Dissecting Training-Free Uncertainty Estimation in Multimodal Large Language Models

# Dissecting Training-Free Uncertainty Estimation in Multimodal LLMs
Source: [https://arxiv.org/html/2609.22206](https://arxiv.org/html/2609.22206)
Vaggelis DorovatasAffiliation:Toyota Motor EuropeLin LiAffiliation:University of OxfordYarin GalAffiliation:University of OxfordRahaf AljundiAffiliation:Toyota Motor Europe

###### Abstract

Multimodal Large Language Models \(MLLMs\) have achieved remarkable performance across a wide range of multimodal tasks, yet understanding and quantifying their predictive uncertainty remains underexplored despite being central for safety critical applications\. In this work, we present a systematic study of training\-free uncertainty quantification strategies for MLLMs, categorizing existing approaches into three conceptual families: token\-level methods, which operate directly in the text output space; verbalized methods, which elicit uncertainty estimates or abstention signals via natural language prompts; and semantic methods, which measure uncertainty in a semantic meaning space\. We benchmark these strategies across multiple datasets, model families, generations, and scales, and find that no single family dominates: token\-level entropy \(at sampling temperature 1\.0\) wins on short answers, verbalized abstention on sentence\-length responses, and semantic methods on long\-form generation\.

††footnotetext:providing contracted services at Toyota Motor Europe\.## 1Introduction

Large language models \(LLMs\)[Brown et al\. \(2020\)](https://arxiv.org/html/2609.22206#bib.bib26);[Zhao et al\. \(2023\)](https://arxiv.org/html/2609.22206#bib.bib27)and their multimodal counterparts \(MLLMs\)[Li et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib28);[Ghosh et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib29)are increasingly relied upon[Eloundou et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib30)for high\-stakes applications, including agentic systems[Wang et al\. \(2024a\)](https://arxiv.org/html/2609.22206#bib.bib31);[Yehudai et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib32)that autonomously execute multi\-step workflows\. Yet no current model is reliable across all tasks, and hallucinated outputs[Huang et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib33);[Liu et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib19);[Li et al\. \(2023\)](https://arxiv.org/html/2609.22206#bib.bib34)constrain deployment in safety\-critical domains such as medical diagnosis[Kim et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib35);[Hakim et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib36)or autonomous driving[Dona et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib37)\. Safe deployment therefore requires reliable uncertainty estimates, enabling a system to abstain, defer to a human, trigger verification, or route the query to a stronger model\.

![Refer to caption](https://arxiv.org/html/2609.22206v1/teaser_tall_2_final.png)Figure 1:We benchmark three families of uncertainty quantification methods — verbalized, token\-level, and semantic — across 8 multimodal LLMs and 5 benchmarks, finding that the optimal strategy depends strongly on response length\.While Uncertainty Estimation \(UE\) has been extensively studied for LLMs[Xia et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib47);[Shorinwa et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib46), MLLMs introduce additional challenges that remain underexplored\. Visual inputs add modality\-specific sources of ambiguity \(occlusion, low resolution, out\-of\-distribution scenes\), and VQA benchmarks span answer formats from single\-token multiple\-choice to multi\-sentence open\-ended descriptions\. Most UE methods, however, are validated on short\-answer QA settings[Zhang et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib48);[Zhang et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib7);[Kadavath et al\. \(2022\)](https://arxiv.org/html/2609.22206#bib.bib41);[Lin et al\. \(2022\)](https://arxiv.org/html/2609.22206#bib.bib40)and a narrow set of models[Zhang et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib7);[Chen et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib49), leaving practitioners without guidance on how UE behavior varies with model family, generation, scale, and response length\.

To address this gap, we present an empirical analysis of training\-free UE in MLLMs, targeting methods that are practical to deploy without additional training or paired data\. We organize existing approaches into three families — verbalized[Lin et al\. \(2022\)](https://arxiv.org/html/2609.22206#bib.bib40);[Kadavath et al\. \(2022\)](https://arxiv.org/html/2609.22206#bib.bib41);[Xiong et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib42), token\-level[Malinin and Gales \(2020\)](https://arxiv.org/html/2609.22206#bib.bib38);[Guerreiro et al\. \(2023\)](https://arxiv.org/html/2609.22206#bib.bib39);[Li et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib11), and semantic[Kuhn et al\. \(2023\)](https://arxiv.org/html/2609.22206#bib.bib43);[Farquhar et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib8);[Nikitin et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib44)— and systematically analyze how their reliability varies along four axes: \(i\) model family, \(ii\) model generation, \(iii\) model size, and \(iv\) response\-length regime\. Concretely, we evaluate representative methods from each family on two MLLM families \(InternVL, QwenVL\) across two generations and two scales \(small: 2B, medium: 7\-8B\) on five VQA benchmarks spanning multiple\-choice, sentence\-length, and open\-ended formats\. Beyond AUROC and Coverage at Risk, we adopt a calibrated hallucination detection accuracy metric \(CHDA\) that calibrates a threshold on a small subset, simulating practical deployment\.

Our analysis yields four main takeaways:

- •Output length dictates which UE family wins\.No single family is consistently best across regimes\.
- •Token\-level uncertainty collapses under deterministic decoding,but higher\-temperature estimation recovers calibrated signals that rival far more expensive semantic methods\.
- •Verbalized self\-uncertainty is unreliable in small and older MLLMs,but emerges as a strong signal in newer medium\-sized models, most notably Qwen3\-VL\-Instruct\.
- •No method achieves low risk at reasonable coverage,indicating a substantial gap for safe deployment of small to medium MLLMs\.

Together, these findings provide concrete guidance for practitioners and motivate the development of more robust UE methods for MLLM deployment at scale\.

## 2Related Work

##### Uncertainty estimation in LLMs\.

Uncertainty estimation has been extensively studied for unimodal LLMs, spanning verbalized confidence[Lin et al\. \(2022\)](https://arxiv.org/html/2609.22206#bib.bib40);[Kadavath et al\. \(2022\)](https://arxiv.org/html/2609.22206#bib.bib41);[Xiong et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib42), token\-level signals[Malinin and Gales \(2020\)](https://arxiv.org/html/2609.22206#bib.bib38);[Guerreiro et al\. \(2023\)](https://arxiv.org/html/2609.22206#bib.bib39);[Li et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib11), semantic\-level methods[Kuhn et al\. \(2023\)](https://arxiv.org/html/2609.22206#bib.bib43);[Farquhar et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib8);[Nikitin et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib44), and long\-form calibration[Zhang et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib48); see[Xia et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib47);[Shorinwa et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib46)for comprehensive overviews\. How these methods transfer to multimodal settings—where visual ambiguity and a wider range of output formats come into play—remains an open question\.

##### Hallucination in multimodal models\.

Recent surveys characterize hallucination in MLLMs as a misalignment between visual inputs and textual outputs, organizing errors into object\-, attribute\-, and relation\-level inconsistencies and reviewing language\-prior bias, weak visual grounding, and decoding\-level mitigations[Bai et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib18);[Liu et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib19)\.[Chen et al\. \(2026\)](https://arxiv.org/html/2609.22206#bib.bib21)extend this with a detailed analysis of faithfulness and factual consistency, including confidence\- and uncertainty\-based detection signals, and[Sahoo et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib20)adopt a broader foundation\-model view across language, image, video, and audio\.

##### Our position\.

Unlike prior surveys that characterize hallucination phenomena in MLLMs or review UE in unimodal LLMs, we center*uncertainty estimation*as a general reliability framework for MLLMs—of which hallucination detection is one downstream application—and propose a taxonomy of training\-free UE methods specific to MLLMs, dissecting their behavior across model families, scales, generations, and response\-length regimes, providing actionable guidance for practitioners and highlighting open challenges for uncertainty\-based reliability modeling\.

## 3ProposedUETaxonomy

Uncertainty in MLLMs can be expressed and measured at distinct granularities, from surface\-level confidence to fine\-grained probabilistic structure and cross\-sample semantic consistency\. We analyze three corresponding families of training\-free uncertainty estimation \(UE\): \(i\)*verbalized uncertainty*, where models explicitly express confidence in natural language; \(ii\)*token\-level uncertainty*, derived from output probability distributions; and \(iii\)*semantic uncertainty*, which captures variability at the meaning level\.

### 3\.1Verbalized Uncertainty

Building on early work teaching LLMs to express uncertainty in words\([Lin et al\., 2022](https://arxiv.org/html/2609.22206#bib.bib40)\), prior studies find that MLLMs are overconfident and poorly calibrated when producing numerical confidence estimates[Groot and Valdenegro \- Toro \(2024\)](https://arxiv.org/html/2609.22206#bib.bib4);[Borszukovszki et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib1);[Xuan et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib2);[Zhao et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib5), while abstention prompting[Wang and Nalisnick \(2025\)](https://arxiv.org/html/2609.22206#bib.bib3)and RL\-based prompt optimization[Kriz et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib6)improve robustness and calibration\. We study two variants: \(i\)*abstention*, where the model outputs “UNKNOWN” when uncertain, and \(ii\)*numerical confidence*, where the model outputs a confidence score alongside each answer\. Both apply to proprietary and open\-source models and incur no extra inference cost, but rely on the model’s self\-calibration\.

### 3\.2Token\-level Uncertainty

Prior work leverages model\-internal signals to detect hallucinations in MLLMs, either by suppressing uncertain visual tokens[Fang et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib12);[Seo et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib13)or by quantifying uncertainty in output token distributions during autoregressive decoding[Li et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib11)\. Following the latter, we adopt token\-level entropy and negative log\-likelihood \(NLL\)\. Given an autoregressive MLLM generating𝐲=\(y1,…,yT\)\\mathbf\{y\}=\(y\_\{1\},\\dots,y\_\{T\}\)conditioned on input𝐱\\mathbf\{x\}, with predictive distributionpθ​\(yt∣𝐱,y<t\)p\_\{\\theta\}\(y\_\{t\}\\mid\\mathbf\{x\},y\_\{<t\}\)over vocabulary𝒱\\mathcal\{V\}:

Ht=−∑v∈𝒱pθ\(v∣𝐱,y<t\)logpθ\(v∣𝐱,y<t\),H\_\{t\}=\-\\\!\\\!\\sum\_\{v\\in\\mathcal\{V\}\}\\\!p\_\{\\theta\}\(v\\mid\\mathbf\{x\},y\_\{<t\}\)\\log p\_\{\\theta\}\(v\\mid\\mathbf\{x\},y\_\{<t\}\),\(1\)NLLt=−log⁡pθ​\(yt∣𝐱,y<t\)\.\\mathrm\{NLL\}\_\{t\}=\-\\log p\_\{\\theta\}\(y\_\{t\}\\mid\\mathbf\{x\},y\_\{<t\}\)\.\(2\)Entropy captures uncertainty over all continuations; NLL reflects confidence in the realized trajectory\. We aggregate each over the response by*mean*\(length\-normalized global uncertainty\) and*max*\(localized spikes corresponding to weakly grounded tokens\)\. These methods require access to internal representations and do not apply to closed\-source models\.

### 3\.3Semantic Uncertainty

Semantic Entropy \(SE\)[Farquhar et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib8)computes uncertainty over*semantic meanings*rather than surface forms, accounting for paraphrastic and lexical invariances\. GivenNNsamples fromp⁡\(s∣x\)p\(s\\mid x\), responses are grouped intoKKsemantic classes\{Ck\}k=1K\\\{C\_\{k\}\\\}\_\{k=1\}^\{K\}via bi\-directional entailment, and entropy is computed over the induced clusters:

SE\(x\)≈−∑k=1Kp^\(Ck∣x\)logp^\(Ck∣x\)\.\\mathrm\{SE\}\(x\)\\approx\-\\sum\_\{k=1\}^\{K\}\\hat\{p\}\(C\_\{k\}\\mid x\)\\log\\hat\{p\}\(C\_\{k\}\\mid x\)\.In our experiments,p^​\(Ck∣x\)\\hat\{p\}\(C\_\{k\}\\mid x\)is estimated from length\-normalized sequence log\-likelihoods following[Farquhar et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib8); for closed\-source models where token\-level likelihoods are unavailable, cluster frequencies\|Ck\|/N\|C\_\{k\}\|/Ncan be used instead\.VL\-Uncertainty[Zhang et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib7)adapts SE to vision–language models by replacing stochastic sampling with progressive perturbations of both modalities \(image blur, text paraphrasing\); clustering and entropy follow SE\.VASE[Liao et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib9)strengthens visual grounding by contrasting clusters obtained from original and noisy images, disentangling linguistic priors from image\-conditioned reasoning\([Leng et al\., 2024](https://arxiv.org/html/2609.22206#bib.bib45)\)\. While applicable to both open\- and closed\-source models, these methods require multiple inference runs, a separate entailment model, and additional overhead for clustering the sampled responses\.

## 4Experimental Analysis

In this section, we conduct a comprehensive empirical analysis of the presented UE families, highlighting their strengths and limitations across diverse model families, scales, generation settings, benchmarks, and evaluation metrics\.

