# Verbalized and Internal Probabilities Are Coupled in Large Language Models

arXiv: https://arxiv.org/abs/2610.00827 · HTML: https://mlsanity.com/paper/2610.00827/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 32 references that are in the map.
- First posted on arXiv 30 Sep 2026.

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

- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [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)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [Reducing conversational agents' overconfidence through linguistic calibration](https://mlsanity.com/paper/2012.14983/) (2020)
- [What Can We Learn from Collective Human Opinions on Natural Language Inference Data?](https://mlsanity.com/paper/2010.03532/) (2020)
- [LM-Polygraph: Uncertainty Estimation for Language Models](https://mlsanity.com/paper/2311.07383/) (2023)
- [LLM Processes: Numerical Predictive Distributions Conditioned on Natural Language](https://mlsanity.com/paper/2405.12856/) (2024)
- [Calibrating Verbal Uncertainty as a Linear Feature to Reduce Hallucinations](https://mlsanity.com/paper/2503.14477/) (2025)
- [When Does Optimizing a Proper Loss Yield Calibration?](https://mlsanity.com/paper/2305.18764/) (2023)
- [Confidence Under the Hood: An Investigation into the Confidence-Probability Alignment in Large Language Models](https://mlsanity.com/paper/2405.16282/) (2024)
- [How do LLMs Compute Verbal Confidence](https://mlsanity.com/paper/2603.17839/) (2026)
- [BED-LLM: Intelligent Information Gathering with LLMs and Bayesian Experimental Design](https://mlsanity.com/paper/2508.21184/) (2025)
- [Do Language Models Mirror Human Confidence? Exploring Psychological Insights to Address Overconfidence in LLMs](https://mlsanity.com/paper/2506.00582/) (2025)
- [Trained on Tokens, Calibrated on Concepts: The Emergence of Semantic Calibration in LLMs](https://mlsanity.com/paper/2511.04869/) (2025)
- [Influential Training Data Retrieval for Explaining Verbalized Confidence of LLMs](https://mlsanity.com/paper/2601.10645/) (2026)
- [LLMs Exhibit Significantly Lower Uncertainty in Creative Writing Than Professional Writers](https://mlsanity.com/paper/2602.16162/) (2026)
- [Uncertainty Propagation in LLM-Based Systems](https://mlsanity.com/paper/2604.23505/) (2026)
- [Interactive Model with Structural Loss for Language-based Abductive Reasoning](https://mlsanity.com/paper/2112.00284/) (2021)
- [When Linguistic and Internal Confidence Diverge in Large Language Models](https://mlsanity.com/paper/2608.28382/) (2026)
- [Direct Confidence Alignment: Aligning Verbalized Confidence with Internal Confidence In Large Language Models](https://mlsanity.com/paper/2512.11998/) (2025)

## Abstract (arXiv)

Large language models carry an internal notion of uncertainty in their sampling distribution, i.e., the probabilities they place on generating one answer rather than another. They can also be asked to state a confidence, in words or as a number: a verbalized uncertainty. Prior work suggests that internal probabilities track relative frequencies in the training data, and that verbalized probabilities track explicit probabilistic assertions in the training data. However, we do not know whether these two readouts are aligned, except when frequencies and probabilistic assertions in the training data happen to align. This limits our understanding of when we can use verbalized uncertainties as a proxy for either training data frequencies, or a model's internal distribution. We resolve this gap by systematically exploring how LLMs probability readouts are impacted by training and in-context data, via intervening on the underlying uncertainty sources in the data. We find that both internal and verbalized probability readouts are impacted by both distributional and asserted uncertainty in the training data. Further, we find that verbalized and internal probabilities are aligned beyond what would be expected by independently tracking the same uncertainty sources, suggesting that verbalized probabilities can be used to probe a model's internal distribution.