# Teaching Models to Express Their Uncertainty in Words

arXiv: https://arxiv.org/abs/2205.14334 · HTML: https://mlsanity.com/paper/2205.14334/

## Key facts

- Cited by 751 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 36 references that are in the map.
- First posted on arXiv 28 May 2022.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Retrieval Augmentation Reduces Hallucination in Conversation](https://mlsanity.com/paper/2104.07567/) (2021)
- [Prompt Programming for Large Language Models: Beyond the Few-Shot Paradigm](https://mlsanity.com/paper/2102.07350/) (2021)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Calibrating Deep Neural Networks using Focal Loss](https://mlsanity.com/paper/2002.09437/) (2020)
- [Calibration of Pre-trained Transformers](https://mlsanity.com/paper/2003.07892/) (2020)
- [Recursively Summarizing Books with Human Feedback](https://mlsanity.com/paper/2109.10862/) (2021)
- [Selective Question Answering under Domain Shift](https://mlsanity.com/paper/2006.09462/) (2020)
- [Reducing conversational agents' overconfidence through linguistic calibration](https://mlsanity.com/paper/2012.14983/) (2020)
- [Domain Adaptation for Visual Applications: A Comprehensive Survey](https://mlsanity.com/paper/1702.05374/) (2017)
- [Truthful AI: Developing and governing AI that does not lie](https://mlsanity.com/paper/2110.06674/) (2021)
- [Soft Calibration Objectives for Neural Networks](https://mlsanity.com/paper/2108.00106/) (2021)
- [Posterior calibration and exploratory analysis for natural language processing models](https://mlsanity.com/paper/1508.05154/) (2015)
- [Confidence Calibration for Domain Generalization under Covariate Shift](https://mlsanity.com/paper/2104.00742/) (2021)

## Built on by (most cited first, 30 of 751)

- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (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)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Aligning Large Multimodal Models with Factually Augmented RLHF](https://mlsanity.com/paper/2309.14525/) (2023)
- [Trustworthy LLMs: a Survey and Guideline for Evaluating Large Language Models' Alignment](https://mlsanity.com/paper/2308.05374/) (2023)
- [Measuring short-form factuality in large language models](https://mlsanity.com/paper/2411.04368/) (2024)
- [Robots That Ask For Help: Uncertainty Alignment for Large Language Model Planners](https://mlsanity.com/paper/2307.01928/) (2023)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Large Language Models Sensitivity to The Order of Options in Multiple-Choice Questions](https://mlsanity.com/paper/2308.11483/) (2023)
- [Prompting GPT-3 To Be Reliable](https://mlsanity.com/paper/2210.09150/) (2022)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [The Alignment Problem from a Deep Learning Perspective](https://mlsanity.com/paper/2209.00626/) (2022)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Survey on Factuality in Large Language Models: Knowledge, Retrieval and Domain-Specificity](https://mlsanity.com/paper/2310.07521/) (2023)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Don't Hallucinate, Abstain: Identifying LLM Knowledge Gaps via Multi-LLM Collaboration](https://mlsanity.com/paper/2402.00367/) (2024)
- [RoleLLM: Benchmarking, Eliciting, and Enhancing Role-Playing Abilities of Large Language Models](https://mlsanity.com/paper/2310.00746/) (2023)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [C3: Zero-shot Text-to-SQL with ChatGPT](https://mlsanity.com/paper/2307.07306/) (2023)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Reasoning Models Know When They're Right: Probing Hidden States for Self-Verification](https://mlsanity.com/paper/2504.05419/) (2025)
- [LM vs LM: Detecting Factual Errors via Cross Examination](https://mlsanity.com/paper/2305.13281/) (2023)
- [Evaluating Correctness and Faithfulness of Instruction-Following Models for Question Answering](https://mlsanity.com/paper/2307.16877/) (2023)
- [Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Models](https://mlsanity.com/paper/2307.01379/) (2023)
- [AbstentionBench: Reasoning LLMs Fail on Unanswerable Questions](https://mlsanity.com/paper/2506.09038/) (2025)
- [Taken out of context: On measuring situational awareness in LLMs](https://mlsanity.com/paper/2309.00667/) (2023)

## Abstract (arXiv)

We show that a GPT-3 model can learn to express uncertainty about its own answers in natural language -- without use of model logits. When given a question, the model generates both an answer and a level of confidence (e.g. "90% confidence" or "high confidence"). These levels map to probabilities that are well calibrated. The model also remains moderately calibrated under distribution shift, and is sensitive to uncertainty in its own answers, rather than imitating human examples. To our knowledge, this is the first time a model has been shown to express calibrated uncertainty about its own answers in natural language. For testing calibration, we introduce the CalibratedMath suite of tasks. We compare the calibration of uncertainty expressed in words ("verbalized probability") to uncertainty extracted from model logits. Both kinds of uncertainty are capable of generalizing calibration under distribution shift. We also provide evidence that GPT-3's ability to generalize calibration depends on pre-trained latent representations that correlate with epistemic uncertainty over its answers.