### 4\.1Models and Benchmarks

We evaluate across 8 MLLMs spanning two widely adopted and extensively benchmarked families: InternVL[Wang et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib23)\(generations 2 and 3\.5\) and QwenVL[Bai et al\. \(2023\)](https://arxiv.org/html/2609.22206#bib.bib24);[Wang et al\. \(2024b\)](https://arxiv.org/html/2609.22206#bib.bib50);[Bai et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib51)\(generations 2 and 3\), with two model sizes \(small and medium\) per generation \(2B and 8B, except Qwen2\-VL which uses 2B and 7B\)\. This setup enables comparison along three axes: model family, generation, and size\.

Our analysis spans a broad range of benchmarks covering multiple\-choice, short free\-form, and sentence\-length free\-form answer formats\. We group benchmarks byresponse\-length:

Short\.ScienceQA[Lu et al\. \(2022\)](https://arxiv.org/html/2609.22206#bib.bib15)\(2,017 validation QA pairs\) is a multiple\-choice \(2–4 options\) dataset that integrates textual, visual, and contextual information to test school\-level scientific reasoning\.MMMU\(Massive Multi\-discipline Multimodal Understanding\)[Yue et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib22)\(825 validation QA pairs\) is a multiple\-choice benchmark \(2–9 options\) assessing multimodal models across disciplines including Art, Business, Medicine, Science, Humanities, and Technology\.MM\-Vet[Yu et al\. \(2023\)](https://arxiv.org/html/2609.22206#bib.bib16)\(218 QA pairs\) targets diverse perceptual and reasoning capabilities through compositional vision–language tasks, with questions directing models to produce concise final answers\.Sentence\-level\.FSVQA\(Full\-Sentence Visual Question Answering\)[Shin et al\. \(2016\)](https://arxiv.org/html/2609.22206#bib.bib25), built on MSCOCO2014 images, extends conventional VQA by requiring complete, grammatically natural responses rather than brief phrases or single\-word answers\. We use a 200\-sample subset \(FSVQA200\) as an intermediate sentence\-length benchmark bridging short\-answer and long\-form generation regimes, and release the sampled IDs\.Long\.LLaVABench[Liu et al\. \(2023\)](https://arxiv.org/html/2609.22206#bib.bib17)\(60 QA pairs\) pairs real\-world images with open\-ended instructions, designed to evaluate visual instruction following and long\-form answering in MLLMs\.MM\-Vet Longis a controlled variant of MM\-Vet where the model is instructed to generate complete responses\.

### 4\.2Metrics

A variety of metrics have been proposed for hallucination detection and mitigation[Borszukovszki et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib1);[Wang and Nalisnick \(2025\)](https://arxiv.org/html/2609.22206#bib.bib3);[Zhao et al\. \(2025\)](https://arxiv.org/html/2609.22206#bib.bib5);[Groot and Valdenegro \- Toro \(2024\)](https://arxiv.org/html/2609.22206#bib.bib4);[Khan and Fu \(2024\)](https://arxiv.org/html/2609.22206#bib.bib10)\. We adopt three complementary metrics: \(i\) AUROC for uncertainty ranking quality, \(ii\) Coverage at Risk for safe deployment under a predefined risk level, and \(iii\) Calibrated Hallucination Detection Accuracy \(CHDA\) under a calibrated threshold simulating a practical setup\. We also report original model accuracy for reference\.

Letℳ\\mathcal\{M\}denote a multimodal LLM and𝒰\\mathcal\{U\}an uncertainty estimator assigning a scalar scoreu⁡\(x\)∈ℝu\(x\)\\in\\mathbb\{R\}to each inputxx, where higher values indicate more uncertain \(and more likely hallucinated\) responses\.

AUROC:We report the area under the receiver operating characteristic curve, computed by treating hallucinations \(wrong answers\) as the positive class\. AUROC ranges from0\.50\.5\(random\) to1\.01\.0\(perfect\) and provides a threshold\-independent measure of how wellu⁡\(x\)u\(x\)ranks correct vs\. incorrect responses\.

Coverage at Risk \(Cov@R\):Following[Whitehead et al\. \(2022\)](https://arxiv.org/html/2609.22206#bib.bib14), we recast hallucination detection as selective prediction: the model abstains on samples whose uncertainty exceeds a thresholdτ\\tau\. CoverageCov⁡\(τ\)\\mathrm\{Cov\}\(\\tau\)is the fraction of answered questions and riskRisk⁡\(τ\)\\mathrm\{Risk\}\(\\tau\)is the error rate on those answers\. Cov@rrdenotes the maximum coverage achievable while keeping risk below budgetrr:

Cov​@​r=maxτ∈ℝ⁡Cov⁡\(τ\)s\.t\.Risk⁡\(τ\)≤r\.\\mathrm\{Cov@\}r=\\max\_\{\\tau\\in\\mathbb\{R\}\}\\mathrm\{Cov\}\(\\tau\)\\quad\\text\{s\.t\.\}\\quad\\mathrm\{Risk\}\(\\tau\)\\leq r\.\(3\)We reportCov​@​20\\mathrm\{Cov@\}20\(r=20%r\{=\}20\\%\); higher values indicate more questions answered within the error tolerance, which matters for safety\-critical deployment\.111Tighter risk budgets yielded near\-zero coverage across all methods, indicating a clear gap for future UE research\.

Calibrated Hallucination Detection Accuracy \(CHDA\):We propose CHDA as our primary deployment\-time metric\. Standard hallucination detection accuracy \(HDA\)[Zhang et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib7)assumes a previously known, fixed threshold for all methods; CHDA instead calibrates the threshold on a small held\-out subset, reflecting realistic deployment where the UE method has to abstain when an uncertain response is detected; otherwise, the model is allowed to respond\. A true positive is an incorrect response correctly flagged as uncertain, while a true negative is a correct response with uncertainty below the threshold\. Hallucination Detection Accuracy \(HDA\) is then defined as:

HDA⁡\(τ,𝒟\)=TP⁡\(τ\)\+TN⁡\(τ\)\|𝒟\|\.\\mathrm\{HDA\}\(\\tau;\\mathcal\{D\}\)=\\frac\{\\mathrm\{TP\}\(\\tau\)\+\\mathrm\{TN\}\(\\tau\)\}\{\|\\mathcal\{D\}\|\}\.\(4\)To obtain CHDA, we proceed in two steps\.\(i\) Calibration:we first calibrate a hallucination detection threshold for each method on a small subset sampled from each of the considered benchmarks, yielding a pooled calibration set𝒟cal\\mathcal\{D\}\_\{\\mathrm\{cal\}\}, and we setτ⋆=arg​maxτ∈ℝ⁡HDA​\(τ,𝒟cal\)\\tau^\{\\star\}=\\operatorname\*\{arg\\,max\}\_\{\\tau\\in\\mathbb\{R\}\}\\mathrm\{HDA\}\(\\tau;\\mathcal\{D\}\_\{\\mathrm\{cal\}\}\)\.\(ii\) Evaluation:we reportCHDA⁡\(ℳ,𝒰\)=HDA⁡\(τ⋆,𝒟eval\)\\mathrm\{CHDA\}\(\\mathcal\{M\},\\mathcal\{U\}\)=\\mathrm\{HDA\}\(\\tau^\{\\star\};\\mathcal\{D\}\_\{\\mathrm\{eval\}\}\)on the full evaluation set\.

### 4\.3Results

We organize our analysis around four questions: how response length shapes the relative performance of UE methods, how model family, scale, and generation affect uncertainty quality, whether current methods meet practical safety requirements, and how individual UE methods compare within and across families\.

Across tables,Boldandunderlinedvalues mark the best and second\-best per column\.

#### 4\.3\.1How does response length affect uncertainty estimation?

Table 1:UE performance grouped by expected answer length,averaged across models\. Cost denotes the number of forward passes per sample required by each method\. No single method dominates across all regimes: token\-level entropy at temperature 1\.0 leads on short answers, while semantic methods perform best on long\-form responses\.Tab\.[1](https://arxiv.org/html/2609.22206#S4.T1)reports the main results across models, benchmarks and metrics, grouped by expected response length222We report detailed results for all methods, benchmarks and models combinations in the Appendix\.\. On average, no single uncertainty estimation method dominates across all answer\-length categories\. Instead, the best\-performing family differs with answer length:

Short\-length regime\.Token\-level methods at temperature 1\.0 achieve the strongest overall performance, while using a common low inference temperature of 0\.1 substantially degrades token\-level estimates\. At low temperatures, the logit distribution becomes overly sharp, collapsing most token probabilities toward zero and reducing the usefulness of entropy as an uncertainty signal\. As shown in Fig\.[2](https://arxiv.org/html/2609.22206#S4.F2), entropy computed at temperature 1\.0 produces a much broader and more informative uncertainty distribution\. This requires one additional forward pass per sample for uncertainty estimation\.

The same figure exposes a key limitation of semantic methods \(with SE, N=10, as a representative\)\. Even at temperature 1\.0, models often generate identical short responses, collapsing generations into a single cluster and driving inter\-cluster entropy toward0\.00\.0\. Table[2](https://arxiv.org/html/2609.22206#S4.T2)confirms this, showing substantially lower average cluster counts on short\-length benchmarks than on the longer counterparts\.

Sentence\-length regime\.On FSVQA200, performance is relatively uniform across method categories, withVerbal: abstaintaking the lead and semantic methods following closely behind\. We hypothesize that verbalized abstention works well on FSVQA200 because each question has a single underlying fact to be uncertain about and a singleUNKNOWNtoken can express the model’s uncertainty about the one underlying fact\. By contrast, multiple\-choice questions bias the model to commit to one of the given options, and long\-form questions spread uncertainty across many sub\-claims that a singleUNKNOWNcannot localize\. This interpretation is supported by Table[2](https://arxiv.org/html/2609.22206#S4.T2), which reports abstention rates averaged across all MLLMs per benchmark: the highest rates occur on MM\-Vet \(single word short answers\) and FSVQA200 \(sentence\-level answers\), while multiple\-choice and long\-form settings exhibit sharply lower rates\. Semantic methods follow closely in the sentence\-length regime where richer lexical variation results in more clusters and broader uncertainty distributions \(Figure[2](https://arxiv.org/html/2609.22206#S4.F2)\)\.

Long\-length regime\.On long\-form generation, semantic methods clearly outperform both other families\. The diverse responses elicited at temperature 1\.0 yield consistently rich clustering in this regime \(Table[2](https://arxiv.org/html/2609.22206#S4.T2)\), giving semantic methods a stable and informative signal—whereas token\-level methods lose ground because the correctness of a long answer depends far less on the entropy of any single token\. Verbal methods also degrade since models tend to be poorly calibrated when verbalizing uncertainty over extended generations, often defaulting to uniformly high confidence regardless of actual correctness\.

Appendix[A\.2](https://arxiv.org/html/2609.22206#A1.SS2)provides qualitative examples per regime, including failure cases where even the regime’s best method assigns low uncertainty to hallucinated responses \(Figures[6](https://arxiv.org/html/2609.22206#A1.F6)–[8](https://arxiv.org/html/2609.22206#A1.F8)\)\.

Figure 2:Uncertainty distributions across answer\-length regimes, aggregated over all MLLMs and seeds \(densities normalized per method\)\. Max Entropy atT=0\.1T\{=\}0\.1collapses near zero as low\-temperature decoding sharpens the logit distribution;T=1\.0T\{=\}1\.0recovers a broad, informative signal\. Semantic Entropy is uninformative on short answers—identical generations fall into a single cluster \(Table[2](https://arxiv.org/html/2609.22206#S4.T2)\)—but yields well\-spread distributions once lexical variation grows in sentence\- and long\-length regimes\.Table 2:Average semantic cluster counts of SE \(T=1\.0T\{=\}1\.0,N=10N\{=\}10\) and mean verbal abstention rates across MLLMs and benchmarks\. Lower cluster diversity on short benchmarks explains SE’s weaker performance in that category; sentence\-level and single\-word answer tasks show the highest abstention rates\.
#### 4\.3\.2How does model generation and scale affect uncertainty estimation?

Tab\.[3](https://arxiv.org/html/2609.22206#S4.T3)reports the effect of MLLM family, scale, and generation on uncertainty estimation, with each entry averaged over three representative methods \(Verbal Abstain, Max Entropy, and Semantic Entropy withN=10N\{=\}10\) and across all benchmarks\. Both scaling parameters and moving to newer generations consistently improve base task accuracy \(e\.g\., Qw2\-VL 2B→\\rightarrow7B:47\.1→60\.247\.1\\rightarrow 60\.2; IVL2→\\rightarrowIVL3\.5 at 8B:55\.7→66\.055\.7\\rightarrow 66\.0\)\. These gains, however, translate unevenly into uncertainty estimation quality:

Method choice dominates AUROC\.AUROC varies substantially across uncertainty\-estimation methods, ranging roughly between0\.580\.58and0\.730\.73\(Tab\.[6](https://arxiv.org/html/2609.22206#S4.T6)\), whereas variation across underlying models is comparatively narrow \(0\.630\.63to0\.670\.67in Tab\.[3](https://arxiv.org/html/2609.22206#S4.T3)\)\. The estimation method is therefore the primary determinant of ranking quality, while model family, scale, and generation have limited effect on discriminative performance\.

