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Cited by 21Adversarial Robustness in Machine LearningTopic ModelingExplainable Artificial Intelligence (XAI)

Calibrating Large Language Models with Sample Consistency

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Lyu, Qing, Shridhar, Kumar, Malaviya, Chaitanya, Zhang, Li, Elazar, Yanai, Tandon, Niket, Apidianaki, Marianna, Sachan, Mrinmaya +1 more·2025·Proceedings of the AAAI Conference on Artificial Intelligence
DOI 10.1609/aaai.v39i18.34120
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Abstract

Accurately gauging the confidence level of Large Language Models' (LLMs) predictions is pivotal for their reliable application. However, LLMs are often uncalibrated inherently and elude conventional calibration techniques due to their proprietary nature and massive scale. In this work, we derive model confidence from the distribution of multiple randomly sampled generations, using three measures of consistency. We extensively evaluate eleven open and closed-source models on nine reasoning datasets. Results show that consistency-based calibration methods outperform existing post-hoc approaches in terms of calibration error. Meanwhile, we find that factors such as intermediate explanations, model scaling, and larger sample sizes enhance calibration, while instruction-tuning makes calibration more difficult. Moreover, confidence scores obtained from consistency can potentially enhance model performance. Finally, we offer guidance on choosing suitable consistency metrics for calibration, tailored to model characteristics such as the exposure to instruction-tuning and RLHF.

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  • Sample consistency has been shown to outperform token level probability and confidence elicitation in the medical domain.

    “Following Lyu et al., we perform uncertainty quantification employing sample consistency40, which has been shown to outperform token level probability and confidence elicitation in the medical domain41.”

    From Limitations of large language models in clinical problem-solving arising from inflexible reasoning (2025) · cites this paper as [40]

  • Measuring consistency in model output across multiple runs is an established method for uncertainty estimation in LLMs and has been shown to outperform posthoc methods.

    “Measuring consistency in model output across multiple runs is an established method for uncertainty estimation in LLMs38,39 and has been shown to outperform posthoc methods at uncertainty estimation40.”

    From Limitations of large language models in clinical problem-solving arising from inflexible reasoning (2025) · cites this paper as [40]

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Research works printed but not linked: 31

