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Token-Level Density-Based Uncertainty Quantification Methods for Eliciting Truthfulness of Large Language Models

Paper · 2025 · Artem Vazhentsev, Lyudmila Rvanova, Ivan Lazichny et al.

Summary

LLMs often produce hallucinated or non-factual output. Many uncertainty quantification (UQ) methods can flag such output, but the strongest ones sample the model repeatedly and are expensive. Density-based scores such as Mahalanobis Distance (MD) are cheap and work well for encoder classifiers, yet earlier sequence-level versions did poorly for generation.

The authors move MD to the token level. They take embeddings of each generated token from several decoder layers and compute MD or Relative MD per token and layer. These scores are averaged over the sequence and reduced with PCA. A linear regressor trained on correctness-annotated responses then turns these features, plus sequence probability, into an uncertainty score.

Across eleven datasets the supervised variants beat existing supervised and unsupervised UQ methods. This holds for both sequence-level selective generation and claim-level fact-checking, and the methods transfer reasonably to out-of-domain data. Because they need no extra sampling, they offer a practical way to judge whether LLM answers can be trusted.

Key points

  • The proposed variants include SATRMD+MSP and HUQ-SATRMD. They build on MD and RMD, where RMD contrasts against a background corpus such as C4.
  • Evaluation covered eleven datasets, among them XSum, SamSum, CNN, PubMedQA, MedQUAD and TruthfulQA, plus claim-level fact-checking. Ablations used Llama 8b v3.1.
  • Extra cost is about 5.3–7.6% over plain inference. Sampling-based methods such as Semantic Entropy, SAR and Lexical Similarity add roughly 315–700%.
  • Performance changes little with the correctness threshold used to pick embeddings for the centroid and covariance. Results are also stable beyond about five PCA components, and 10 was the default.
  • Limitations: the methods need supervision data, performance drops somewhat out of domain, and only 7–9b models were tested.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓The University of MelbourneMelbourne · Australia102 works · 22,618 citations

 Fields, topics and concepts

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 18,614 worksArtificial Intelligence · 17,965 worksArts and Humanities · 17,450 worksLanguage and Linguistics · 17,296 works

🧭 Topics 1Research subjects and languages the work is about.Language models & pretraining · 3,894 works

Cite

Cite as Artem Vazhentsev, Lyudmila Rvanova, Ivan Lazichny, Alexander Panchenko, Maxim Panov, Timothy Baldwin and Artem Shelmanov. 2025. Token-Level Density-Based Uncertainty Quantification Methods for Eliciting Truthfulness of Large Language Models. Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2025.naacl-long.113

@inproceedings{vazhentsev2025token,
  title = {{Token-Level Density-Based Uncertainty Quantification Methods for Eliciting Truthfulness of Large Language Models}},
  author = {Artem Vazhentsev, Lyudmila Rvanova, Ivan Lazichny, Alexander Panchenko, Maxim Panov, Timothy Baldwin and Artem Shelmanov},
  booktitle = {Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers)},
  year = {2025},
  doi = {10.18653/v1/2025.naacl-long.113},
  url = {https://doi.org/10.18653/v1/2025.naacl-long.113}
}