Model choice dominates coverage\.Coverage, in contrast, is driven primarily by the base model\. Across base models, Cov@20 spans 0\.28 points \(0\.11 to 0\.39; Tab\.[3](https://arxiv.org/html/2609.22206#S4.T3)\), nearly twice the 0\.15\-point spread across estimation methods \(0\.20 to 0\.35; Tab\.[6](https://arxiv.org/html/2609.22206#S4.T6)\)\. This pattern largely reflects differences in base accuracy \(47\.1%47\.1\\%to66\.7%66\.7\\%\): stronger models achieve higher selective coverage under the same confidence\-thresholding regime\. Within a family, scale \(e\.g\., Qw3\-VL 2B→\\rightarrow8B:0\.23→0\.390\.23\\rightarrow 0\.39\) and newer generations \(e\.g\., IVL2→\\rightarrowIVL3\.5 at 8B:0\.25→0\.340\.25\\rightarrow 0\.34\) yield gains in both accuracy and coverage, with minimal impact on AUROC\.

CHDA improves with model quality, but modestly\.CHDA measures how well a single decision threshold, calibrated once on a small subset of data, generalizes across benchmarks at deployment time\. It ranges from61\.961\.9to68\.468\.4across models—a meaningful but compressed spread relative to Cov@20\. Gains track both scale and generation \(e\.g\., IVL3\.5 2B→\\rightarrow8B:63\.1→68\.463\.1\\rightarrow 68\.4; Qw3\-VL 2B→\\rightarrow8B:61\.9→68\.261\.9\\rightarrow 68\.2; IVL2→\\rightarrowIVL3\.5 at 8B:63\.7→68\.463\.7\\rightarrow 68\.4\), indicating that stronger MLLMs produce uncertainty signals whose calibrated decision boundaries transfer more reliably\. Notably, within the new Qwen\-Instruct generation, the medium\-sized model exhibits a striking ability to estimate its own uncertainty via the Verbal\-Abstain method, outperforming all other uncertainty estimation methods by a significant margin \(\+5%\)\.

Together, these observations suggest that practitioners should prioritize*method selection*for ranking\-quality use cases,*model selection*for selective prediction, and*both jointly*for fixed\-threshold deployment\.

#### 4\.3\.3Are UE methods compatible with safety requirements?

We assess deployment readiness via Cov@20, the fraction of questions answered while keeping the error rate below20%20\\%\. Even at this loose threshold, no method achieves coverage compatible with practical deployment: the best aggregate Cov@20 we observe is0\.450\.45\(VASE, sentence\-length, Table[1](https://arxiv.org/html/2609.22206#S4.T1)\), and on long\-form generation the best method \(Semantic Entropy,N=10N\{=\}10\) reaches only0\.210\.21\. At tighter budgets the picture worsens \(see individual benchmark results in the Appendix\)\.

To isolate the UE contribution from base\-model accuracy, observe that a hypothetical perfect UE method — one that ranks every correct answer above every wrong one — achievesCov@​r=a/\(1−r\)\\text\{Cov@\}r=a/\(1\-r\), whereaais base accuracy: it answers all correct samples plus as many wrong samples as the risk budget allows\. Withr=20%r=20\\%and observed accuracies of0\.500\.50–0\.670\.67across regimes, the perfect\-UE ceilings are0\.630\.63\(long\),0\.710\.71\(short\), and0\.840\.84\(sentence\)\. Current methods deliver0\.210\.21,0\.430\.43, and0\.450\.45respectively — only 33–63% of the achievable coverage\. The gap is driven by “confidently wrong” predictions: samples the model gets incorrect but UE scores as low\-uncertainty\. AUROCs of 0\.65–0\.75 confirm that current methods rank correct above wrong answers only imperfectly, and this ranking noise is what prevents tight risk budgets from yielding meaningful coverage\. Closing this gap — not just increasing base accuracy — is a prerequisite for safety\-critical deployment, and motivates future work on training\-based and hybrid UE methods\.

#### 4\.3\.4How does the choice of UE method affect performance?

Verbal methods\.Verbal Abstainperforms inconsistently across models and benchmarks\. However,when paired with newer and larger generations of MLLMs its performance consistently improves, attaining the best overall CHDA across all methods and benchmarks \(Qwen3\-VL\-8B, Table[6](https://arxiv.org/html/2609.22206#S4.T6)\)\. In contrast, as shown in Table[4](https://arxiv.org/html/2609.22206#S4.T4), the weakest model in this regard \(InternVL2\-2B\) rarely abstains and performs poorly across all metrics, whereas the best\-calibrated model \(Qwen3\-VL\-8B\) substantially outperforms it\.Verbal Confidenceis among the worst\-performing uncertainty measures in our evaluation, exhibiting two systematic failure modes: overconfidence collapse and format non\-compliance\. Specifically \(Tab\.[5](https://arxiv.org/html/2609.22206#S4.T5)\), on average 79\.4% of predictions exceed 0\.9 confidence regardless of correctness, and 10\.3% fail to parse \(range: 3\.4–25\.9%\) as the MLLM does not generate the answers and confidence values in the specified format\. Scale does not resolve these issues: InternVL3\.5\-8B parses cleanly \(4\.6%\) yet is the most overconfident InternVL variant \(90\.2%\)\. Together, these failures render ranking metrics such as AUROC and Cov@20 difficult to interpret for this specific method\.

Table 3:Effect of MLLM family, size, and generation on uncertainty metrics\. Each cell reports the mean over benchmarks and representative methods of each family:Verbal Abstain\(verbalised\),Max Entropy\(single\-pass token\-level\), andSemantic Entropy\(N=10N\{=\}10, semantic\)\. AUROC is largely insensitive to the underlying model, CHDA improves moderately with scale and generation, and selective coverage tracks base task accuracy and improves with both size and generation\.Table 4:Verbal abstention rate \(Abst\.\) and calibrated hallucination detection accuracy \(CHDA\) for the weakest \(InternVL2\-2B\) and strongest \(Qwen3\-VL\-8B\) MLLMs across answer\-length regimes\. The method fails on the weaker model \(rare abstention, poor CHDA\) but succeeds on the stronger one\.Token\-level methods\.These methods achieve overall strong performance when estimating the uncertainty with a temperature scaling of 1\.0, especially when considering the compute cost advantage over semantic methods \(Tab\.[1](https://arxiv.org/html/2609.22206#S4.T1)and[6](https://arxiv.org/html/2609.22206#S4.T6)\), making them a suitable choice for settings where rapid response is required under limited compute\.Max EntropyoutperformsAvg Entropyoverall, as it captures the uncertainty signal from the most uncertain token rather than smoothing it across the full generated text\.Max NLLandAvg NLLclosely follow the performance of their entropy\-based counterparts \(see individual benchmark results in the Appendix\)\.

Table 5:Failure modes ofVerbal Confidenceprompting across MLLMs \(IVL = InternVL, Qw = Qwen\-VL\)\.PF\(Parse Fail\) is the percentage of responses where a numeric confidence score could not be extracted;OC\(Overconf\.\) is the percentage of parseable responses assigned the maximum confidence value\. Even when parsing succeeds, models default to extreme overconfidence in roughly four out of five cases\.Table 6:Cross\-benchmark averages for a representative method from each UE family \(for SE N=10 and for Max Entropy T=1\)\. The three methods reach comparable average AUROC, each dominating in a different answer\-length regime \(Sec\.[4\.3\.1](https://arxiv.org/html/2609.22206#S4.SS3.SSS1)\)\.Semantic methods\.These methods rank most consistently among the top performers in our evaluation across answer\-length regimes \(Tab\.[1](https://arxiv.org/html/2609.22206#S4.T1)\)\.VASEis the strongest method in this family, withSemantic EntropyandVL\-Uncertaintyfollowing closely behind\. Textual perturbations do not yield consistent improvements over their non\-perturbed counterparts \(Tab\.[7](https://arxiv.org/html/2609.22206#S4.T7)\), while visual perturbations offer only occasional incremental gains\. In practice, most of the useful signal appears to come from temperature\-induced sampling diversity rather than from the perturbation mechanism\. However, the performance gains from additional samples exhibit diminishing returns \(Tab\.[8](https://arxiv.org/html/2609.22206#S4.T8)\), suggesting that smaller sample budgets \(e\.g\., 5 samples for SE\) may offer a more favorable cost–performance trade\-off while retaining most benefits\.

Table 7:Effect of textual \(LLM rephrasing\) and visual \(blurring\) perturbations on Semantic Entropy, averaged across MLLMs on a dataset subset\. Neither textual perturbations, visual perturbations, nor their combination with increased temperature \(VL\-Uncertainty\) consistently improve over base SE\.Table 8:Ablation on the number of samplesNNfor Semantic Entropy, averaged across Qwen\-family MLLMs on a subset of benchmarks\. LargerNNbrings diminishing returns relative to its cost\.

## 5Conclusion and Main Takeaways

In this work, we propose a taxonomy of training\-free uncertainty estimation \(UE\) methods for MLLMs and systematically analyze their empirical behavior across model families, scales, benchmarks, and answer\-length regimes, providing practical guidance for reliable deployment\. Our results can be summarized in the following points:\(1\)UE methods are highly sensitive to response length: token\-level entropy performs best for short answers, verbalized uncertainty is strongest on sentence\-length responses and semantic methods are most effective for long\-form generation;\(2\)token\-level uncertainty should be computed at a higher temperature than decoding: standard low\-temperature inference collapses the entropy signal, while a second forward pass atT=1\.0T\{=\}1\.0recovers strong uncertainty estimates at modest additional cost;\(3\)Verbalized uncertainty improves with better and bigger models: recent medium\-scale models such as Qwen3\-VL\-8B show strong verbal abstention performance while numeric verbal confidence is unreliable in practice, and\(4\)Existing UE methods remain insufficient for safe deployment:they achieve limited coverage even under relaxed risk thresholds\.

## Limitations

Despite the large\-scale evaluation in this work, several limitations remain\. First, we restrict our study to small and medium model sizes due to computational constraints and practical deployment considerations, and focus on two generations of widely used model families; extending to larger scales and additional families is an important direction for future work\. Second, we study multimodal LLMs in isolation, motivated by the lack of in\-depth uncertainty analyses in this setting; a direct comparison with unimodal LLMs is left for future work\. Third, we evaluate only training\-free uncertainty estimation methods for their ease of deployment and compatibility, however training\-based approaches may yield more reliable behavior in safety\-critical settings where current methods fall short\. Finally, we focus on general\-purpose multimodal benchmarks and standard methods; domain\-specific evaluations may lead to different conclusions\.

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## Appendix AAppendix

### A\.1Individual Benchmark Results

In this section we provide the results for all model, method and metric combinations for the individual benchmarks studied in the main paper\. We organize the discussion by benchmark, ordered along the answer\-length axis—from multiple\-choice \(ScienceQA, MMMU\) through short open\-ended \(MM\-Vet\), sentence\-length \(FSVQA200\), and finally long\-form multi\-sentence generation \(MM\-Vet Long, LLaVA\-Bench\)—which we find to be the principal axis along which the optimal uncertainty estimator varies\. For each benchmark we report AUROC, selective\-prediction coverage at risk levels10%/20%/30%10\\%/20\\%/30\\%, and CHDA, the deployment\-time metric we focus on in the main paper\.

##### ScienceQA[Lu et al\. \(2022\)](https://arxiv.org/html/2609.22206#bib.bib15)

Table[9](https://arxiv.org/html/2609.22206#A1.T9)reports our full results on the multiple\-choice ScienceQA benchmark \(2–4 options\)\. Consistent with the main paper, token\-level methods with temperature\-1 offer the best cost\-quality tradeoff: at only2×2\\timesinference cost,Max NLL \(T=1\)matches or exceeds semantic methods in average AUROC while using significantly less compute\. Semantic methods yield tangible gains only on the strongest backbones \(e\.g\., Semantic Entropy achieves0\.880\.88AUROC on InternVL2\-8B\), while verbalized methods remain unreliable across all models—since the multiple\-choice format biases models toward expressing confidence in a single option regardless of internal uncertainty\. At the tightest selective\-prediction operating point,Cov@10, semantic methods lead on average, with token\-level T=1 methods close behind\.Cov@20andCov@30saturate near1\.01\.0due to the base model’s high accuracy\. The CHDA, which captures deployment\-time utility most directly, shows that cheap1×1\\timestoken\-level estimators \(e\.g\.,Max NLLat82\.682\.6\) edge out the more expensive T=1 and semantic variants on average, indicating that in this high\-accuracy short\-form regime even minimal uncertainty signals are sufficient to drive deployment\-time selection\.

