Calibrating Verbalized Confidence with Self-Generated Distractors (2509.25532v1)

Abstract: Calibrated confidence estimates are necessary for LLM outputs to be trusted by human users. While LLMs can express their confidence in human-interpretable ways, verbalized LLM-generated confidence scores have empirically been found to be miscalibrated, reporting high confidence on instances with low accuracy and thereby harming trust and safety. We hypothesize that this overconfidence often stems from a given LLM's heightened suggestibility when faced with claims that it encodes little information about; we empirically validate this hypothesis, finding more suggestibility on lower-accuracy claims. Building on this finding, we introduce Distractor-Normalized Coherence (DINCO), which estimates and accounts for an LLM's suggestibility bias by having the model verbalize its confidence independently across several self-generated distractors (i.e. alternative claims), and normalizes by the total verbalized confidence. To further improve calibration, we leverage generator-validator disagreement, augmenting normalized validator confidence with a consistency-based estimate of generator confidence. Here, we frame the popular approach of self-consistency as leveraging coherence across sampled generations, and normalized verbalized confidence as leveraging coherence across validations on incompatible claims, allowing us to integrate these complementary dimensions of coherence into DINCO. Moreover, our analysis shows that DINCO provides less saturated -- and therefore more usable -- confidence estimates, and that further sampling alone cannot close the gap between DINCO and baselines, with DINCO at 10 inference calls outperforming self-consistency at 100.

• The paper introduces DiNCo, a method that normalizes verbalized LLM confidence using self-generated distractors to counteract overconfidence.
• It leverages independent distractor generation and self-consistency integration to yield finer, less saturated confidence estimates.
• Empirical evaluations on TriviaQA, SimpleQA, and FActScore show significant reduction in Expected Calibration Error and enhanced inference efficiency.

Calibrating Verbalized Confidence in LLMs via Self-Generated Distractors

Motivation and Problem Statement

LLMs are increasingly deployed in decision-critical contexts, necessitating reliable confidence estimates for their outputs. While LLMs can verbalize their confidence in human-interpretable formats, empirical evidence demonstrates that these verbalized confidence scores are often miscalibrated, exhibiting overconfidence and confidence saturation—where most scores cluster at high values, reducing their informativeness. The paper hypothesizes that this overconfidence is rooted in LLM suggestibility: when presented with claims about topics for which the model has limited knowledge, it tends to report high confidence regardless of actual correctness. This phenomenon is validated empirically, showing increased suggestibility on low-accuracy claims.

DiNCo: Distractor-Normalized Coherence

To address these calibration failures, the paper introduces DiNCo (Distractor-Normalized Coherence), a method that normalizes verbalized confidence by leveraging self-generated distractors—alternative claims produced by the LLM itself. The core idea is that if the model assigns high confidence to multiple mutually exclusive claims, its confidence in any single claim should be discounted. DiNCo operationalizes this by:

1. Distractor Generation: For each main claim, the LLM generates several plausible distractors using beam search or direct prompting, ensuring minimal pairwise differences to encourage mutual exclusivity.
2. Independent Confidence Elicitation: The model is prompted to verbalize its confidence for each distractor independently.
3. Normalization: The main claim's confidence is divided by the sum of confidences assigned to all distractors, weighted by uniqueness and counterfactuality, as determined by an NLI model.

This process is illustrated in the following figure:

Figure 1: DiNCo normalizes the main claim's verbalized confidence by the sum of distractor confidences, weighted for uniqueness and counterfactuality.

The normalization factor $\beta$ is computed as the sum of verbalized confidences over the distractor set, adjusted for redundancy and logical relationships. This approach corrects for suggestibility-induced bias and produces less saturated, more granular confidence estimates.

Integration with Self-Consistency

DiNCo further augments calibration by integrating self-consistency—a method that estimates confidence based on the frequency of a claim's generation across multiple samples. The final DiNCo confidence is a weighted average of normalized verbalized confidence and self-consistency, capturing coherence both within validation (verbalized confidence) and generation (self-consistency). This dual-axis approach leverages generator-validator disagreement, a documented source of inconsistency in LLM outputs.

Empirical Evaluation

DiNCo is evaluated on both short-form (TriviaQA, SimpleQA) and long-form (FActScore) QA tasks, using open-source and frontier models (Qwen3-8B, Llama-3.2-3B-Instruct, Gemma-3-4B-IT, GPT-4.1, Gemini-2.5-Flash). Calibration is assessed via Expected Calibration Error (ECE), Brier Score (BS), and Area Under the ROC Curve (AUC).

