Verbalized Confidence in AI Models

• Verbalized Confidence (VC) is a metric that quantifies a model's self-assessed certainty by eliciting numeric or categorical estimates after answer generation.
• VC employs various prompting strategies, including chain-of-thought and zero-shot methods, and is evaluated using metrics like Expected Calibration Error and Brier Score.
• Hybrid approaches combining VC with agreement-based signals have demonstrated improved AUROC and reliability, especially in safety-critical and multimodal domains.

Verbalized Confidence (VC) is a model-generated, natural-language or numeric estimate of certainty, designed to quantify how likely a model believes its own output is correct. VC is central to the trustworthiness, interpretability, and practical reliability of modern LLMs and vision-LLMs (VLMs), serving as a lightweight, prompt- and model-agnostic uncertainty quantification approach. In its most common instantiation, VC is elicited by directly prompting the model—often after solution reasoning—to output a probability or score (e.g., 1–100, 0–1, discrete bin, or textual descriptor) that captures its subjective confidence. The fidelity, calibration, and behavioral correlates of VC have become defining benchmarks for model metacognition, reliability under chain-of-thought (CoT) reasoning, and deployment in safety-critical domains.

1. Definitions, Formalization, and Prompt Design

VC is operationalized as a scalar or categorical value, appended to or included with a model’s answer, representing the model’s self-assessed likelihood of correctness. In LLMs, this is typically:

• Numeric scale: e.g., $c \in [0,100]$ or $c \in [0,1]$. Elicited via prompts such as:

  “Give a confidence number from 1 to 100 that represents how confident you are in your final answer. Treat your final answer as fixed…” (Del et al., 19 Mar 2026) “Answer: <ANSWER>. Confidence: <CONFIDENCE SCORE>” (Yang et al., 2024)

• Categorical bins: e.g., “Almost certain (0.9–1.0)”, “Highly likely (0.8–0.9)”, or via letter/word scales (Yoon et al., 20 May 2025, Yang et al., 2024).

• Binary indicators: e.g., appending “certain”/“uncertain” or using a {0,1} flag (Ni et al., 2024, Ding et al., 26 Aug 2025).

Formally, for a question $q$, answer $a$, and VC $c$, the VC process is:

• Model outputs $a$ in response to $q$, then $c \sim \mathcal{M}(q, a, p)$, where $p$ is a confidence-specific prompt (Xia et al., 15 Jan 2026).
• VC is interpreted as an estimate of $P(\text{answer } a \text{ is correct} \mid q)$ (Seo et al., 13 Oct 2025).

Prompting strategies for VC vary, including zero-shot, few-shot (examples covering a range of confidences), explicit chain-of-thought preceding confidence elicitation, and advanced templates that describe task difficulty and uncertainty concepts (Yang et al., 2024). In multimodal VLM/VQA models, VC often appears in XML-tagged form (e.g., <confidence\>76%</confidence>) (Xuan et al., 26 May 2025, Wu et al., 17 Dec 2025).

2. Calibration Theory and Evaluation Metrics

A foundational requirement of VC is calibration: for any stated confidence $c$, the empirical proportion of correct responses among outputs labeled $c$ should match $c$. Several quantitative calibration metrics are standard:

• Expected Calibration Error (ECE):

$$\mathrm{ECE} = \sum_{m=1}^M \frac{|B_m|}{N} |\mathrm{acc}(B_m) - \mathrm{conf}(B_m)|$$

where $B_m$ is the set of instances with VC in bin $m$, $\mathrm{acc}(B_m)$ is empirical accuracy, and $\mathrm{conf}(B_m)$ is average confidence (Del et al., 19 Mar 2026, Yang et al., 2024, Zhao et al., 21 Apr 2025).

• Brier Score (BS):

$$\mathrm{BS} = \frac{1}{N}\sum_{i=1}^N (c_i - y_i)^2$$

with $y_i \in \{0,1\}$ the ground-truth label (Yoon et al., 20 May 2025).