##### MMMU[Yue et al\. \(2024\)](https://arxiv.org/html/2609.22206#bib.bib22)

Table[10](https://arxiv.org/html/2609.22206#A1.T10)reports our full results on this multiple\-choice benchmark, which extends ScienceQA’s setup to a larger answer space \(2–9 options\) and consequently a substantially lower average accuracy \(40\.9%40\.9\\%vs\.80\.9%80\.9\\%on ScienceQA\)\. The harder regime sharpens the trends observed in the main paper: token\-level methods with temperature\-1 lead on average across most metrics, while semantic methods trail at33–5×5\\timeshigher cost\. Verbalized methods degrade further than on ScienceQA, which we attribute to the larger answer space amplifying the model’s bias toward committing to a single option rather than expressing uncertainty or abstaining\. Unlike ScienceQA,Cov@10/Cov@20/Cov@30averages≤0\.02\\leq 0\.02remain well below1\.01\.0reflecting the base model’s low accuracy for such risk budgets\. The CHDA story diverges from AUROC in a deployment\-relevant way: although semantic methods are competitive on AUROC, they fall well behind on CHDA \(average4444–4848\) while token\-level T=1 methods lead \(∼62\.7\\sim\\\!62\.7forMax Entropy \(T=1\)\), suggesting that ranking\-only metrics overstate the deployment value of expensive semantic estimators in this regime\. Overall, this benchmark reinforces that token\-level T=1 resampling is the most robust choice for multi\-choice \(short\) regimes, while semantic and verbalized methods become progressively less competitive as the task hardens\.

##### MM\-Vet[Yu et al\. \(2023\)](https://arxiv.org/html/2609.22206#bib.bib16)

Table[11](https://arxiv.org/html/2609.22206#A1.T11)reports results on MM\-Vet, where models produce short open\-ended free\-form answers\. Token\-level methods with temperature\-1 resampling dominate on average AUROC and CHDA \(Max Entropy \(T=1\)reaching0\.770\.77AUROC and72\.072\.0CHDA\), outperforming semantic methods at substantially lower cost\. Logit\-level entropy retains fine\-grained discriminative power at short\-answer lengths, and T=1 resampling sharpens this further by exposing alternative completions that greedy decoding suppresses\. The open short\-form format admits a clean “unknown” surface form for the Verbal Abstain method as models abstain on∼19\.5%\\sim\\\!19\.5\\%of MM\-Vet samples—the highest abstention rate across all our benchmarks \(Tab\.[2](https://arxiv.org/html/2609.22206#S4.T2)\)\. WhileVerbal Abstainachieves a moderate0\.680\.68average AUROC, its CHDA \(65\.665\.6\) trails the leading T=1 methods, indicating that frequent abstention produces a usable but suboptimal deployment\-time signal in this regime—and on certain backbones \(notably Qwen3\-VL\-8B, whereVerbal Abstainreaches77\.877\.8CHDA\) it can in fact be the preferred choice, hinting that the optimal estimator is not entirely backbone\-agnostic\. Low coverage@Risk values at tight budgets further reflect the low base accuracy, which leaves too few correct answers to populate a confident\-correct head\.

##### FSVQA200[Shin et al\. \(2016\)](https://arxiv.org/html/2609.22206#bib.bib25)

Table[12](https://arxiv.org/html/2609.22206#A1.T12)reports our full results on FSVQA200, where models produce sentence\-length free\-form answers\. Consistent with the main paper, the longer answer format inverts the trends observed in our short\-form benchmarks:Verbal Abstainleads on average AUROC \(0\.670\.67\),CHDA\(73\.473\.4\), andCov@30\(0\.930\.93\), surpassing every token\-level and semantic alternative at single\-pass1×1\\timescost\. Token\-level methods degrade markedly, as uncertainty is no longer localized in a few decisive tokens but diffused across the generated meaning\. Semantic methods stay competitive on the strongest backbones—VASE attains the best averageCov@10\(0\.170\.17\) andCov@20\(0\.450\.45\), and Semantic Entropy reaches0\.730\.73AUROC on InternVL3\.5\-8B—but their66–11×11\\timescost is hard to justify againstVerbal Abstain\.Cov@30approaches1\.01\.0for most methods on the higher\-accuracy backbones, paralleling ScienceQA’s saturation; the harder Qwen2\-VL\-2B\-Instruct setting \(accuracy49\.3%49\.3\\%\) remains the principal discriminator, whereVerbal Abstainstill leads \(0\.840\.84\) by a wide margin\. From a deployment perspective, the CHDA picture aligns cleanly with AUROC here:Verbal Abstain’s∼10\\sim\\\!10point CHDA margin over the next\-best family makes it the unambiguous recommendation at sentence\-length,1×1\\timescost\.

##### MM\-Vet Long

Table[13](https://arxiv.org/html/2609.22206#A1.T13)reports results on MM\-Vet Long, a variant of MM\-Vet[Yu et al\. \(2023\)](https://arxiv.org/html/2609.22206#bib.bib16)in which the instruction to produce a short final answer is replaced with one requesting a complete, multi\-sentence response \(base accuracy46\.6%46\.6\\%, comparable to MM\-Vet’s50\.4%50\.4\\%\)\. The format change inverts the method ranking observed on MM\-Vet: semantic methods now lead average AUROC, while token\-level T=1 methods—which dominated MM\-Vet—collapse\. We attribute this to two complementary effects\. First, the per\-token entropy and NLL signals that concentrated in MM\-Vet’s short answers are diluted across many tokens spanning multiple sentences, eroding token\-level discriminative power\. Second, semantic\-level consistency across resampled long\-form generations captures meaning\-level disagreement that the short\-form regime does not expose\. The CHDA picture aligns with AUROC: semantic methods lead the deployment metric on average, making this the first regime in our suite where the cost of semantic estimators is straightforwardly justified at deployment time\. Verbalized methods remain weak:Verbal Abstaindrops to near\-random \(0\.570\.57AUROC, vs\.0\.680\.68on MM\-Vet\), as instructing the model to produce a complete answer suppresses the abstention option \(see the low abstention rate in Tab\.[2](https://arxiv.org/html/2609.22206#S4.T2)\)\. Overall, MM\-Vet Long isolates the effect of answer length on uncertainty estimation: holding difficulty fixed and only lengthening the response shifts the optimum from token\-level resampling to semantic\-level methods\.

##### LLaVABench[Liu et al\. \(2023\)](https://arxiv.org/html/2609.22206#bib.bib17)

Table[14](https://arxiv.org/html/2609.22206#A1.T14)reports results on LLaVA\-Bench, where models produce long\-form, multi\-sentence open\-ended responses\. The results reinforce and strengthen the trend observed on MM\-Vet Long: semantic methods dominate decisively on both AUROC and CHDA, while token\-level methods—both T=0 and T=1 variants—collapse, the largest relative gap of any benchmark in our suite\. This indicates that meaning\-level consistency across resampled responses captures uncertainty that becomes inaccessible to per\-token signals once generations span multiple sentences and discourse structure\. On CHDA, VASE leads at69\.269\.2, comfortably above the best token\-level result;Verbal Abstainis a notable outlier at63\.563\.5, driven by strong per\-backbone performance on Qwen3\-VL\-8B \(77\.877\.8\) and Qwen2\-VL\-2B \(73\.373\.3\), suggesting that for cost\-sensitive deployments on specific backbones, the1×1\\timesverbal route remains a defensible fallback even in long\-form regimes\. Verbal methods nevertheless remain weak on AUROC\. Overall, LLaVA\-Bench cements semantic methods as the robust choice for genuinely long\-form open\-ended generation: as answer length grows from sentence\-level \(FSVQA200\) to multi\-sentence \(MM\-Vet Long, LLaVA\-Bench\), the optimal method moves from cheap token\-level and verbalized abstention through to costly semantic\-level consistency, with the cost premium of semantic methods becoming progressively easier to justify\.

MetricMethodCostInternVL2InternVL3\.5Qwen2\-VLQwen3\-VLAvg2B8B2B8B2B\-Instruct7B\-Instruct2B\-Instruct8B\-InstructModel Acc–83\.4±\\pm1\.789\.5±\\pm1\.080\.0±\\pm1\.589\.8±\\pm0\.461\.7±\\pm4\.177\.6±\\pm3\.375\.1±\\pm1\.689\.8±\\pm0\.580\.9AUROC↑\\uparrowVerbal Abstain1×1\\times0\.500\.510\.690\.570\.590\.560\.620\.680\.59Verbal Confidence1×1\\times0\.550\.600\.770\.570\.480\.570\.490\.480\.56Avg Entropy1×1\\times0\.570\.550\.650\.530\.610\.600\.700\.580\.60Max Entropy1×1\\times0\.560\.550\.640\.530\.600\.600\.710\.580\.60Avg NLL1×1\\times0\.570\.550\.640\.530\.610\.590\.700\.580\.60Max NLL1×1\\times0\.570\.560\.650\.530\.610\.590\.720\.580\.60Avg Entropy \(T=1\)2×2\\times0\.760\.810\.800\.790\.700\.820\.780\.770\.78Max Entropy \(T=1\)2×2\\times0\.820\.820\.820\.780\.690\.820\.840\.770\.80Avg NLL \(T=1\)2×2\\times0\.800\.790\.820\.800\.790\.870\.790\.770\.80Max NLL \(T=1\)2×2\\times0\.840\.760\.830\.800\.760\.850\.840\.770\.80Semantic Entropy \(N=10\)11×11\\times0\.800\.880\.740\.750\.740\.840\.800\.740\.78Semantic Entropy \(N=5\)6×6\\times0\.740\.810\.660\.710\.700\.790\.720\.700\.73VASE \(N=5\)6×6\\times0\.780\.860\.740\.770\.690\.810\.790\.760\.78VL\-Uncertainty \(N=10\)11×11\\times0\.780\.840\.760\.740\.750\.840\.770\.710\.77Cov@10↑\\uparrowVerbal Abstain1×1\\times0\.000\.730\.000\.940\.000\.000\.000\.960\.33Verbal Confidence1×1\\times0\.001\.000\.621\.000\.000\.000\.001\.000\.45Avg Entropy1×1\\times0\.081\.000\.021\.000\.000\.000\.021\.000\.39Max Entropy1×1\\times0\.081\.000\.021\.000\.000\.000\.021\.000\.39Avg NLL1×1\\times0\.081\.000\.021\.000\.000\.000\.021\.000\.39Max NLL1×1\\times0\.081\.000\.021\.000\.000\.000\.021\.000\.39Avg Entropy \(T=1\)2×2\\times0\.620\.960\.700\.980\.130\.580\.580\.990\.69Max Entropy \(T=1\)2×2\\times0\.750\.970\.710\.990\.110\.540\.620\.990\.71Avg NLL \(T=1\)2×2\\times0\.740\.950\.710\.990\.270\.670\.580\.990\.74Max NLL \(T=1\)2×2\\times0\.790\.930\.730\.990\.260\.630\.620\.990\.74Semantic Entropy \(N=10\)11×11\\times0\.861\.000\.731\.000\.310\.730\.681\.000\.79Semantic Entropy \(N=5\)6×6\\times0\.821\.000\.001\.000\.110\.690\.001\.000\.58VASE \(N=5\)6×6\\times0\.821\.000\.701\.000\.140\.680\.661\.000\.75VL\-Uncertainty \(N=10\)11×11\\times0\.811\.000\.721\.000\.300\.740\.641\.000\.78Cov@20↑\\uparrowVerbal Abstain1×1\\times1\.001\.000\.001\.000\.000\.530\.171\.000\.59Verbal Confidence1×1\\times1\.001\.000\.971\.000\.060\.971\.001\.000\.87Avg Entropy1×1\\times1\.001\.001\.001\.000\.000\.990\.881\.000\.86Max Entropy1×1\\times1\.001\.001\.001\.000\.000\.990\.911\.000\.86Avg NLL1×1\\times1\.001\.001\.001\.000\.001\.000\.891\.000\.86Max NLL1×1\\times1\.001\.001\.001\.000\.001\.000\.921\.000\.87Avg Entropy \(T=1\)2×2\\times1\.001\.000\.971\.000\.230\.830\.851\.000\.86Max Entropy \(T=1\)2×2\\times1\.001\.000\.971\.000\.200\.820\.911\.000\.86Avg NLL \(T=1\)2×2\\times1\.001\.000\.951\.000\.420\.880\.851\.000\.89Max NLL \(T=1\)2×2\\times0\.991\.000\.971\.000\.400\.850\.921\.000\.89Semantic Entropy \(N=10\)11×11\\times1\.001\.001\.001\.000\.521\.000\.881\.000\.92Semantic Entropy \(N=5\)6×6\\times1\.001\.001\.001\.000\.440\.990\.881\.000\.91VASE \(N=5\)6×6\\times1\.001\.001\.001\.000\.360\.990\.881\.000\.90VL\-Uncertainty \(N=10\)11×11\\times1\.001\.001\.001\.000\.530\.990\.861\.000\.92Cov@30↑\\uparrowVerbal Abstain1×1\\times1\.001\.000\.971\.000\.011\.001\.001\.000\.87Verbal Confidence1×1\\times1\.001\.001\.001\.000\.091\.001\.001\.000\.89Avg Entropy1×1\\times1\.001\.001\.001\.000\.811\.001\.001\.000\.98Max Entropy1×1\\times1\.001\.001\.001\.000\.791\.001\.001\.000\.97Avg NLL1×1\\times1\.001\.001\.001\.000\.801\.001\.001\.000\.97Max NLL1×1\\times1\.001\.001\.001\.000\.801\.001\.001\.000\.97Avg Entropy \(T=1\)2×2\\times1\.001\.001\.001\.000\.481\.001\.001\.000\.94Max Entropy \(T=1\)2×2\\times1\.001\.001\.001\.000\.521\.001\.001\.000\.94Avg NLL \(T=1\)2×2\\times1\.001\.001\.001\.000\.621\.001\.001\.000\.95Max NLL \(T=1\)2×2\\times1\.001\.001\.001\.000\.591\.001\.001\.000\.95Semantic Entropy \(N=10\)11×11\\times1\.001\.001\.001\.000\.831\.001\.001\.000\.98Semantic Entropy \(N=5\)6×6\\times1\.001\.001\.001\.000\.791\.001\.001\.000\.97VASE \(N=5\)6×6\\times1\.001\.001\.001\.000\.801\.001\.001\.000\.97VL\-Uncertainty \(N=10\)11×11\\times1\.001\.001\.001\.000\.821\.001\.001\.000\.98CHDA↑\\uparrowVerbal Abstain1×1\\times15\.989\.780\.090\.264\.779\.877\.791\.573\.7Verbal Confidence1×1\\times53\.287\.581\.990\.342\.178\.580\.590\.275\.5Avg Entropy1×1\\times84\.684\.483\.290\.067\.380\.376\.090\.082\.0Max Entropy1×1\\times84\.384\.482\.989\.866\.879\.782\.490\.082\.5Avg NLL1×1\\times84\.584\.382\.989\.967\.680\.073\.690\.081\.6Max NLL1×1\\times84\.784\.683\.190\.067\.279\.981\.390\.082\.6Avg Entropy \(T=1\)2×2\\times74\.282\.772\.089\.760\.975\.571\.989\.777\.1Max Entropy \(T=1\)2×2\\times81\.988\.981\.189\.663\.575\.582\.589\.381\.5Avg NLL \(T=1\)2×2\\times79\.780\.478\.490\.166\.881\.875\.090\.280\.3Max NLL \(T=1\)2×2\\times82\.176\.481\.989\.267\.777\.078\.989\.480\.3Semantic Entropy \(N=10\)11×11\\times84\.690\.381\.389\.968\.280\.274\.790\.282\.4Semantic Entropy \(N=5\)6×6\\times84\.590\.080\.489\.966\.378\.774\.690\.181\.8VASE \(N=5\)6×6\\times84\.590\.280\.990\.066\.579\.674\.589\.882\.0VL\-Uncertainty \(N=10\)11×11\\times84\.490\.081\.390\.066\.880\.774\.690\.082\.2

