# ConfTuner: Training Large Language Models to Express Their Confidence Verbally

arXiv: https://arxiv.org/abs/2508.18847 · HTML: https://mlsanity.com/paper/2508.18847/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 27 of 27)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (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)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [MediQ: Question-Asking LLMs and a Benchmark for Reliable Interactive Clinical Reasoning](https://mlsanity.com/paper/2406.00922/) (2024)
- [SaySelf: Teaching LLMs to Express Confidence with Self-Reflective Rationales](https://mlsanity.com/paper/2405.20974/) (2024)
- [A Comprehensive Survey of Hallucination in Large Language, Image, Video and Audio Foundation Models](https://mlsanity.com/paper/2405.09589/) (2024)
- [Large Language Models Must Be Taught to Know What They Don't Know](https://mlsanity.com/paper/2406.08391/) (2024)
- [Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration](https://mlsanity.com/paper/2102.12182/) (2021)
- [When Does Optimizing a Proper Loss Yield Calibration?](https://mlsanity.com/paper/2305.18764/) (2023)
- [Multi-Class Uncertainty Calibration via Mutual Information Maximization-based Binning](https://mlsanity.com/paper/2006.13092/) (2020)
- [As Confidence Aligns: Exploring the Effect of AI Confidence on Human Self-confidence in Human-AI Decision Making](https://mlsanity.com/paper/2501.12868/) (2025)
- [A Survey on LLM Inference-Time Self-Improvement](https://mlsanity.com/paper/2412.14352/) (2024)
- [LACIE: Listener-Aware Finetuning for Confidence Calibration in Large Language Models](https://mlsanity.com/paper/2405.21028/) (2024)
- [Scoring Rules and Calibration for Imprecise Probabilities](https://mlsanity.com/paper/2410.23001/) (2024)

## Built on by (most cited first, 30 of 39)

- [Trace Length is a Simple Uncertainty Signal in Reasoning Models](https://mlsanity.com/paper/2510.10409/) (2025)
- [Just-In-Time Reinforcement Learning: Continual Learning in LLM Agents Without Gradient Updates](https://mlsanity.com/paper/2601.18510/) (2026)
- [ADVICE: Answer-Dependent Verbalized Confidence Estimation](https://mlsanity.com/paper/2510.10913/) (2025)
- [Calibrating LLM Judges: Linear Probes for Fast and Reliable Uncertainty Estimation](https://mlsanity.com/paper/2512.22245/) (2025)
- [Closing the Confidence-Faithfulness Gap in Large Language Models](https://mlsanity.com/paper/2603.25052/) (2026)
- [Open-Jev Judgments on CallScreenBench: Calibrated One-Pass Scam Screening with a Small Language Model](https://mlsanity.com/paper/2609.23959/) (2026)
- [Teaching Language Models to Faithfully Express their Uncertainty](https://mlsanity.com/paper/2510.12587/) (2025)
- [On Calibration of Large Language Models: From Response To Capability](https://mlsanity.com/paper/2602.13540/) (2026)
- [NOVA: NOise-aware Verbal Confidence CAlibration for Robust Large Language Models in RAG Systems](https://mlsanity.com/paper/2601.11004/) (2026)
- [Generalized Correctness Models: Learning Calibrated and Model-Agnostic Correctness Predictors from Historical Patterns](https://mlsanity.com/paper/2509.24988/) (2025)
- [Verbalizing LLM's Higher-order Uncertainty via Imprecise Probabilities](https://mlsanity.com/paper/2603.10396/) (2026)
- [I-CALM: Incentivizing Confidence-Aware Abstention for LLM Selective Answering](https://mlsanity.com/paper/2604.03904/) (2026)
- [CritiCal: Can Critique Help LLM Uncertainty or Confidence Calibration?](https://mlsanity.com/paper/2510.24505/) (2025)
- [ORCE: Order-Aware Alignment of Verbalized Confidence in Large Language Models](https://mlsanity.com/paper/2605.12446/) (2026)
- [Aligning LLMs with Human Uncertainty: A Beta-Bernoulli Calibrator for LLM Forecasting](https://mlsanity.com/paper/2605.27668/) (2026)
- [Just how sure are you? Improving Verbalized Uncertainty Calibration in Medical VQA](https://mlsanity.com/paper/2606.27023/) (2026)
- [Process Supervision of Confidence Margin for Calibrated LLM Reasoning](https://mlsanity.com/paper/2604.23333/) (2026)
- [Quantifying Faithful Confidence Expression in Large Reasoning Models](https://mlsanity.com/paper/2606.03969/) (2026)
- [Unlocking the Pre-Trained Model as a Dual-Alignment Calibrator for Post-Trained LLMs](https://mlsanity.com/paper/2601.04277/) (2026)
- [Confidence Should Be Calibrated More Than One Turn Deep](https://mlsanity.com/paper/2604.05397/) (2026)
- [When Does Visual Token Pruning Improve Calibration? The Role of Evidence Coverage in MLLMs](https://mlsanity.com/paper/2604.12035/) (2026)
- [Calibrating LLMs with Semantic-level Reward](https://mlsanity.com/paper/2605.15588/) (2026)
- [Confidence Calibration in Large Language Models](https://mlsanity.com/paper/2605.23909/) (2026)
- [CALIBER: Calibrating Confidence Before and After Reasoning in Language Models](https://mlsanity.com/paper/2606.24281/) (2026)
- [CoMet: Context and Multiplicity Decomposition for Multimodal Uncertainty Estimation](https://mlsanity.com/paper/2606.32012/) (2026)
- [Confident at the moment of action: belief miscalibration in LLM play under hidden information](https://mlsanity.com/paper/2608.24691/) (2026)
- [Logical Consistency as a Bridge: Improving LLM Hallucination Detection via Label Constraint Modeling between Responses and Self-Judgments](https://mlsanity.com/paper/2605.03971/) (2026)
- [From Critic to Confidence: PPO for Language-Based Quantitative Prediction with Confidence Estimation](https://mlsanity.com/paper/2607.12687/) (2026)
- [From token probabilities to calibrated confidence: An empirical study of mathematical question answering](https://mlsanity.com/paper/2608.07827/) (2026)
- [RadFusion: Towards Threshold-Controllable Radiology Report Generation](https://mlsanity.com/paper/2608.10505/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) are increasingly deployed in high-stakes domains such as science, law, and healthcare, where accurate expressions of uncertainty are essential for reliability and trust. However, current LLMs are often observed to generate incorrect answers with high confidence, a phenomenon known as "overconfidence". Recent efforts have focused on calibrating LLMs' verbalized confidence: i.e., their expressions of confidence in text form, such as "I am 80% confident that...". Existing approaches either rely on prompt engineering or fine-tuning with heuristically generated uncertainty estimates, both of which have limited effectiveness and generalizability. Motivated by the notion of proper scoring rules for calibration in classical machine learning models, we introduce ConfTuner, a simple and efficient fine-tuning method that introduces minimal overhead and does not require ground-truth confidence scores or proxy confidence estimates. ConfTuner relies on a new loss function, tokenized Brier score, which we theoretically prove to be a proper scoring rule, intuitively meaning that it "correctly incentivizes the model to report its true probability of being correct". ConfTuner improves calibration across diverse reasoning tasks and generalizes to black-box models such as GPT-4o. Our results further show that better-calibrated confidence enables downstream gains in self-correction and model cascade, advancing the development of trustworthy LLM systems. The code is available at https://github.com/liushiliushi/ConfTuner.