# Uncertainty Distillation: Teaching Language Models to Express Semantic Confidence

arXiv: https://arxiv.org/abs/2503.14749 · HTML: https://mlsanity.com/paper/2503.14749/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 38 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 29 of 29)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [mT5: A massively multilingual pre-trained text-to-text transformer](https://mlsanity.com/paper/2010.11934/) (2020)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Super-NaturalInstructions: Generalization via Declarative Instructions on 1600+ NLP Tasks](https://mlsanity.com/paper/2204.07705/) (2022)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Quantifying Language Models' Sensitivity to Spurious Features in Prompt Design or: How I learned to start worrying about prompt formatting](https://mlsanity.com/paper/2310.11324/) (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)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Hallucination of Multimodal Large Language Models: A Survey](https://mlsanity.com/paper/2404.18930/) (2024)
- [Pretrained Transformers Improve Out-of-Distribution Robustness](https://mlsanity.com/paper/2004.06100/) (2020)
- [A Long Way to Go: Investigating Length Correlations in RLHF](https://mlsanity.com/paper/2310.03716/) (2023)
- [Reducing conversational agents' overconfidence through linguistic calibration](https://mlsanity.com/paper/2012.14983/) (2020)
- [Learning to Ask: Neural Question Generation for Reading Comprehension](https://mlsanity.com/paper/1705.00106/) (2017)
- [The Troubling Emergence of Hallucination in Large Language Models -- An Extensive Definition, Quantification, and Prescriptive Remediations](https://mlsanity.com/paper/2310.04988/) (2023)
- [Relying on the Unreliable: The Impact of Language Models' Reluctance to Express Uncertainty](https://mlsanity.com/paper/2401.06730/) (2024)
- [On Verbalized Confidence Scores for LLMs](https://mlsanity.com/paper/2412.14737/) (2024)
- [LUQ: Long-text Uncertainty Quantification for LLMs](https://mlsanity.com/paper/2403.20279/) (2024)
- [MambaByte: Token-free Selective State Space Model](https://mlsanity.com/paper/2401.13660/) (2024)
- [Uncertainty in Natural Language Processing: Sources, Quantification, and Applications](https://mlsanity.com/paper/2306.04459/) (2023)
- [Hallucination Detection in LLMs: Fast and Memory-Efficient Fine-Tuned Models](https://mlsanity.com/paper/2409.02976/) (2024)

## Built on by (most cited first, 13 of 13)

- [Seeing is Believing, but How Much? A Comprehensive Analysis of Verbalized Calibration in Vision-Language Models](https://mlsanity.com/paper/2505.20236/) (2025)
- [Anthropomimetic Uncertainty: What Verbalized Uncertainty in Language Models is Missing](https://mlsanity.com/paper/2507.10587/) (2025)
- [Feedback Friction: LLMs Struggle to Fully Incorporate External Feedback](https://mlsanity.com/paper/2506.11930/) (2025)
- [GrACE: A Generative Approach to Better Confidence Elicitation and Efficient Test-Time Scaling in Large Language Models](https://mlsanity.com/paper/2509.09438/) (2025)
- [Confident RAG: Enhancing the Performance of LLMs for Mathematics Question Answering through Multi-Embedding and Confidence Scoring](https://mlsanity.com/paper/2507.17442/) (2025)
- [Efficient semantic uncertainty quantification in language models via diversity-steered sampling](https://mlsanity.com/paper/2510.21310/) (2025)
- [Confidence Should Be Calibrated More Than One Turn Deep](https://mlsanity.com/paper/2604.05397/) (2026)
- [Capability Self-Assessment in Large Language Models](https://mlsanity.com/paper/2606.00251/) (2026)
- [CALIBER: Calibrating Confidence Before and After Reasoning in Language Models](https://mlsanity.com/paper/2606.24281/) (2026)
- [When Do We Need LLMs? A Diagnostic for Language-Driven Bandits](https://mlsanity.com/paper/2604.05859/) (2026)
- [Inducing Artificial Uncertainty in Language Models](https://mlsanity.com/paper/2605.13595/) (2026)
- [Can a Model Catch Its Own Hallucinations for Free?: Label-Free Doubt Signals Hold Their Own Against a Labelled Dataset for Abstention](https://mlsanity.com/paper/2608.26121/) (2026)
- [On the Pitfalls of Verbalized Confidence Priors for Calibrating Large Reasoning Models](https://mlsanity.com/paper/2609.32470/) (2026)

## Abstract (arXiv)

As large language models (LLMs) are increasingly used for factual question-answering, it becomes more important for LLMs to have the capability to communicate the likelihood that their answer is correct. For these verbalized expressions of uncertainty to be meaningful, they should reflect the error rates at the expressed level of confidence. However, when prompted to express confidence, the error rates of current LLMs are inconsistent with their communicated confidences, highlighting the need for uncertainty quantification methods. Many prior methods calculate lexical uncertainty, estimating a model's confidence in the specific string it generated. In some cases, however, it may be more useful to estimate semantic uncertainty, or the model's confidence in the answer regardless of how it is verbalized. We propose a simple procedure, uncertainty distillation, to teach an LLM to verbalize calibrated semantic confidences. Using held-out data to map initial uncertainty estimates to meaningful probabilities, we create examples annotated with verbalized probabilities for supervised fine-tuning. We find that our method yields verbalized confidences that correlate well with observed error rates, even when compared to strong baselines, some of which are more than twenty times slower at inference time. Additionally, we demonstrate that our method can be applied to black-box models that allow API-based fine-tuning, resulting in estimates of uncertainty that are both more effective and more efficient than any of our baselines.