Table 9:Per\-model results on multiple\-choice benchmarkScienceQAacross AUROC, selective\-prediction coverage @ Risk, and CHDA\. Token\-level methods with T=1 resampling match or exceed far costlier semantic methods on average AUROC, while semantic methods lead at the tightest coverage budget \(Cov@10\); verbalized methods are consistently unreliable\.MetricMethodCostInternVL2InternVL3\.5Qwen2\-VLQwen3\-VLAvg2B8B2B8B2B\-Instruct7B\-Instruct2B\-Instruct8B\-InstructModel Acc–31\.6±\\pm2\.042\.3±\\pm1\.734\.6±\\pm2\.454\.2±\\pm2\.233\.4±\\pm2\.247\.0±\\pm2\.730\.8±\\pm3\.053\.3±\\pm0\.640\.9AUROC↑\\uparrowVerbal Abstain1×1\\times0\.500\.500\.530\.520\.580\.660\.610\.550\.56Verbal Confidence1×1\\times0\.510\.490\.680\.600\.520\.520\.530\.520\.55Avg Entropy1×1\\times0\.540\.550\.700\.610\.550\.550\.710\.560\.60Max Entropy1×1\\times0\.540\.540\.740\.600\.590\.540\.740\.560\.61Avg NLL1×1\\times0\.540\.540\.720\.610\.550\.560\.720\.560\.60Max NLL1×1\\times0\.550\.530\.750\.610\.600\.550\.740\.560\.61Avg Entropy \(T=1\)2×2\\times0\.590\.650\.620\.750\.580\.710\.590\.700\.65Max Entropy \(T=1\)2×2\\times0\.610\.680\.800\.790\.650\.720\.780\.720\.72Avg NLL \(T=1\)2×2\\times0\.620\.640\.690\.760\.610\.740\.610\.710\.67Max NLL \(T=1\)2×2\\times0\.640\.670\.790\.790\.660\.720\.770\.720\.72Semantic Entropy \(N=10\)11×11\\times0\.590\.690\.650\.740\.620\.700\.660\.680\.66Semantic Entropy \(N=5\)6×6\\times0\.570\.650\.590\.700\.590\.670\.610\.630\.63VASE \(N=5\)6×6\\times0\.570\.680\.630\.730\.620\.680\.640\.670\.65VL\-Uncertainty \(N=10\)11×11\\times0\.580\.680\.630\.730\.620\.690\.620\.660\.65Cov@10↑\\uparrowVerbal Abstain1×1\\times0\.000\.000\.000\.000\.000\.000\.000\.000\.00Verbal Confidence1×1\\times0\.000\.000\.000\.000\.000\.000\.000\.000\.00Avg Entropy1×1\\times0\.000\.010\.000\.000\.000\.000\.000\.000\.00Max Entropy1×1\\times0\.000\.010\.000\.000\.000\.000\.000\.000\.00Avg NLL1×1\\times0\.000\.010\.000\.000\.000\.000\.000\.000\.00Max NLL1×1\\times0\.000\.010\.000\.000\.000\.000\.000\.000\.00Avg Entropy \(T=1\)2×2\\times0\.000\.000\.030\.030\.000\.050\.000\.000\.02Max Entropy \(T=1\)2×2\\times0\.000\.000\.030\.010\.030\.080\.000\.000\.02Avg NLL \(T=1\)2×2\\times0\.000\.000\.030\.010\.020\.090\.000\.000\.02Max NLL \(T=1\)2×2\\times0\.000\.000\.030\.010\.030\.090\.000\.000\.02Semantic Entropy \(N=10\)11×11\\times0\.000\.020\.000\.000\.010\.010\.000\.000\.01Semantic Entropy \(N=5\)6×6\\times0\.000\.000\.000\.000\.000\.010\.000\.000\.00VASE \(N=5\)6×6\\times0\.000\.000\.000\.000\.010\.000\.000\.000\.00VL\-Uncertainty \(N=10\)11×11\\times0\.000\.020\.000\.000\.000\.070\.000\.000\.01Cov@20↑\\uparrowVerbal Abstain1×1\\times0\.010\.010\.000\.000\.000\.000\.000\.000\.00Verbal Confidence1×1\\times0\.000\.000\.000\.020\.000\.000\.000\.000\.00Avg Entropy1×1\\times0\.010\.010\.000\.010\.000\.000\.000\.010\.00Max Entropy1×1\\times0\.010\.010\.000\.010\.000\.000\.000\.010\.00Avg NLL1×1\\times0\.010\.010\.000\.010\.000\.000\.000\.010\.00Max NLL1×1\\times0\.010\.010\.000\.010\.000\.000\.000\.010\.00Avg Entropy \(T=1\)2×2\\times0\.020\.020\.110\.400\.010\.160\.030\.000\.09Max Entropy \(T=1\)2×2\\times0\.020\.090\.110\.420\.050\.170\.030\.040\.12Avg NLL \(T=1\)2×2\\times0\.020\.080\.110\.420\.030\.180\.030\.080\.12Max NLL \(T=1\)2×2\\times0\.020\.080\.110\.430\.040\.180\.030\.040\.12Semantic Entropy \(N=10\)11×11\\times0\.000\.120\.000\.280\.040\.210\.000\.000\.08Semantic Entropy \(N=5\)6×6\\times0\.000\.000\.000\.010\.010\.020\.000\.000\.01VASE \(N=5\)6×6\\times0\.010\.150\.000\.310\.020\.170\.000\.000\.08VL\-Uncertainty \(N=10\)11×11\\times0\.000\.040\.000\.280\.030\.200\.000\.000\.07Cov@30↑\\uparrowVerbal Abstain1×1\\times0\.010\.010\.000\.000\.000\.000\.000\.000\.00Verbal Confidence1×1\\times0\.000\.010\.110\.420\.000\.020\.000\.000\.07Avg Entropy1×1\\times0\.010\.010\.000\.190\.000\.000\.000\.010\.03Max Entropy1×1\\times0\.010\.010\.000\.190\.000\.000\.000\.010\.03Avg NLL1×1\\times0\.010\.010\.000\.190\.000\.000\.000\.010\.03Max NLL1×1\\times0\.010\.010\.000\.190\.000\.000\.000\.010\.03Avg Entropy \(T=1\)2×2\\times0\.030\.130\.150\.530\.020\.280\.080\.530\.22Max Entropy \(T=1\)2×2\\times0\.040\.210\.210\.620\.070\.290\.090\.540\.26Avg NLL \(T=1\)2×2\\times0\.040\.180\.190\.590\.040\.310\.090\.540\.25Max NLL \(T=1\)2×2\\times0\.030\.140\.190\.630\.070\.310\.090\.540\.25Semantic Entropy \(N=10\)11×11\\times0\.000\.250\.000\.610\.060\.350\.020\.470\.22Semantic Entropy \(N=5\)6×6\\times0\.000\.230\.000\.590\.010\.310\.000\.000\.14VASE \(N=5\)6×6\\times0\.010\.230\.000\.580\.040\.280\.000\.430\.20VL\-Uncertainty \(N=10\)11×11\\times0\.020\.190\.000\.540\.060\.350\.000\.460\.20CHDA↑\\uparrowVerbal Abstain1×1\\times68\.841\.337\.249\.540\.559\.941\.955\.849\.4Verbal Confidence1×1\\times45\.749\.365\.858\.259\.050\.647\.254\.553\.8Avg Entropy1×1\\times47\.049\.771\.258\.757\.253\.645\.955\.354\.8Max Entropy1×1\\times46\.549\.471\.058\.653\.048\.969\.053\.756\.3Avg NLL1×1\\times46\.249\.371\.757\.656\.653\.933\.755\.453\.1Max NLL1×1\\times47\.148\.672\.058\.555\.450\.662\.053\.956\.0Avg Entropy \(T=1\)2×2\\times57\.764\.770\.063\.967\.261\.147\.358\.461\.3Max Entropy \(T=1\)2×2\\times55\.964\.268\.153\.871\.464\.071\.852\.562\.7Avg NLL \(T=1\)2×2\\times65\.858\.956\.761\.069\.765\.134\.757\.958\.7Max NLL \(T=1\)2×2\\times68\.258\.969\.357\.570\.160\.053\.952\.761\.3Semantic Entropy \(N=10\)11×11\\times36\.351\.134\.155\.763\.652\.530\.354\.647\.3Semantic Entropy \(N=5\)6×6\\times39\.954\.440\.256\.054\.555\.931\.654\.048\.3VASE \(N=5\)6×6\\times33\.046\.134\.554\.860\.048\.130\.053\.545\.0VL\-Uncertainty \(N=10\)11×11\\times33\.042\.734\.154\.549\.356\.030\.354\.044\.2

