# Calibrating Verbalized Confidence with Self-Generated Distractors

arXiv: https://arxiv.org/abs/2509.25532 · HTML: https://mlsanity.com/paper/2509.25532/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Self-rewarding alignment and self-training, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 44 of its 60 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-rewarding alignment and self-training](https://mlsanity.com/synth/self-rewarding-alignment-and-self-training/)

## Builds on (most cited first, 30 of 44)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [Measuring short-form factuality in large language models](https://mlsanity.com/paper/2411.04368/) (2024)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [Fine-tuning Language Models for Factuality](https://mlsanity.com/paper/2311.08401/) (2023)
- [Don't Hallucinate, Abstain: Identifying LLM Knowledge Gaps via Multi-LLM Collaboration](https://mlsanity.com/paper/2402.00367/) (2024)
- [Maieutic Prompting: Logically Consistent Reasoning with Recursive Explanations](https://mlsanity.com/paper/2205.11822/) (2022)
- [LM-Polygraph: Uncertainty Estimation for Language Models](https://mlsanity.com/paper/2311.07383/) (2023)
- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [To Believe or Not to Believe Your LLM](https://mlsanity.com/paper/2406.02543/) (2024)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Taming Overconfidence in LLMs: Reward Calibration in RLHF](https://mlsanity.com/paper/2410.09724/) (2024)
- [What Large Language Models Know and What People Think They Know](https://mlsanity.com/paper/2401.13835/) (2024)
- [The Generative AI Paradox: "What It Can Create, It May Not Understand"](https://mlsanity.com/paper/2311.00059/) (2023)
- [LUQ: Long-text Uncertainty Quantification for LLMs](https://mlsanity.com/paper/2403.20279/) (2024)
- [Are You Sure? Challenging LLMs Leads to Performance Drops in The FlipFlop Experiment](https://mlsanity.com/paper/2311.08596/) (2023)

## Built on by (most cited first, 14 of 14)

- [SWAY: A Counterfactual Computational Linguistic Approach to Measuring and Mitigating Sycophancy](https://mlsanity.com/paper/2604.02423/) (2026)
- [Verbalizing LLM's Higher-order Uncertainty via Imprecise Probabilities](https://mlsanity.com/paper/2603.10396/) (2026)
- [Beyond Consensus: Trace-Level Synthesis in Mixture of Agents](https://mlsanity.com/paper/2605.29116/) (2026)
- [Verbal Confidence Saturation in 3-9B Open-Weight Instruction-Tuned LLMs: A Pre-Registered Psychometric Validity Screen](https://mlsanity.com/paper/2604.22215/) (2026)
- [Process Supervision of Confidence Margin for Calibrated LLM Reasoning](https://mlsanity.com/paper/2604.23333/) (2026)
- [A Systematic Evaluation of Black-Box Uncertainty Estimation Methods for Large Language Models](https://mlsanity.com/paper/2606.19868/) (2026)
- [CalVerT: Augmenting Agents with Calibrated Verifier Telemetry Improves Action and Learning in Knowledge-Intensive Tasks](https://mlsanity.com/paper/2606.21777/) (2026)
- [Confident at the moment of action: belief miscalibration in LLM play under hidden information](https://mlsanity.com/paper/2608.24691/) (2026)
- [Distilling Self-Consistency into Verbal Confidence: A Pre-Registered Negative Result and Post-Hoc Rescue on Gemma 3 4B](https://mlsanity.com/paper/2604.24070/) (2026)
- [DirEAG: Dirichlet Evidence Aggregation for Calibrating Verbalized Confidence in Mathematical Reasoning](https://mlsanity.com/paper/2608.20717/) (2026)
- [Calibrating Small Language Models for Claim Check-Worthiness Detection](https://mlsanity.com/paper/2608.30731/) (2026)
- [Replication Without Persistence in Hosted LLMs: Measurement Sensitivity in Action-Time Belief Evaluation](https://mlsanity.com/paper/2609.22478/) (2026)
- [On the Pitfalls of Verbalized Confidence Priors for Calibrating Large Reasoning Models](https://mlsanity.com/paper/2609.32470/) (2026)
- [Evaluating Persistent Calibration under Evolving Model Knowledge](https://mlsanity.com/paper/2609.38797/) (2026)

## Abstract (arXiv)

Calibrated confidence estimates are necessary for large language model (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.