  1. Brier, G. W. 1950. Verification of forecasts expressed in terms of probability. Monthly weather review, 78(1): 1-3.
  2. Brohan, A.; Chebotar, Y.; Finn, C.; Hausman, K.; Herzog, A.; Ho, D.; Ibarz, J.; Irpan, A.; Jang, E.; Julian, R.; et al. 2023. Do as i can, not as i say: Grounding language in robotic affordances. In Conference on robot learning, 287- 318.
  3. PMLR.
  4. Brown, T. B.; Mann, B.; Ryder, N.; Subbiah, M.; Kaplan, J.; Dhariwal, P.; Neelakantan, A.; Shyam, P.; Sastry, G.; Askell, A.; Agarwal, S.; Herbert-Voss, A.; Krueger, G.; Henighan, T.; Child, R.; Ramesh, A.; Ziegler, D. M.; Wu, J.; Winter, C.; Hesse, C.; Chen, M.; Sigler, E.; Litwin, M.; Gray, S.; Chess, B.; Clark, J.; Berner, C.; McCandlish, S.; Radford, A.; Sutskever, I.; and Amodei, D. 2020. Language Models are Few-Shot Learners. In Larochelle, H.; Ranzato, M.; Hadsell, R.; Balcan, M.; and Lin, H., eds., Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual.
  5. Chen, Y.; Yuan, L.; Cui, G.; Liu, Z.; and Ji, H. 2023. A Close Look into the Calibration of Pre-trained Language Models. In Rogers, A.; Boyd-Graber, J.; and Okazaki, N., eds., Proceedings of the 61st Annual Meeting of the Associa- tion for Computational Linguistics (Volume 1: Long Papers), 1343-1367. Toronto, Canada: Association for Computational Linguistics.
  6. Gal, Y.; and Ghahramani, Z. 2016. Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning. In Balcan, M.; and Weinberger, K. Q., eds., Pro- ceedings of the 33nd International Conference on Machine Learning, ICML 2016, New York City, NY, USA, June 19- 24, 2016, volume 48 of JMLR Workshop and Conference Proceedings, 1050-1059. JMLR.org.
  7. Gao, L.; Madaan, A.; Zhou, S.; Alon, U.; Liu, P.; Yang, Y.; Callan, J.; and Neubig, G. 2023. Pal: Program-aided language models. In International Conference on Machine Learning, 10764-10799.
  8. PMLR.
  9. Geva, M.; Khashabi, D.; Segal, E.; Khot, T.; Roth, D.; and Berant, J. 2021. Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies. Transactions of the Association for Computational Linguis- tics, 9: 346-361.
  10. Guo, C.; Pleiss, G.; Sun, Y.; and Weinberger, K. Q. 2017. On Calibration of Modern Neural Networks. In Precup, D.; and Teh, Y. W., eds., Proceedings of the 34th International Conference on Machine Learning, ICML 2017, Sydney, NSW, Australia, 6-11 August 2017, volume 70 of Proceedings of Machine Learning Research, 1321-1330.
  11. PMLR.
  12. Huang, J.; Chen, X.; Mishra, S.; Zheng, H. S.; Yu, A. W.; Song, X.; and Zhou, D. 2023. Large Language Models Can- not Self-Correct Reasoning Yet. In The Twelfth International Conference on Learning Representations.
  13. Jiang, Z.; Araki, J.; Ding, H.; and Neubig, G. 2021. How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering. Transactions of the Association for Computational Linguistics, 9: 962-977.
  14. Lakshminarayanan, B.; Pritzel, A.; and Blundell, C. 2017. Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles. In Guyon, I.; von Luxburg, U.; Bengio, S.; Wallach, H. M.; Fergus, R.; Vishwanathan, S. V. N.; and Garnett, R., eds., Advances in Neural Information Process- ing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4-9, 2017, Long Beach, CA, USA, 6402-6413.
  15. Lee, K.; Lee, K.; Lee, H.; and Shin, J. 2018. A Simple Uni- fied Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks. In Bengio, S.; Wallach, H. M.; Larochelle, H.; Grauman, K.; Cesa-Bianchi, N.; and Garnett, R., eds., Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3-8, 2018, Montréal, Canada, 7167-7177.
  16. Lin, S.; Hilton, J.; and Evans, O. 2022. Teaching Models to Express Their Uncertainty in Words. Transactions on Machine Learning Research.
  17. Manakul, P.; Liusie, A.; and Gales, M. 2023. SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Gener- ative Large Language Models. In Bouamor, H.; Pino, J.; and Bali, K., eds., Proceedings of the 2023 Conference on Empir- ical Methods in Natural Language Processing, 9004-9017. Singapore: Association for Computational Linguistics.
  18. Miao, S.-y.; Liang, C.-C.; and Su, K.-Y. 2020. A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, 975-984. Online: Association for Computational Linguistics.
  19. Mielke, S. J.; Szlam, A.; Dinan, E.; and Boureau, Y.-L. 2022. Reducing Conversational Agents' Overconfidence Through Linguistic Calibration. Transactions of the Association for Computational Linguistics, 10: 857-872.
  20. Nye, M. I.; Tessler, M. H.; Tenenbaum, J. B.; and Lake, B. M. 2021. Improving Coherence and Consistency in Neural Se- quence Models with Dual-System, Neuro-Symbolic Reason- ing. In Ranzato, M.; Beygelzimer, A.; Dauphin, Y. N.; Liang, P.; and Vaughan, J. W., eds., Advances in Neural Information Processing Systems 34: Annual Conference on Neural Infor- mation Processing Systems 2021, NeurIPS 2021, December 6-14, 2021, virtual, 25192-25204.
  21. Papadopoulos, G.; Edwards, P. J.; and Murray, A. F. 2001. Confidence estimation methods for neural networks: A prac- tical comparison. IEEE transactions on neural networks, 12(6): 1278-1287.
  22. Patel, A.; Bhattamishra, S.; and Goyal, N. 2021. Are NLP Models really able to Solve Simple Math Word Problems? In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, 2080-2094. Online: Associ- ation for Computational Linguistics.
  23. Chang, K.-W.; Mehrabi, N.; Pruksachatkun, Y.; Galystan, A.; Dhamala, J.; Verma, A.; Cao, T.; Kumar, A.; and Gupta, R., eds., Proceedings of the 3rd Workshop on Trustworthy Natural Language Processing (TrustNLP 2023), 326-362.
  24. Rafailov, R.; Sharma, A.; Mitchell, E.; Manning, C. D.; Er- mon, S.; and Finn, C. 2024. Direct preference optimization: Your language model is secretly a reward model. Advances in Neural Information Processing Systems, 36.
  25. Roy, S.; and Roth, D. 2015. Solving General Arithmetic Word Problems. In Proceedings of the 2015 Conference on Empir- ical Methods in Natural Language Processing, 1743-1752. Lisbon, Portugal: Association for Computational Linguistics.
  26. Shridhar, K.; Macina, J.; El-Assady, M.; Sinha, T.; Kapur, M.; and Sachan, M. 2022. Automatic Generation of Socratic Sub- questions for Teaching Math Word Problems. In Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, 4136-4149. Abu Dhabi, United Arab Emirates: Association for Computational Linguistics.
  27. Sinha, K.; Sodhani, S.; Dong, J.; Pineau, J.; and Hamilton, W. L. 2019. CLUTRR: A Diagnostic Benchmark for In- ductive Reasoning from Text. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Pro- cessing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), 4506-4515. Hong Kong, China: Association for Computational Linguistics.
  28. Wang, X.; Wei, J.; Schuurmans, D.; Le, Q. V.; Chi, E. H.; Narang, S.; Chowdhery, A.; and Zhou, D. 2023. Self- Consistency Improves Chain of Thought Reasoning in Lan- guage Models. In The Eleventh International Conference on Learning Representations.
  29. Wei, J.; Wang, X.; Schuurmans, D.; Bosma, M.; brian ichter; Xia, F.; Chi, E. H.; Le, Q. V.; and Zhou, D. 2022. Chain of Thought Prompting Elicits Reasoning in Large Language Models. In Oh, A. H.; Agarwal, A.; Belgrave, D.; and Cho, K., eds., Advances in Neural Information Processing Systems.
  30. Xiong, M.; Hu, Z.; Lu, X.; Li, Y.; Fu, J.; He, J.; and Hooi, B. 2023. Can LLMs Express Their Uncertainty? An Empir- ical Evaluation of Confidence Elicitation in LLMs. ArXiv preprint, abs/2306.13063. · arXiv
  31. Zhou, D.; Schärli, N.; Hou, L.; Wei, J.; Scales, N.; Wang, X.; Schuurmans, D.; Cui, C.; Bousquet, O.; Le, Q. V.; and Chi, E. H. 2023. Least-to-Most Prompting Enables Complex Reasoning in Large Language Models. In The Eleventh International Conference on Learning Representations.