Table 10:Per\-model results on multiple\-choice benchmarkMMMU\. Token\-level methods with T=1 resampling lead on every metric, while semantic methods trail at33–5×5\\timeshigher cost; verbalized methods degrade further than on ScienceQA, and selective\-prediction coverage never saturates due to the lower base accuracy\.MetricMethodCostInternVL2InternVL3\.5Qwen2\-VLQwen3\-VLAvg2B8B2B8B2B\-Instruct7B\-Instruct2B\-Instruct8B\-InstructModel Acc–34\.2±\\pm2\.946\.3±\\pm3\.253\.9±\\pm2\.765\.4±\\pm1\.240\.3±\\pm3\.247\.9±\\pm3\.051\.6±\\pm3\.063\.5±\\pm2\.450\.4AUROC↑\\uparrowVerbal Abstain1×1\\times0\.550\.570\.660\.720\.690\.720\.740\.750\.68Verbal Confidence1×1\\times0\.620\.630\.620\.620\.550\.590\.560\.590\.60Avg Entropy1×1\\times0\.660\.640\.660\.680\.650\.630\.670\.630\.65Max Entropy1×1\\times0\.680\.650\.660\.660\.650\.630\.680\.630\.65Avg NLL1×1\\times0\.640\.640\.670\.670\.670\.630\.660\.630\.65Max NLL1×1\\times0\.670\.670\.660\.670\.630\.620\.650\.630\.65Avg Entropy \(T=1\)2×2\\times0\.870\.800\.770\.760\.750\.770\.720\.680\.77Max Entropy \(T=1\)2×2\\times0\.880\.840\.790\.740\.740\.790\.720\.700\.77Avg NLL \(T=1\)2×2\\times0\.860\.790\.810\.760\.720\.750\.710\.680\.76Max NLL \(T=1\)2×2\\times0\.850\.810\.770\.740\.800\.760\.700\.710\.77Semantic Entropy \(N=10\)11×11\\times0\.750\.730\.700\.610\.660\.730\.710\.620\.69Semantic Entropy \(N=5\)6×6\\times0\.730\.700\.700\.600\.620\.700\.690\.600\.67VASE \(N=5\)6×6\\times0\.760\.720\.700\.610\.660\.720\.690\.610\.69VL\-Uncertainty \(N=10\)11×11\\times0\.750\.720\.650\.560\.700\.720\.700\.660\.68Cov@10↑\\uparrowVerbal Abstain1×1\\times0\.000\.000\.000\.000\.000\.000\.020\.010\.00Verbal Confidence1×1\\times0\.000\.000\.020\.000\.000\.000\.000\.000\.00Avg Entropy1×1\\times0\.000\.000\.000\.000\.000\.000\.010\.010\.00Max Entropy1×1\\times0\.000\.000\.000\.000\.000\.000\.010\.010\.00Avg NLL1×1\\times0\.000\.000\.000\.000\.000\.000\.010\.010\.00Max NLL1×1\\times0\.000\.000\.000\.000\.000\.000\.010\.010\.00Avg Entropy \(T=1\)2×2\\times0\.080\.190\.010\.380\.020\.140\.000\.000\.10Max Entropy \(T=1\)2×2\\times0\.130\.140\.070\.320\.050\.150\.000\.000\.11Avg NLL \(T=1\)2×2\\times0\.130\.160\.070\.310\.000\.140\.000\.000\.10Max NLL \(T=1\)2×2\\times0\.120\.130\.090\.310\.050\.150\.000\.000\.11Semantic Entropy \(N=10\)11×11\\times0\.140\.150\.180\.070\.120\.210\.010\.020\.11Semantic Entropy \(N=5\)6×6\\times0\.130\.080\.020\.000\.050\.190\.020\.000\.06VASE \(N=5\)6×6\\times0\.120\.110\.110\.060\.110\.180\.010\.000\.09VL\-Uncertainty \(N=10\)11×11\\times0\.120\.070\.170\.200\.090\.170\.000\.150\.12Cov@20↑\\uparrowVerbal Abstain1×1\\times0\.000\.000\.000\.000\.000\.000\.020\.010\.00Verbal Confidence1×1\\times0\.000\.000\.020\.000\.000\.000\.000\.000\.00Avg Entropy1×1\\times0\.000\.000\.000\.000\.000\.000\.010\.010\.00Max Entropy1×1\\times0\.000\.000\.000\.000\.000\.000\.010\.010\.00Avg NLL1×1\\times0\.000\.000\.000\.000\.000\.000\.010\.010\.00Max NLL1×1\\times0\.000\.000\.000\.000\.000\.000\.010\.010\.00Avg Entropy \(T=1\)2×2\\times0\.210\.280\.350\.580\.070\.210\.000\.410\.26Max Entropy \(T=1\)2×2\\times0\.190\.290\.350\.520\.170\.240\.000\.400\.27Avg NLL \(T=1\)2×2\\times0\.200\.250\.370\.560\.080\.170\.000\.400\.25Max NLL \(T=1\)2×2\\times0\.230\.270\.360\.510\.190\.220\.000\.380\.27Semantic Entropy \(N=10\)11×11\\times0\.220\.220\.310\.440\.170\.300\.210\.310\.27Semantic Entropy \(N=5\)6×6\\times0\.190\.210\.350\.390\.120\.270\.130\.000\.21VASE \(N=5\)6×6\\times0\.210\.210\.360\.440\.150\.290\.130\.300\.26VL\-Uncertainty \(N=10\)11×11\\times0\.160\.220\.250\.300\.150\.270\.210\.460\.25Cov@30↑\\uparrowVerbal Abstain1×1\\times0\.010\.000\.000\.690\.000\.000\.030\.780\.19Verbal Confidence1×1\\times0\.000\.000\.330\.810\.000\.000\.000\.840\.25Avg Entropy1×1\\times0\.000\.000\.000\.900\.000\.000\.020\.730\.21Max Entropy1×1\\times0\.000\.000\.000\.880\.000\.000\.020\.710\.20Avg NLL1×1\\times0\.000\.000\.000\.890\.000\.000\.020\.740\.21Max NLL1×1\\times0\.000\.000\.000\.880\.000\.000\.020\.700\.20Avg Entropy \(T=1\)2×2\\times0\.330\.390\.510\.810\.210\.450\.370\.720\.47Max Entropy \(T=1\)2×2\\times0\.320\.430\.530\.910\.220\.440\.360\.750\.49Avg NLL \(T=1\)2×2\\times0\.280\.360\.540\.850\.200\.380\.360\.700\.46Max NLL \(T=1\)2×2\\times0\.320\.460\.470\.850\.310\.410\.290\.760\.49Semantic Entropy \(N=10\)11×11\\times0\.280\.450\.510\.670\.220\.450\.560\.620\.47Semantic Entropy \(N=5\)6×6\\times0\.280\.420\.480\.640\.230\.410\.540\.610\.45VASE \(N=5\)6×6\\times0\.280\.400\.540\.670\.240\.440\.530\.610\.46VL\-Uncertainty \(N=10\)11×11\\times0\.290\.350\.420\.530\.250\.430\.510\.670\.43CHDA↑\\uparrowVerbal Abstain1×1\\times60\.953\.463\.073\.258\.068\.270\.277\.865\.6Verbal Confidence1×1\\times58\.961\.956\.964\.751\.559\.253\.263\.658\.7Avg Entropy1×1\\times64\.263\.364\.571\.363\.856\.062\.164\.463\.7Max Entropy1×1\\times63\.964\.365\.668\.360\.747\.464\.963\.862\.4Avg NLL1×1\\times63\.064\.765\.170\.263\.855\.555\.564\.262\.7Max NLL1×1\\times63\.065\.266\.767\.361\.953\.562\.262\.462\.8Avg Entropy \(T=1\)2×2\\times77\.573\.567\.568\.371\.369\.262\.566\.769\.6Max Entropy \(T=1\)2×2\\times82\.376\.070\.370\.272\.373\.167\.264\.772\.0Avg NLL \(T=1\)2×2\\times82\.171\.470\.868\.770\.366\.959\.964\.269\.3Max NLL \(T=1\)2×2\\times81\.774\.969\.369\.374\.968\.264\.462\.970\.7Semantic Entropy \(N=10\)11×11\\times74\.866\.265\.160\.267\.968\.369\.463\.666\.9Semantic Entropy \(N=5\)6×6\\times73\.465\.464\.160\.665\.668\.070\.062\.466\.2VASE \(N=5\)6×6\\times76\.067\.466\.762\.467\.767\.368\.763\.367\.4VL\-Uncertainty \(N=10\)11×11\\times73\.966\.559\.457\.668\.866\.767\.865\.465\.8

Table 11:Per\-model results on short open\-ended benchmarkMM\-Vet\. Token\-level methods with T=1 resampling lead on average AUROC and CHDA, outperforming semantic methods at substantially lower cost; verbalized abstention is frequent but only weakly correlated with correctness, and tight coverage budgets remain unsaturated due to the low base accuracy\.MetricMethodCostInternVL2InternVL3\.5Qwen2\-VLQwen3\-VLAvg2B8B2B8B2B\-Instruct7B\-Instruct2B\-Instruct8B\-InstructModel Acc–66\.4±\\pm4\.267\.0±\\pm3\.769\.0±\\pm2\.071\.0±\\pm1\.749\.3±\\pm9\.565\.2±\\pm7\.370\.3±\\pm2\.576\.3±\\pm2\.266\.8AUROC↑\\uparrowVerbal Abstain1×1\\times0\.570\.530\.670\.630\.830\.690\.720\.700\.67Verbal Confidence1×1\\times0\.520\.620\.530\.580\.580\.660\.600\.600\.59Avg Entropy1×1\\times0\.640\.550\.580\.570\.580\.600\.600\.600\.59Max Entropy1×1\\times0\.620\.560\.600\.580\.630\.610\.640\.550\.60Avg NLL1×1\\times0\.620\.560\.620\.550\.580\.650\.550\.590\.59Max NLL1×1\\times0\.610\.550\.600\.570\.640\.600\.600\.570\.59Avg Entropy \(T=1\)2×2\\times0\.630\.640\.650\.590\.560\.680\.680\.660\.64Max Entropy \(T=1\)2×2\\times0\.640\.640\.690\.610\.570\.650\.640\.640\.64Avg NLL \(T=1\)2×2\\times0\.660\.670\.650\.600\.590\.690\.700\.640\.65Max NLL \(T=1\)2×2\\times0\.610\.640\.610\.600\.580\.670\.630\.610\.62Semantic Entropy \(N=10\)11×11\\times0\.640\.650\.610\.730\.580\.590\.670\.710\.65Semantic Entropy \(N=5\)6×6\\times0\.610\.620\.610\.700\.570\.610\.640\.650\.63VASE \(N=5\)6×6\\times0\.610\.670\.630\.730\.630\.650\.660\.660\.65VL\-Uncertainty \(N=10\)11×11\\times0\.610\.620\.610\.660\.610\.600\.630\.620\.62Cov@10↑\\uparrowVerbal Abstain1×1\\times0\.060\.030\.020\.010\.010\.050\.010\.030\.03Verbal Confidence1×1\\times0\.000\.090\.010\.020\.000\.240\.000\.070\.05Avg Entropy1×1\\times0\.050\.020\.030\.010\.010\.030\.100\.180\.05Max Entropy1×1\\times0\.050\.020\.030\.010\.010\.030\.080\.130\.04Avg NLL1×1\\times0\.050\.020\.030\.010\.010\.030\.080\.140\.04Max NLL1×1\\times0\.050\.020\.030\.010\.010\.030\.110\.120\.05Avg Entropy \(T=1\)2×2\\times0\.120\.150\.040\.060\.090\.170\.160\.260\.13Max Entropy \(T=1\)2×2\\times0\.120\.110\.160\.150\.040\.120\.110\.190\.12Avg NLL \(T=1\)2×2\\times0\.090\.140\.110\.100\.100\.150\.210\.160\.13Max NLL \(T=1\)2×2\\times0\.110\.090\.100\.150\.080\.130\.180\.140\.12Semantic Entropy \(N=10\)11×11\\times0\.150\.140\.090\.350\.050\.050\.150\.280\.16Semantic Entropy \(N=5\)6×6\\times0\.080\.140\.070\.160\.010\.010\.080\.280\.10VASE \(N=5\)6×6\\times0\.210\.220\.050\.290\.060\.140\.100\.270\.17VL\-Uncertainty \(N=10\)11×11\\times0\.150\.150\.030\.240\.030\.060\.140\.220\.13Cov@20↑\\uparrowVerbal Abstain1×1\\times0\.080\.060\.050\.230\.740\.950\.430\.890\.43Verbal Confidence1×1\\times0\.020\.310\.290\.070\.000\.950\.160\.980\.35Avg Entropy1×1\\times0\.470\.030\.360\.330\.010\.300\.280\.760\.32Max Entropy1×1\\times0\.340\.030\.370\.260\.010\.300\.480\.570\.29Avg NLL1×1\\times0\.350\.030\.360\.360\.010\.300\.210\.660\.28Max NLL1×1\\times0\.390\.030\.360\.270\.010\.300\.340\.700\.30Avg Entropy \(T=1\)2×2\\times0\.280\.300\.320\.340\.130\.270\.530\.780\.37Max Entropy \(T=1\)2×2\\times0\.210\.210\.540\.340\.100\.280\.440\.670\.35Avg NLL \(T=1\)2×2\\times0\.200\.320\.400\.400\.150\.260\.630\.620\.37Max NLL \(T=1\)2×2\\times0\.240\.280\.200\.360\.120\.220\.430\.630\.31Semantic Entropy \(N=10\)11×11\\times0\.430\.380\.250\.650\.100\.150\.530\.880\.42Semantic Entropy \(N=5\)6×6\\times0\.370\.360\.340\.620\.040\.200\.470\.770\.39VASE \(N=5\)6×6\\times0\.330\.530\.230\.670\.120\.310\.590\.820\.45VL\-Uncertainty \(N=10\)11×11\\times0\.350\.430\.360\.570\.070\.230\.420\.580\.38Cov@30↑\\uparrowVerbal Abstain1×1\\times0\.960\.830\.850\.970\.841\.000\.951\.000\.93Verbal Confidence1×1\\times0\.560\.901\.001\.000\.001\.000\.991\.000\.81Avg Entropy1×1\\times0\.910\.850\.940\.980\.270\.600\.981\.000\.82Max Entropy1×1\\times1\.000\.880\.951\.000\.270\.680\.941\.000\.84Avg NLL1×1\\times0\.910\.820\.971\.000\.270\.830\.951\.000\.84Max NLL1×1\\times0\.960\.990\.911\.000\.270\.650\.941\.000\.84Avg Entropy \(T=1\)2×2\\times0\.440\.720\.880\.960\.200\.420\.981\.000\.70Max Entropy \(T=1\)2×2\\times0\.450\.450\.860\.980\.150\.400\.861\.000\.64Avg NLL \(T=1\)2×2\\times0\.560\.660\.910\.930\.220\.560\.961\.000\.72Max NLL \(T=1\)2×2\\times0\.440\.390\.800\.980\.220\.461\.001\.000\.66Semantic Entropy \(N=10\)11×11\\times0\.890\.960\.981\.000\.150\.580\.991\.000\.82Semantic Entropy \(N=5\)6×6\\times0\.860\.950\.961\.000\.080\.740\.991\.000\.82VASE \(N=5\)6×6\\times0\.840\.960\.981\.000\.220\.720\.951\.000\.83VL\-Uncertainty \(N=10\)11×11\\times0\.910\.930\.891\.000\.170\.570\.961\.000\.80CHDA↑\\uparrowVerbal Abstain1×1\\times32\.470\.373\.375\.986\.085\.081\.083\.073\.4Verbal Confidence1×1\\times59\.057\.370\.370\.559\.077\.270\.879\.868\.0Avg Entropy1×1\\times52\.551\.753\.060\.662\.766\.957\.071\.859\.5Max Entropy1×1\\times51\.352\.051\.866\.360\.365\.132\.769\.656\.1Avg NLL1×1\\times52\.253\.352\.664\.362\.168\.165\.873\.461\.5Max NLL1×1\\times52\.350\.552\.264\.562\.862\.539\.873\.157\.2Avg Entropy \(T=1\)2×2\\times45\.052\.338\.062\.662\.961\.255\.772\.356\.2Max Entropy \(T=1\)2×2\\times49\.448\.856\.969\.765\.056\.033\.072\.056\.3Avg NLL \(T=1\)2×2\\times44\.557\.350\.366\.765\.764\.366\.872\.861\.1Max NLL \(T=1\)2×2\\times45\.150\.352\.261\.962\.653\.043\.274\.355\.3Semantic Entropy \(N=10\)11×11\\times57\.554\.463\.870\.456\.057\.765\.872\.662\.3Semantic Entropy \(N=5\)6×6\\times52\.847\.858\.069\.956\.552\.763\.669\.958\.9VASE \(N=5\)6×6\\times55\.355\.768\.373\.756\.964\.067\.570\.364\.0VL\-Uncertainty \(N=10\)11×11\\times58\.061\.266\.469\.358\.055\.764\.863\.762\.2