References

64 references, 24 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. Asma Ben Abacha and Dina Demner-Fushman. 2019. A question-entailment approach to question answering. BMC Bioinform., 20(1):511:1–511:23. find
  2. Amos Azaria and Tom Mitchell. 2023. The internal state of an LLM knows when it’s lying. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 967–976, Singapore. Association for Computational Linguistics.
  3. Joris Baan, Nico Daheim, Evgenia Ilia, Dennis Ulmer, Haau-Sing Li, Raquel Fernández, Barbara Plank, Rico Sennrich, Chrysoula Zerva, and Wilker Aziz. 2023. Uncertainty in natural language generation: From theory to applications. arXiv preprint arXiv:2307.15703. — [arXiv:2307.15703](https://arxiv.org/abs/2307.15703) find
  4. Sky CH-Wang, Benjamin Van Durme, Jason Eisner, and Chris Kedzie. 2024. Do androids know they’re only dreaming of electric sheep? In Findings of the Association for Computational Linguistics ACL 2024, pages 4401–4420, Bangkok, Thailand and virtual meeting. Association for Computational Linguistics. find
  5. Jireh Chan, Steven Leow, Khean Bea, Wai Khuen Cheng, Seuk Wai Phoong, Zeng-Wei Hong, and Yen-Lin Chen. 2022. Mitigating the multicollinearity problem and its machine learning approach: A review. Mathematics, 10:1283. find
  6. Chao Chen, Kai Liu, Ze Chen, Yi Gu, Yue Wu, Mingyuan Tao, Zhihang Fu, and Jieping Ye. 2024. INSIDE: llms’ internal states retain the power of hallucination detection. In The Twelfth International Conference on Learning Representations, ICLR 2024, Vienna, Austria, May 7-11, 2024. OpenReview.net.
  7. Yuyan Chen, Qiang Fu, Yichen Yuan, Zhihao Wen, Ge Fan, Dayiheng Liu, Dongmei Zhang, Zhixu Li, and Yanghua Xiao. 2023. Hallucination detection: Robustly discerning reliable answers in large language models. In Proceedings of the 32nd ACM International Conference on Information and Knowledge Managemen… find
  8. Julius Cheng and Andreas Vlachos. 2024. Measuring uncertainty in neural machine translation with similarity-sensitive entropy. In Proceedings of the 18th Conference of the European Chapter of the Association for Computational Linguistics (Volume 1: Long Papers), pages 2115–2128, St. Julian’s, Malta.… find
  9. Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, Christopher Hesse, and John Schulman. 2021. Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168.
  10. Maxime Darrin, Pablo Piantanida, and Pierre Colombo. 2023. RainProof: An umbrella to shield text generator from out-of-distribution data. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 5831–5857, Singapore. Association for Computational Linguistics. find
  11. Jinhao Duan, Hao Cheng, Shiqi Wang, Alex Zavalny, Chenan Wang, Renjing Xu, Bhavya Kailkhura, and Kaidi Xu. 2024. Shifting attention to relevance: Towards the predictive uncertainty quantification of free-form large language models. In Proceedings of the 62nd Annual Meeting of the Association for Com… find
  12. Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, Anirudh Goyal, Anthony Hartshorn, Aobo Yang, Archi Mitra, Archie Sravankumar, Artem Korenev, Arthur Hinsvark, Arun Rao, Aston Zhang, Aurélien Rodriguez,… — The Llama 3 Herd of Models
  13. Nouha Dziri, Sivan Milton, Mo Yu, Osmar Zaiane, and Siva Reddy. 2022. On the origin of hallucinations in conversational models: Is it the datasets or the models? In Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Techn…
  14. Ekaterina Fadeeva, Aleksandr Rubashevskii, Artem Shelmanov, Sergey Petrakov, Haonan Li, Hamdy Mubarak, Evgenii Tsymbalov, Gleb Kuzmin, Alexander Panchenko, Timothy Baldwin, Preslav Nakov, and Maxim Panov. 2024. Fact-checking the output of large language models via token-level uncertainty quantificat…
  15. Ekaterina Fadeeva, Roman Vashurin, Akim Tsvigun, Artem Vazhentsev, Sergey Petrakov, Kirill Fedyanin, Daniil Vasilev, Elizaveta Goncharova, Alexander Panchenko, Maxim Panov, Timothy Baldwin, and Artem Shelmanov. 2023. LM-Polygraph: Uncertainty estimation for language models. In Proceedings of the 202… find
  16. Sebastian Farquhar, Jannik Kossen, Lorenz Kuhn, and Yarin Gal. 2024. Detecting hallucinations in large language models using semantic entropy. Nature, 630(8017):625–630. find
  17. Shangbin Feng, Weijia Shi, Yike Wang, Wenxuan Ding, Vidhisha Balachandran, and Yulia Tsvetkov. 2024. Don’t hallucinate, abstain: Identifying LLM knowledge gaps via multi-LLM collaboration. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Pape… find