• AUROC: Discriminative power, $$P(\mathrm{score}(\text{correct}) > \mathrm{score}(\text{incorrect}))$$, reflecting the VC’s ranking of correct versus incorrect answers (Del et al., 19 Mar 2026).
• Signal Detection Theory metrics: meta-d′ and metacognitive efficiency $M_\text{ratio}$ for scale variant studies (Dai, 10 Mar 2026).

Important caveats include heavy discretization of VC (e.g., overuse of round-number anchors), scale effects, and the instability of ECE when output distributions are sparse (Dai, 10 Mar 2026).

3. Elicitation Methodologies and Domain-Specific Behaviors

VC can be obtained:

• Direct black-box prompting: Elicits confidence post hoc, often after CoT reasoning. Low overhead, fully model-agnostic, does not require internal access to token probabilities (Del et al., 19 Mar 2026, Yang et al., 2024).
• Self-consistency / agreement-based methods: Bootstrap collective sample statistics and map to a VC (e.g., average over samples agreeing with majority answer) (Del et al., 19 Mar 2026).
• Chain-of-thought (CoT) integration: Slow thinking behaviors—such as verifying steps, backtracking, and explicitly reasoning about uncertainty—influence dynamically updated VC (Yoon et al., 20 May 2025).
• Multi-modal or vision-centric prompting: Models trained to interleave perception, structured reasoning, and verbalized confidence achieve superior calibration, particularly in vision-centric VLMs (Xuan et al., 26 May 2025, Wu et al., 17 Dec 2025).

Domain-specific scaling is prominent: mathematics and RLVR-trained domains exhibit stronger VC discrimination and more sustained AUROC gains with modest sampling ($K=2$ to 5), while STEM/humanities domains rapidly saturate (Del et al., 19 Mar 2026). Vision-based models with explicit stepwise visual reasoning exhibit lower ECE than text-centric baselines (Xuan et al., 26 May 2025).

4. Training Strategies for Calibrated VC

Several frameworks have been developed to enhance VC calibration and answer-groundedness:

• Contrastive and margin-based fine-tuning (ADVICE): Trains direct answer-dependent VC by maximizing Jensen-Shannon divergence and margin between correct/incorrect answers’ confidence distributions, leading to reduced overconfidence and faithful answer-conditioning (Seo et al., 13 Oct 2025).
• RL-based calibration (e.g., LoVeC, EmoCaliber GRPO): Uses policy optimization with calibration-driven reward (e.g., log-likelihood penalty, correctness/format/calibration on tokenized confidence) to align verbalized scores with factuality probability (Zhang et al., 29 May 2025, Wu et al., 17 Dec 2025).
• Self-critique and natural language critiques (CritiCal): Leverages critiques—generated either by the model itself or by a teacher—to semantically link reasoning quality to expressed confidence, offering out-of-distribution robustness and direct semantic calibration (Zong et al., 28 Oct 2025).
• Uncertainty Distillation: Trains models to express calibrated semantic confidence bins by distilling Monte Carlo semantic uncertainty estimates into verbalized tokens via supervised fine-tuning (Hager et al., 18 Mar 2025).
• Direct Confidence Alignment (DCA): Aligns verbalized confidence to internal token-probability confidence estimates using direct preference optimization, improving alignment for some architectures (e.g., Gemma-2-9B) (Zhang et al., 12 Dec 2025).
• Semantic perturbation for object-level calibration in VLMs (CSP): Perturbs key object regions with controlled noise and trains VLMs to emit VC scores reflecting visual ambiguity, augmenting calibration at the object answer level (Zhao et al., 21 Apr 2025).

Empirical findings indicate large calibration gains using these methods, with ECE dropping from typical 0.1–0.4 (uncalibrated) to as low as 0.025 (RL-optimized or answer-dependent frameworks) (Seo et al., 13 Oct 2025, Zhang et al., 29 May 2025, Wu et al., 17 Dec 2025).