Table 12:Per\-model results on sentence\-length free\-form benchmarkFSVQA200\.Verbal Abstainleads on average AUROC, CHDA, andCov@30at1×1\\timescost, token\-level methods lose the advantage they hold in short\-form regimes, while semantic methods remain competitive\.MetricMethodCostInternVL2InternVL3\.5Qwen2\-VLQwen3\-VLAvg2B8B2B8B2B\-Instruct7B\-Instruct2B\-Instruct8B\-InstructModel Acc–33\.6±\\pm2\.343\.2±\\pm3\.448\.0±\\pm4\.561\.5±\\pm5\.938\.2±\\pm4\.851\.6±\\pm3\.943\.9±\\pm3\.452\.5±\\pm4\.446\.6AUROC↑\\uparrowVerbal Abstain1×1\\times0\.510\.510\.510\.520\.620\.560\.510\.510\.53Verbal Confidence1×1\\times0\.620\.670\.680\.610\.560\.630\.590\.630\.62Avg Entropy1×1\\times0\.530\.580\.510\.530\.520\.510\.540\.520\.53Max Entropy1×1\\times0\.520\.570\.550\.550\.600\.550\.540\.510\.55Avg NLL1×1\\times0\.520\.560\.520\.600\.530\.540\.530\.510\.54Max NLL1×1\\times0\.510\.570\.570\.600\.590\.530\.500\.510\.55Avg Entropy \(T=1\)2×2\\times0\.600\.630\.540\.560\.570\.530\.560\.550\.57Max Entropy \(T=1\)2×2\\times0\.730\.680\.580\.580\.630\.570\.560\.480\.60Avg NLL \(T=1\)2×2\\times0\.610\.660\.550\.580\.550\.560\.520\.520\.57Max NLL \(T=1\)2×2\\times0\.650\.670\.590\.590\.630\.580\.540\.500\.59Semantic Entropy \(N=10\)11×11\\times0\.760\.680\.700\.660\.760\.700\.740\.700\.71Semantic Entropy \(N=5\)6×6\\times0\.700\.670\.650\.640\.740\.670\.680\.680\.68VASE \(N=5\)6×6\\times0\.750\.710\.700\.650\.770\.710\.720\.690\.71VL\-Uncertainty \(N=10\)11×11\\times0\.740\.730\.650\.620\.740\.710\.700\.700\.70Cov@10↑\\uparrowVerbal Abstain1×1\\times0\.000\.000\.000\.000\.000\.000\.000\.000\.00Verbal Confidence1×1\\times0\.000\.000\.010\.020\.000\.000\.000\.010\.01Avg Entropy1×1\\times0\.000\.000\.020\.000\.000\.000\.000\.000\.00Max Entropy1×1\\times0\.000\.000\.020\.000\.000\.000\.000\.000\.00Avg NLL1×1\\times0\.000\.000\.020\.000\.000\.000\.000\.000\.00Max NLL1×1\\times0\.000\.000\.020\.000\.000\.000\.000\.000\.00Avg Entropy \(T=1\)2×2\\times0\.020\.000\.010\.040\.010\.000\.000\.010\.01Max Entropy \(T=1\)2×2\\times0\.030\.020\.010\.050\.030\.040\.000\.000\.02Avg NLL \(T=1\)2×2\\times0\.010\.020\.000\.060\.000\.010\.000\.000\.01Max NLL \(T=1\)2×2\\times0\.030\.020\.010\.040\.020\.020\.000\.000\.02Semantic Entropy \(N=10\)11×11\\times0\.060\.010\.020\.090\.070\.020\.000\.010\.03Semantic Entropy \(N=5\)6×6\\times0\.020\.010\.010\.090\.030\.050\.000\.010\.03VASE \(N=5\)6×6\\times0\.050\.000\.000\.080\.100\.050\.030\.000\.04VL\-Uncertainty \(N=10\)11×11\\times0\.040\.020\.030\.040\.030\.070\.000\.000\.03Cov@20↑\\uparrowVerbal Abstain1×1\\times0\.000\.000\.000\.010\.000\.010\.000\.000\.00Verbal Confidence1×1\\times0\.000\.000\.060\.030\.000\.000\.000\.060\.02Avg Entropy1×1\\times0\.000\.000\.050\.060\.000\.000\.000\.000\.01Max Entropy1×1\\times0\.000\.000\.030\.000\.000\.000\.000\.000\.00Avg NLL1×1\\times0\.000\.000\.040\.290\.000\.000\.000\.000\.04Max NLL1×1\\times0\.000\.000\.030\.080\.000\.000\.000\.000\.01Avg Entropy \(T=1\)2×2\\times0\.030\.020\.010\.100\.010\.000\.000\.010\.02Max Entropy \(T=1\)2×2\\times0\.070\.080\.010\.060\.040\.060\.000\.000\.04Avg NLL \(T=1\)2×2\\times0\.030\.050\.000\.090\.000\.020\.000\.000\.02Max NLL \(T=1\)2×2\\times0\.030\.140\.010\.080\.020\.050\.000\.000\.04Semantic Entropy \(N=10\)11×11\\times0\.100\.010\.040\.340\.110\.110\.010\.170\.11Semantic Entropy \(N=5\)6×6\\times0\.070\.030\.010\.210\.160\.140\.000\.110\.09VASE \(N=5\)6×6\\times0\.090\.000\.020\.160\.180\.130\.100\.040\.09VL\-Uncertainty \(N=10\)11×11\\times0\.100\.050\.040\.110\.080\.210\.000\.080\.08Cov@30↑\\uparrowVerbal Abstain1×1\\times0\.020\.020\.000\.480\.000\.010\.000\.000\.07Verbal Confidence1×1\\times0\.000\.000\.720\.950\.000\.000\.080\.820\.32Avg Entropy1×1\\times0\.000\.000\.050\.320\.010\.000\.000\.000\.05Max Entropy1×1\\times0\.000\.000\.110\.190\.010\.000\.000\.030\.04Avg NLL1×1\\times0\.000\.000\.040\.670\.010\.000\.000\.000\.09Max NLL1×1\\times0\.000\.000\.080\.570\.010\.000\.000\.000\.08Avg Entropy \(T=1\)2×2\\times0\.040\.060\.010\.150\.010\.000\.000\.010\.04Max Entropy \(T=1\)2×2\\times0\.090\.190\.010\.090\.060\.080\.000\.000\.07Avg NLL \(T=1\)2×2\\times0\.040\.140\.010\.140\.010\.030\.000\.000\.05Max NLL \(T=1\)2×2\\times0\.050\.260\.050\.210\.030\.090\.000\.000\.09Semantic Entropy \(N=10\)11×11\\times0\.180\.020\.150\.600\.270\.380\.200\.340\.27Semantic Entropy \(N=5\)6×6\\times0\.140\.110\.010\.530\.260\.360\.080\.340\.23VASE \(N=5\)6×6\\times0\.220\.020\.280\.580\.340\.420\.220\.310\.30VL\-Uncertainty \(N=10\)11×11\\times0\.150\.190\.160\.590\.220\.380\.120\.410\.28CHDA↑\\uparrowVerbal Abstain1×1\\times63\.350\.954\.467\.050\.558\.347\.253\.455\.6Verbal Confidence1×1\\times60\.165\.067\.069\.750\.265\.152\.465\.761\.9Avg Entropy1×1\\times63\.559\.354\.059\.359\.852\.149\.854\.756\.6Max Entropy1×1\\times63\.357\.554\.356\.362\.253\.554\.553\.956\.9Avg NLL1×1\\times64\.559\.353\.464\.959\.354\.248\.955\.657\.5Max NLL1×1\\times63\.958\.954\.663\.462\.553\.654\.053\.558\.0Avg Entropy \(T=1\)2×2\\times69\.157\.655\.558\.065\.450\.558\.553\.758\.5Max Entropy \(T=1\)2×2\\times70\.560\.758\.759\.972\.956\.763\.348\.461\.4Avg NLL \(T=1\)2×2\\times68\.061\.956\.754\.167\.757\.852\.855\.559\.3Max NLL \(T=1\)2×2\\times70\.358\.456\.461\.269\.753\.257\.148\.459\.4Semantic Entropy \(N=10\)11×11\\times73\.763\.166\.163\.964\.462\.668\.365\.566\.0Semantic Entropy \(N=5\)6×6\\times70\.964\.862\.763\.867\.461\.465\.464\.165\.1VASE \(N=5\)6×6\\times72\.965\.667\.064\.563\.964\.965\.864\.766\.2VL\-Uncertainty \(N=10\)11×11\\times73\.467\.761\.265\.365\.861\.763\.365\.365\.5

