# Are Large Language Models More Honest in Their Probabilistic or Verbalized Confidence?

arXiv: https://arxiv.org/abs/2408.09773 · HTML: https://mlsanity.com/paper/2408.09773/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 24 references that are in the map.
- First posted on arXiv 19 Aug 2024.

## Builds on (most cited first, 21 of 21)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [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)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Calibration of Pre-trained Transformers](https://mlsanity.com/paper/2003.07892/) (2020)
- [Prompting GPT-3 To Be Reliable](https://mlsanity.com/paper/2210.09150/) (2022)
- [Do Large Language Models Know What They Don't Know?](https://mlsanity.com/paper/2305.18153/) (2023)
- [Alignment for Honesty](https://mlsanity.com/paper/2312.07000/) (2023)
- [When Do LLMs Need Retrieval Augmentation? Mitigating LLMs' Overconfidence Helps Retrieval Augmentation](https://mlsanity.com/paper/2402.11457/) (2024)
- [Benchmarking Knowledge Boundary for Large Language Models: A Different Perspective on Model Evaluation](https://mlsanity.com/paper/2402.11493/) (2024)
- [Reformatted Alignment](https://mlsanity.com/paper/2402.12219/) (2024)
- [A Comparative Study of Training Objectives for Clarification Facet Generation](https://mlsanity.com/paper/2310.00703/) (2023)

## Built on by (most cited first, 23 of 23)

- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Towards Fully Exploiting LLM Internal States to Enhance Knowledge Boundary Perception](https://mlsanity.com/paper/2502.11677/) (2025)
- [Investigating the Impact of Quantization Methods on the Safety and Reliability of Large Language Models](https://mlsanity.com/paper/2502.15799/) (2025)
- [MetaFaith: Faithful Natural Language Uncertainty Expression in LLMs](https://mlsanity.com/paper/2505.24858/) (2025)
- [Anthropomimetic Uncertainty: What Verbalized Uncertainty in Language Models is Missing](https://mlsanity.com/paper/2507.10587/) (2025)
- [Read Your Own Mind: Reasoning Helps Surface Self-Confidence Signals in LLMs](https://mlsanity.com/paper/2505.23845/) (2025)
- [Do Large Language Models Know What They Are Capable Of?](https://mlsanity.com/paper/2512.24661/) (2025)
- [Focusing by Contrastive Attention: Enhancing VLMs' Visual Reasoning](https://mlsanity.com/paper/2509.06461/) (2025)
- [Line of Duty: Evaluating LLM Self-Knowledge via Consistency in Feasibility Boundaries](https://mlsanity.com/paper/2503.11256/) (2025)
- [Popular but Wrong: Understanding and Mitigating LLM Overconfidence through Knowledge Popularity](https://mlsanity.com/paper/2505.17537/) (2025)
- [Same Answer, Different Confidence: Protocol Sensitivity in LLM Confidence Calibration](https://mlsanity.com/paper/2605.27752/) (2026)
- [Do LVLMs Know What They Know? A Systematic Study of Knowledge Boundary Perception in LVLMs](https://mlsanity.com/paper/2508.19111/) (2025)
- [LLM Performance Predictors: Learning When to Escalate in Hybrid Human-AI Moderation Systems](https://mlsanity.com/paper/2601.07006/) (2026)
- [Influential Training Data Retrieval for Explaining Verbalized Confidence of LLMs](https://mlsanity.com/paper/2601.10645/) (2026)
- [Towards Harmonized Uncertainty Estimation for Large Language Models](https://mlsanity.com/paper/2505.19073/) (2025)
- [Annotation-Efficient Universal Honesty Alignment](https://mlsanity.com/paper/2510.17509/) (2025)
- [Calibration Is Not Enough: Evaluating Confidence Estimation Under Language Variations](https://mlsanity.com/paper/2601.08064/) (2026)
- [Direct Confidence Alignment: Aligning Verbalized Confidence with Internal Confidence In Large Language Models](https://mlsanity.com/paper/2512.11998/) (2025)
- [Speaking in Self-Assessing Tongues: On the Verbalized Confidence of LLMs in Machine Translation](https://mlsanity.com/paper/2606.17234/) (2026)
- [Toward Better Generalisation in Uncertainty Estimators: Leveraging Data-Agnostic Features](https://mlsanity.com/paper/2507.03998/) (2025)
- [Beyond Semantic Equivalence: Logical Graphs for LLM Uncertainty Quantification](https://mlsanity.com/paper/2607.16868/) (2026)
- [Can You Trust the Confidence? ConfBench for Vision-Language Models on Document Extraction](https://mlsanity.com/paper/2608.01792/) (2026)
- [On the Pitfalls of Verbalized Confidence Priors for Calibrating Large Reasoning Models](https://mlsanity.com/paper/2609.32470/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have been found to produce hallucinations when the question exceeds their internal knowledge boundaries. A reliable model should have a clear perception of its knowledge boundaries, providing correct answers within its scope and refusing to answer when it lacks knowledge. Existing research on LLMs' perception of their knowledge boundaries typically uses either the probability of the generated tokens or the verbalized confidence as the model's confidence in its response. However, these studies overlook the differences and connections between the two. In this paper, we conduct a comprehensive analysis and comparison of LLMs' probabilistic perception and verbalized perception of their factual knowledge boundaries. First, we investigate the pros and cons of these two perceptions. Then, we study how they change under questions of varying frequencies. Finally, we measure the correlation between LLMs' probabilistic confidence and verbalized confidence. Experimental results show that 1) LLMs' probabilistic perception is generally more accurate than verbalized perception but requires an in-domain validation set to adjust the confidence threshold. 2) Both perceptions perform better on less frequent questions. 3) It is challenging for LLMs to accurately express their internal confidence in natural language.