5. Failure Modes, Content Groundness, and Limitations

The reliability of VC is compromised by several key limitations:

• Superficial mimicry: Models may ground VC in lexically generic expressions of certainty (“confidence,” “sure”) rather than content-relevant evidence, as diagnosed by retrieval and gradient-influence analysis (“content groundness”; $\mathrm{ccr}$) (Xia et al., 15 Jan 2026).
• Answer-independence: Off-the-shelf LLMs often produce confidence scores negligibly influenced by their own answers, yielding systemic overconfidence; ADVICE directly reduces this effect (Seo et al., 13 Oct 2025).
• Heavy discretization and round-number bias: Nearly all models over-concentrate VC on a small set of anchor scores (90, 95, 100), reducing the informativeness and granularity of the output; scale manipulation (0–20) can ameliorate this (Dai, 10 Mar 2026).
• Overconfidence under binary or coarse prompting: Use of “certain/uncertain” or scaled binarized VC strongly raises false confidence rates, especially in common and within-domain questions, with weaker correlation to internal probabilistic measures (Ni et al., 2024, Ding et al., 26 Aug 2025).
• Reasoning/cross-domain calibration tax: Reasoning-specific training sharply improves VC calibration in reasoning domains while often degrading it in factual-out-of-domain settings, an instance of a “calibration tax” as models lose knowledge-boundary sensitivity (Zeng et al., 9 Apr 2025).
• Limited generalization and subjectivity: Calibration typically targets objective tasks; VC in subjective or open-ended domains (e.g., emotion classification) requires additional semantic and reasoning priors (Wu et al., 17 Dec 2025).

6. Complementarity and Hybrid Uncertainty Estimation

Recent studies show that combining VC with other black-box uncertainty signals (self-consistency/agreement) yields greater discriminative power than either approach alone (Del et al., 19 Mar 2026). In particular, for chain-of-thought reasoning:

• The hybrid estimator

$$\mathrm{SCVC} = 0.5\,\mathrm{SC} + 0.5\,\mathrm{VC}$$

yields large AUROC gains; with as few as two samples, SCVC outperforms 8-sample VC or SC alone.

• Complementarity is strongest in mathematics domains (RLVR-optimized), where correlation between SC and VC is initially low but increases with more samples, indicating their distinct, synergistic contributions.
• Static agreement signals tend to be coarse and improve with larger sample budgets, whereas VC offers finer initial discrimination and more domain-stable scaling (Del et al., 19 Mar 2026).

7. Model Behavior, Mechanistic Insights, and Practical Recommendations

Recent mechanistic analyses reveal that LLMs compute VC via internal “cached” representations at answer-adjacent positions, not as mere fluency readouts or just-in-time calculations. These representations encode second-order answer-quality information beyond token probabilities, as shown by activation steering, patching, attention-blocking, and variance partitioning (Kumaran et al., 18 Mar 2026). VC thus reflects a sophisticated, automatic, metacognitive self-evaluation process.

Key recommendations for practitioners:

• Prefer explicit VC elicitation and hybrid combinations with agreement-based signals.
• Use at least two samples and simple averaging/hybridization for efficient uncertainty calibration.
• Calibrate and interpret VC with care; inspect output distributional properties and domain dependence, especially regarding scale discretization and boundary compression (Dai, 10 Mar 2026).
• For high-stakes applications, prefer answer-dependent, answer-grounded, or RL-calibrated VC frameworks, and supplement black-box VC with content-groundness audits as in TracVC (Xia et al., 15 Jan 2026).
• In vision-language and multimodal settings, employ modality-specific chain-of-thought reasoning, semantic perturbation, or multi-stage confidence-aware prompting to improve reliability (Xuan et al., 26 May 2025, Zhao et al., 21 Apr 2025, Wu et al., 17 Dec 2025).
• Treat the confidence scale and prompting template as critical experimental design variables; report meta-d′ and output distribution diagnostics in addition to ECE (Dai, 10 Mar 2026).

Together, these advances establish VC not only as a central concept for uncertainty quantification in LLMs and VLMs, but also as a window into model self-evaluation and alignment with human standards of trust and reliability.