Table 13:Per\-model results on long open\-form benchmarkMM\-Vet Long\. Semantic methods lead on average by exploiting meaning\-level consistency across multi\-sentence responses, while token\-level T=1 methods—which dominate on short\-form MM\-Vet—collapse\.MetricMethodCostInternVL2InternVL3\.5Qwen2\-VLQwen3\-VLAvg2B8B2B8B2B\-Instruct7B\-Instruct2B\-Instruct8B\-InstructModel Acc–34\.8±\\pm4\.844\.7±\\pm5\.649\.2±\\pm5\.054\.0±\\pm4\.053\.0±\\pm6\.867\.5±\\pm5\.656\.9±\\pm6\.861\.5±\\pm6\.952\.7AUROC↑\\uparrowVerbal Abstain1×1\\times0\.490\.500\.520\.520\.610\.650\.690\.590\.57Verbal Confidence1×1\\times0\.480\.610\.640\.610\.520\.460\.630\.580\.57Avg Entropy1×1\\times0\.600\.620\.530\.610\.470\.640\.520\.530\.57Max Entropy1×1\\times0\.520\.540\.500\.690\.570\.590\.450\.610\.56Avg NLL1×1\\times0\.520\.540\.510\.620\.520\.660\.540\.450\.55Max NLL1×1\\times0\.550\.600\.550\.610\.580\.630\.490\.470\.56Avg Entropy \(T=1\)2×2\\times0\.630\.630\.570\.640\.570\.570\.530\.570\.59Max Entropy \(T=1\)2×2\\times0\.650\.600\.630\.640\.610\.590\.550\.570\.61Avg NLL \(T=1\)2×2\\times0\.590\.600\.550\.630\.580\.590\.630\.570\.59Max NLL \(T=1\)2×2\\times0\.580\.530\.540\.580\.570\.530\.530\.470\.54Semantic Entropy \(N=10\)11×11\\times0\.750\.770\.730\.770\.630\.770\.720\.700\.73Semantic Entropy \(N=5\)6×6\\times0\.700\.720\.640\.750\.620\.720\.670\.690\.69VASE \(N=5\)6×6\\times0\.790\.740\.720\.790\.650\.730\.720\.710\.73VL\-Uncertainty \(N=10\)11×11\\times0\.800\.810\.730\.780\.750\.790\.680\.700\.76Cov@10↑\\uparrowVerbal Abstain1×1\\times0\.000\.030\.000\.030\.010\.030\.030\.190\.04Verbal Confidence1×1\\times0\.010\.000\.040\.150\.000\.010\.210\.170\.07Avg Entropy1×1\\times0\.020\.070\.020\.050\.090\.090\.000\.000\.04Max Entropy1×1\\times0\.020\.090\.020\.130\.110\.280\.000\.030\.08Avg NLL1×1\\times0\.020\.080\.020\.090\.080\.220\.000\.020\.06Max NLL1×1\\times0\.020\.090\.020\.050\.130\.220\.020\.020\.07Avg Entropy \(T=1\)2×2\\times0\.050\.040\.040\.060\.030\.040\.000\.000\.03Max Entropy \(T=1\)2×2\\times0\.030\.040\.060\.110\.050\.030\.000\.010\.04Avg NLL \(T=1\)2×2\\times0\.020\.040\.020\.050\.050\.050\.000\.000\.03Max NLL \(T=1\)2×2\\times0\.030\.020\.060\.120\.060\.110\.010\.010\.05Semantic Entropy \(N=10\)11×11\\times0\.070\.040\.020\.080\.070\.440\.120\.130\.12Semantic Entropy \(N=5\)6×6\\times0\.040\.060\.010\.150\.090\.350\.010\.020\.09VASE \(N=5\)6×6\\times0\.090\.040\.080\.180\.040\.310\.100\.100\.12VL\-Uncertainty \(N=10\)11×11\\times0\.050\.170\.060\.170\.150\.410\.020\.040\.13Cov@20↑\\uparrowVerbal Abstain1×1\\times0\.000\.030\.000\.030\.010\.350\.130\.840\.17Verbal Confidence1×1\\times0\.010\.210\.070\.280\.000\.010\.570\.940\.26Avg Entropy1×1\\times0\.020\.110\.080\.140\.160\.520\.000\.000\.13Max Entropy1×1\\times0\.020\.120\.080\.190\.160\.410\.060\.170\.15Avg NLL1×1\\times0\.020\.130\.080\.160\.130\.620\.080\.020\.15Max NLL1×1\\times0\.020\.120\.090\.120\.230\.460\.060\.020\.14Avg Entropy \(T=1\)2×2\\times0\.070\.040\.040\.130\.040\.180\.000\.000\.06Max Entropy \(T=1\)2×2\\times0\.060\.050\.090\.160\.070\.090\.000\.140\.08Avg NLL \(T=1\)2×2\\times0\.020\.040\.020\.140\.080\.170\.210\.080\.10Max NLL \(T=1\)2×2\\times0\.030\.050\.070\.140\.110\.130\.030\.040\.07Semantic Entropy \(N=10\)11×11\\times0\.150\.210\.170\.310\.250\.770\.350\.310\.31Semantic Entropy \(N=5\)6×6\\times0\.070\.080\.080\.390\.230\.620\.170\.310\.25VASE \(N=5\)6×6\\times0\.210\.160\.150\.400\.170\.750\.190\.410\.31VL\-Uncertainty \(N=10\)11×11\\times0\.190\.280\.240\.380\.330\.790\.080\.170\.31Cov@30↑\\uparrowVerbal Abstain1×1\\times0\.000\.200\.000\.400\.130\.900\.771\.000\.42Verbal Confidence1×1\\times0\.010\.320\.430\.620\.190\.590\.921\.000\.51Avg Entropy1×1\\times0\.120\.200\.090\.280\.180\.970\.310\.120\.28Max Entropy1×1\\times0\.120\.200\.120\.520\.230\.940\.210\.640\.37Avg NLL1×1\\times0\.120\.180\.090\.280\.170\.910\.240\.020\.25Max NLL1×1\\times0\.120\.170\.130\.220\.420\.940\.110\.210\.29Avg Entropy \(T=1\)2×2\\times0\.070\.040\.130\.310\.160\.880\.280\.420\.29Max Entropy \(T=1\)2×2\\times0\.120\.060\.160\.220\.100\.270\.130\.310\.17Avg NLL \(T=1\)2×2\\times0\.030\.110\.040\.420\.210\.650\.350\.350\.27Max NLL \(T=1\)2×2\\times0\.070\.060\.090\.180\.170\.210\.140\.150\.13Semantic Entropy \(N=10\)11×11\\times0\.280\.310\.380\.620\.460\.910\.670\.740\.55Semantic Entropy \(N=5\)6×6\\times0\.140\.270\.340\.620\.350\.890\.360\.710\.46VASE \(N=5\)6×6\\times0\.260\.460\.430\.640\.370\.970\.700\.780\.57VL\-Uncertainty \(N=10\)11×11\\times0\.290\.590\.440\.660\.560\.960\.520\.600\.58CHDA↑\\uparrowVerbal Abstain1×1\\times56\.153\.950\.660\.661\.175\.073\.377\.863\.5Verbal Confidence1×1\\times56\.162\.862\.866\.153\.956\.170\.667\.862\.0Avg Entropy1×1\\times70\.062\.851\.463\.346\.174\.453\.957\.259\.9Max Entropy1×1\\times70\.060\.654\.464\.455\.070\.045\.067\.160\.8Avg NLL1×1\\times70\.060\.653\.358\.350\.070\.659\.460\.960\.4Max NLL1×1\\times68\.362\.854\.456\.151\.758\.349\.461\.157\.8Avg Entropy \(T=1\)2×2\\times72\.258\.758\.963\.154\.450\.051\.165\.059\.2Max Entropy \(T=1\)2×2\\times73\.370\.058\.959\.461\.149\.452\.860\.360\.7Avg NLL \(T=1\)2×2\\times69\.460\.656\.763\.360\.049\.762\.264\.860\.8Max NLL \(T=1\)2×2\\times68\.361\.762\.860\.054\.446\.151\.757\.857\.8Semantic Entropy \(N=10\)11×11\\times70\.467\.270\.671\.145\.871\.166\.763\.965\.8Semantic Entropy \(N=5\)6×6\\times70\.467\.262\.870\.058\.364\.466\.267\.865\.9VASE \(N=5\)6×6\\times76\.170\.066\.175\.051\.175\.568\.970\.669\.2VL\-Uncertainty \(N=10\)11×11\\times76\.077\.268\.367\.258\.368\.966\.767\.868\.8

Table 14:Per\-model results on long\-form open\-ended benchmarkLLaVA\-Bench\. Semantic methods dominate decisively, with the largest gap to token\-level methods we observe in any benchmark; verbalized methods recover partially at the loosest coverage budget \(Cov@30\) but remain near random on AUROC, confirming that long\-form regimes require meaning\-level uncertainty signals\.![Refer to caption](https://arxiv.org/html/2609.22206v1/figs/qualitative/short_length_hallucination_blurred.png)Figure 3:Short\-form hallucinations correctly flagged by Max Entropy \(T=1\.0T\{=\}1\.0\)\. For each MLLM, bars show where the hallucinated response ranks \(uncertainty percentile\) under each method; Max Entropy \(T=1\.0T\{=\}1\.0\) consistently places it in the high\-uncertainty tail, while Semantic Entropy collapses to zero \(identical resamples\) and Verbal Abstain never fires\.![Refer to caption](https://arxiv.org/html/2609.22206v1/figs/qualitative/sentence_length_hallucination_blurred.png)Figure 4:Sentence\-length hallucinations correctly flagged by Verbal Abstain\. Models reliably emit “unknown” on FSVQA200 questions they get wrong \(100th percentile\), while token\-level and semantic signals are weaker and less consistent across MLLMs in this regime\.![Refer to caption](https://arxiv.org/html/2609.22206v1/figs/qualitative/long_form_hallucination_blurred.png)Figure 5:Long\-form hallucinations correctly flagged by Semantic Entropy\. Per\-token signals dilute across multi\-sentence responses \(Max Entropy in the low\-to\-mid percentiles\), and Verbal Abstain never fires once the model is instructed to produce a complete answer — leaving meaning\-level disagreement across resamples as the only reliable signal\.![Refer to caption](https://arxiv.org/html/2609.22206v1/figs/qualitative/short_form_hallucination_fail_blurred.png)Figure 6:Short\-form hallucinations*missed*by Max Entropy \(T=1\.0T\{=\}1\.0\)\. The regime’s best\-performing method assigns near\-zero uncertainty \(0th percentile\) to incorrect responses, while another family — typically Semantic Entropy or Verbal Abstain — catches them\. These cases make concrete the residual error behind Max Entropy’s sub\-perfect AUROC and suggest that family\-level signals remain partially complementary even within the regime where one family dominates on average\.![Refer to caption](https://arxiv.org/html/2609.22206v1/sentence_length_hallucination_fail.png)Figure 7:Sentence\-length hallucinations*missed*by Verbal Abstain\. The model commits confidently to a wrong answer without emitting “unknown,” while either Max Entropy \(T=1\.0T\{=\}1\.0\) or Semantic Entropy correctly places the response in the high\-uncertainty tail\. The dominant failure pattern is hallucinated specifics \(named entities, attributes, counts\) delivered fluently — the kind of error where abstention prompting offers no leverage\.![Refer to caption](https://arxiv.org/html/2609.22206v1/figs/qualitative/long_form_hallucination_fail_blurred.png)Figure 8:Long\-form hallucinations*missed*by Semantic Entropy\. The method produces non\-trivial uncertainty values but ranks the hallucinated response below other \(correct\) responses in the benchmark, while Verbal Abstain or Max Entropy \(T=1\.0T\{=\}1\.0\) places it in the high\-uncertainty tail\. These cases reflect the residual ranking error behind Semantic Entropy’s sub\-perfect AUROC \(0\.73 on LLaVA\-Bench\) and the “confidently wrong” failures driving the coverage gap in Section[4\.3\.3](https://arxiv.org/html/2609.22206#S4.SS3.SSS3)\.

### A\.2Qualitative Results

Figures[3](https://arxiv.org/html/2609.22206#A1.F3)–[5](https://arxiv.org/html/2609.22206#A1.F5)illustrate the regime\-dependent behavior summarized in Section[4\.3](https://arxiv.org/html/2609.22206#S4.SS3)on individual hallucinated examples, one per MLLM\. For each sample, we report the per\-benchmark uncertainty percentile assigned by each method \(higher = more uncertain\), with the method that successfully flags the hallucination highlighted\. The examples make the failure modes concrete: on short\-form questions \(Fig\.[3](https://arxiv.org/html/2609.22206#A1.F3)\), Max Entropy \(T=1\.0T\{=\}1\.0\) places the wrong answer in the high\-uncertainty tail while Semantic Entropy collapses to zero — repeated samples produce the same short string, yielding a single cluster — and Verbal Abstain rarely fires\. On sentence\-length FSVQA200 \(Fig\.[4](https://arxiv.org/html/2609.22206#A1.F4)\), the inverse pattern holds: models cleanly emit “unknown” on questions they get wrong, while token\-level and semantic scores remain mid\-range\. On long\-form generation \(Fig\.[5](https://arxiv.org/html/2609.22206#A1.F5)\), per\-token entropy is diluted across many tokens and the abstention option is suppressed by the instruction to produce a complete answer, leaving meaning\-level disagreement across resamples as the only signal that consistently separates correct from hallucinated responses\.

For transparency, we additionally include one failure case per regime \(Figures[6](https://arxiv.org/html/2609.22206#A1.F6)–[8](https://arxiv.org/html/2609.22206#A1.F8)\), where the regime’s best\-performing method scores a hallucinated response as low\-uncertainty\. These cases reflect the imperfect AUROC of even the strongest methods \(0\.67–0\.76\) and motivate the gap analysis in Section[4\.3\.3](https://arxiv.org/html/2609.22206#S4.SS3.SSS3)\.

### A\.3Licenses and Intended Use

All models and benchmarks used in this work are publicly released for research purposes\. InternVL2 and InternVL3\.5 are publicly released under the MIT License for their codebase, while their model weights are subject to the underlying Qwen and Apache 2\.0 licenses depending on the checkpoint\. Qwen2\-VL is released under Apache 2\.0 \(for the 2B and 7B variants\) and the Qwen license \(for the 72B variant\), while Qwen3\-VL is released under the Apache 2\.0 license\. ScienceQA \(CC BY\-NC\-SA 4\.0\), MMMU \(Apache 2\.0\), MM\-Vet \(code under Apache 2\.0; dataset under CC BY\-NC 4\.0\), FSVQA \(released for academic research use; derived from VQA and MS COCO and subject to their respective terms\), and LLaVA\-Bench \(Apache 2\.0\) are used in accordance with their respective licenses and intended use for academic research on multimodal reasoning and evaluation\. Any artifacts released as part of this work \(including the FSVQA200 sample IDs and evaluation code\) will be distributed under a permissive license such as MIT or CC BY 4\.0, excluding any third\-party benchmark content \(notably the non\-commercial ScienceQA and MM\-Vet data\), which remains subject to its original license\.