Figure 2: Calibration metrics for Qwen3-8B on TriviaQA. DiNCo relieves confidence saturation and improves calibration compared to vanilla verbalized confidence.

Key results include:

• Short-form QA: DiNCo outperforms the best baseline (self-consistency) by an average ECE margin of 0.099 on TriviaQA and 0.092 on SimpleQA. DiNCo achieves superior granularity, ranking positives above negatives even when verbalized confidence is saturated at 1.
• Long-form QA: On FActScore, DiNCo improves Pearson and Spearman correlation with passage-level factuality by 0.072 and 0.074, respectively, over the best baseline.
• Inference Efficiency: DiNCo at 10 inference calls outperforms self-consistency at 100, demonstrating that further sampling alone cannot close the calibration gap.
• Saturation Analysis: DiNCo produces substantially more distinct confidence scores, alleviating saturation and enabling more usable confidence estimates.

Implementation Details

Distractor Generation

• Beam Search: For models with logit access, beam search is used to efficiently sample diverse, high-probability distractors.
• Black-box Setting: For API-access models without logit access, direct prompting is used to elicit distractors.
• Redundancy Handling: An NLI model (DeBERTa-v3-base-mnli-fever-anli) quantifies entailment and contradiction, downweighting redundant distractors.

Confidence Normalization

Given a main claim $c_0$ and distractor set $C$, the normalized confidence is:

$$f^{\rm NVC}(c_0) = \frac{f^{\rm VC}(c_0)}{\beta(C)}$$

where

$$\beta(C) = \max\left(1, f^{\rm VC}(c_0) + \sum_{c \in C} f^{\rm VC}(c) \cdot w_{\rm unique}(c) \cdot w_{\rm contra}(c)\right)$$

$w_{\rm unique}$ and $w_{\rm contra}$ are weights for uniqueness and counterfactuality, respectively.

Self-Consistency Integration

Self-consistency confidence is computed as the proportion of sampled generations matching the main claim, with semantic equivalence determined via NLI. DiNCo combines both axes:

$$f^{DiNCo}(c) = \frac{1}{2} f^{\rm SC}(c) + \frac{1}{2} f^{\rm NVC}(c)$$

Resource Requirements

• Inference Budget: DiNCo is designed for efficiency, typically using 5 distractors and 5 self-consistency samples per instance.
• NLI Model: Access to an off-the-shelf NLI model is required for redundancy handling, but this is a minimal departure from zero-resource settings.

Deployment Considerations

• Open- and Closed-Source Models: DiNCo is applicable to both, with adaptations for logit access.
• Short- and Long-form Tasks: The method generalizes across QA formats, including claim-level calibration in long-form generation.

Theoretical and Practical Implications

DiNCo advances the state of confidence calibration in LLMs by explicitly correcting for suggestibility and leveraging incoherence across related claims. The method demonstrates that independent elicitation and normalization of verbalized confidence, combined with self-consistency, yields superior calibration and more actionable confidence estimates. This has direct implications for the deployment of LLMs in safety-critical and decision-support systems, where reliable uncertainty quantification is essential.

Theoretically, the work connects LLM calibration failures to human-like suggestibility and probabilistic incoherence, suggesting avenues for further research in rationality and belief revision in neural models. The integration of NLI-based redundancy handling and dual-axis coherence estimation may inform future architectures for uncertainty quantification.

Future Directions

Potential extensions include:

• Adaptive Distractor Generation: Dynamic selection of distractor set size based on model uncertainty.
• Fine-grained Calibration: Application to multi-hop reasoning and complex generation tasks.
• End-to-End Training: Incorporation of DiNCo principles into model training objectives for improved native calibration.
• Human-AI Collaboration: Leveraging calibrated confidence for interactive systems and agentic frameworks.

Conclusion

DiNCo provides a robust, zero-resource method for calibrating verbalized confidence in LLMs by normalizing over self-generated distractors and integrating self-consistency. It achieves strong empirical results across diverse models and tasks, mitigates confidence saturation, and offers a principled approach to correcting suggestibility-induced bias. The method is practical, efficient, and broadly applicable, representing a significant step toward trustworthy LLM deployment.