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Authors
Lyu, Q., Shridhar, K., Malaviya, C., Zhang, L., Elazar, Y., Tandon, N., Apidianaki, M., Sachan, M., & Callison-Burch, C.
Affiliations
  • University of Pennsylvania (US)
  • ETH Zurich (CH)
  • Drexel University (US)
  • Allen Institute for Artificial Intelligence (US)
  • Microsoft (United States) (US)
ORCID
Venue
Proceedings of the AAAI Conference on Artificial Intelligence
Publisher
Association for the Advancement of Artificial Intelligence (AAAI)
Published
2025-04-11
Volume
39
Issue
18
Pages
19260-19268
ISSN
  • 2159-5399 (ISSN-L)
  • 2374-3468
DOI
10.1609/aaai.v39i18.34120
OpenAlex
W4409363988
Cited by
21
References
0
Citations by year
2026: 13 · 2025: 7 · 2024: 1
FWCI
18.97
Type
conference paper
Language
en
Open access
Locations
  • Proceedings of the AAAI Conference on Artificial Intelligence (publishedVersion)
  • arXiv (Cornell University) (submittedVersion, cc-by-nc-sa)
  • arXiv (Cornell University)
Funders
  • Office of the Director of National Intelligence
  • Allen Institute for Artificial Intelligence
  • Defense Advanced Research Projects Agency (HR00112520300)
  • Advanced Research Projects Agency
  • Intelligence Advanced Research Projects Activity
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Adversarial Robustness in Machine Learning
  • Physical Sciences › Computer Science › Artificial Intelligence › Topic Modeling
  • Physical Sciences › Computer Science › Artificial Intelligence › Explainable Artificial Intelligence (XAI)
Keywords
large language models, calibration, sample consistency, confidence estimation, multiple generations, consistency metrics, post-hoc calibration, reasoning datasets, instruction tuning, reinforcement learning from human feedback, model scaling

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