term, we propose prediction confidence as a natural way to extract this signal in the absence of labels. This motivates Transductive Sharpening (TS): a loss-level modification that minimizes prediction entropy on unlabeled nodes while counterbalancing this effect on labeled nodes. We evaluate Transductive Sharpening across a wide range of node-classification benchmarks and observe consistent performance improvements without requiring any changes to the backbone architecture. Code is available at https://github.com/transductive-sharpening/tunedGNN.

Linguistic ambiguity is critical to the robustness of Large Language Models (LLMs), yet existing research focuses mostly on English, with limited attention devoted to Chinese. Existing Chinese ambiguity datasets (e.g., CHAmbi) suffer from poor scalability. Guided by Potential Ambiguity (PA) Theory, we design a semi-automatic pipeline to construct CHA-Gen. It is the first PA Theory-grounded Chinese ambiguity dataset, which comprises 5,712 sentences (2,414 ambiguous, 3,298 unambiguous) across 18 potential ambiguous structures. Evaluating LLMs (e.g. Gemma 3, Qwen 2.5/3 series) via direct querying and machine translation, we find that LLMs struggle with ambiguity detection (improved by CoT prompting). Analysis of Qwen3-32B's CoT rationales reveals three common failure modes: ambiguity blindness, misattribution, and premature resolution. Uncertainty quantification with semantic entropy metric shows higher uncertainty for ambiguous sentences. Moreover, instruction tuning induces overconfidence, whereas Base models better capture semantic diversity. We further observe that models exhibit a bias toward dominant interpretations. Our work provides a scalable approach for Chinese ambiguity corpus and insights into LLMs' ambiguity handling, laying a foundation for enhancing Chinese ambiguity research in LLMs.

Measuring the breadth of a word's meaning, or its spread across contexts, has become feasible with contextualized token embeddings. A word type can be represented as a cloud of token vectors, with dispersion-based statistics serving as proxies for contextual diversity (Nagata and Tanaka-Ishii, ACL2025). These measurements are useful for deciding appropriate sense distinctions when constructing thesauri and domain-specific dictionaries. However, when comparing the breadth of two word types, naive hypothesis testing on dispersion can be misleading: differences in semantic direction can masquerade as dispersion differences, inflating Type-I error and yielding "statistically significant" outcomes even when there is no true breadth difference. This is problematic because significance testing should distinguish genuine effects from incidental fluctuations in small-difference regimes. We propose a Householder-aligned permutation test to isolate dispersion differences from directional differences. Our method applies a single Householder reflection to align the mean directions of the two word types and then performs a permutation test on the aligned token clouds, yielding calibrated, non-parametric p-values. For practicality, we introduce a GPU-oriented implementation that batches permutations and linear algebra operations. Empirically, our alignment reduced Type-I error by 32.5% while preserving sensitivity to genuine breadth differences, and achieved a 23x speedup over the CPU baseline.

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

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.

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.

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.

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.

Hallucination in large language models (LLMs), defined as the generation of factually incorrect or unsupported content, remains a critical barrier to reliable deployment. We present BEACON (Behavioral Entropy Aggregation for Cross-model hallucination detectiON), a black-box hallucination detection framework that operates purely on model outputs without requiring access to internal representations or external knowledge bases. BEACON extracts a 31-dimensional feature vector from structured multi-pass generation, integrating NLI-based semantic entropy, embedding geometry, chain-of-thought consistency, and paraphrase stability signals. A gradient-boosted classifier trained on 7,617 labeled examples across seven benchmarks achieves 0.8123 +/- 0.0102 AUROC (95% CI: 0.7632-0.8251), outperforming standalone semantic entropy (+0.2298) and SelfCheckGPT-style consistency baselines (+0.2457). Feature importance analysis shows that hallucination is inherently multi-dimensional, requiring combined uncertainty signals. An efficient 5-call variant achieves 0.7795 AUROC, enabling practical deployment across black-box LLM APIs.

Humans and large language models can predict next letter or word from its prior context much better than random guessing, indicating strong redundancy of language viewed as a stochastic process. Quantitatively this redundancy was estimated by Shannon to be around 80%, which means that every letter of a printed English text conveys approximately 1 bit of information and not 4.8 bits that 27 letters (including spaces) could potentially carry. This estimate was later confirmed by using autoregressive token probabilies computed by large language models. However, the statistical organization of language that give rise to such a large redundancy remains unclear. Here we introduce a statistical framework of language linking its redundancy to the hierarchical semantic organization of text. To this end, we use large language models to recursively segment any given text into semantically coherent chunks, inducing a semantic tree'' that spans the whole range of text organization, beginning from its main idea to individual tokens (words). For a large corpus of texts of a particular type, say fiction stories, the resulting ensemble of semantic trees is characterized by specific statistical regularities, giving rise to a structural'' entropy rate defined in this study. Surprisingly, we discovered that for several datasets considered in this work, semantic tree entropy rate was quite close to LLM-measured quantity and exhibited a similar trend across corpus. In particular, simpler texts like children stories exhibit lower branching in their semantic trees and correspondingly lower entropy rates, whereas fiction and poetry exhibit progressively larger branching factors and greater entropy rates. These results suggest that hierarchical semantic organization of texts is an important factor in their overall information transmission rates.