  18. Marina Fomicheva, Shuo Sun, Lisa Yankovskaya, Frédéric Blain, Francisco Guzmán, Mark Fishel, Nikolaos Aletras, Vishrav Chaudhary, and Lucia Specia. 2020. Unsupervised quality estimation for neural machine translation. Transactions of the Association for Computational Linguistics, 8:539–555.
  19. Yarin Gal and Zoubin Ghahramani. 2016. Dropout as a Bayesian approximation: Representing model uncertainty in deep learning. In Proceedings of The 33rd International Conference on Machine Learning, volume 48 of Proceedings of Machine Learning Research, pages 1050–1059, New York, New York, USA. PMLR. find
  20. Jiahui Geng, Fengyu Cai, Yuxia Wang, Heinz Koeppl, Preslav Nakov, and Iryna Gurevych. 2024. A survey of confidence estimation and calibration in large language models. In Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language…
  21. Bogdan Gliwa, Iwona Mochol, Maciej Biesek, and Aleksander Wawer. 2019. SAMSum corpus: A human-annotated dialogue dataset for abstractive summarization. In Proceedings of the 2nd Workshop on New Frontiers in Summarization, pages 70–79, Hong Kong, China. Association for Computational Linguistics.
  22. Jianfeng He, Linlin Yu, Shuo Lei, Chang-Tien Lu, and Feng Chen. 2024a. Uncertainty estimation on sequential labeling via uncertainty transmission. In Findings of the Association for Computational Linguistics: NAACL 2024, pages 2823–2835, Mexico City, Mexico. Association for Computational Linguistics… find
  23. Jianfeng He, Xuchao Zhang, Shuo Lei, Zhiqian Chen, Fanglan Chen, Abdulaziz Alhamadani, Bei Xiao, and Chang-Tien Lu. 2020. Towards more accurate uncertainty estimation in text classification. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing, EMNLP 2020, Online… find
  24. Jinwen He, Yujia Gong, Zijin Lin, Cheng’an Wei, Yue Zhao, and Kai Chen. 2024b. LLM factoscope: Uncovering LLMs’ factual discernment through measuring inner states. In Findings of the Association for Computational Linguistics ACL 2024, pages 10218– 10230, Bangkok, Thailand and virtual meeting. Associ… find
  25. Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Jacob Steinhardt. 2021. Measuring massive multitask language understanding. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net.
  26. Albert Q. Jiang, Alexandre Sablayrolles, Arthur Mensch, Chris Bamford, Devendra Singh Chaplot, Diego de Las Casas, Florian Bressand, Gianna Lengyel, Guillaume Lample, Lucile Saulnier, Lélio Renard Lavaud, Marie-Anne Lachaux, Pierre Stock, Teven Le Scao, Thibaut Lavril, Thomas Wang, Timothée Lacroix,… find
  27. Qiao Jin, Bhuwan Dhingra, Zhengping Liu, William Cohen, and Xinghua Lu. 2019. PubMedQA: A dataset for biomedical research question answering. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Proce…
  28. Mandar Joshi, Eunsol Choi, Daniel Weld, and Luke Zettlemoyer. 2017. TriviaQA: A large scale distantly supervised challenge dataset for reading comprehension. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 1601–1611, Vancouver…
  29. Nikita Kotelevskii, Aleksandr Artemenkov, Kirill Fedyanin, Fedor Noskov, Alexander Fishkov, Artem Shelmanov, Artem Vazhentsev, Aleksandr Petiushko, and Maxim Panov. 2022. Nonparametric uncertainty quantification for single deterministic neural network. In Advances in Neural Information Processing Sy… find
  30. Lorenz Kuhn, Yarin Gal, and Sebastian Farquhar. 2023. Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language generation. In The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023. falsehoods. In Proceedings of…
  31. Zhen Lin, Shubhendu Trivedi, and Jimeng Sun. 2023. Generating with confidence: Uncertainty quantification for black-box large language models. Transactions on Machine Learning Research. find
  32. Jeremiah Liu, Zi Lin, Shreyas Padhy, Dustin Tran, Tania Bedrax Weiss, and Balaji Lakshminarayanan. 2020. Simple and principled uncertainty estimation with deterministic deep learning via distance awareness. In Advances in Neural Information Processing Systems, volume 33, pages 7498–7512. Curran Asso… find
  33. Andrey Malinin and Mark J. F. Gales. 2021. Uncertainty estimation in autoregressive structured prediction. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net. find
  34. Potsawee Manakul, Adian Liusie, and Mark Gales. 2023. SelfCheckGPT: Zero-resource black-box hallucination detection for generative large language models. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 9004–9017. find
  35. Sewon Min, Kalpesh Krishna, Xinxi Lyu, Mike Lewis, Wen-tau Yih, Pang Koh, Mohit Iyyer, Luke Zettlemoyer, and Hannaneh Hajishirzi. 2023. FActScore: Fine-grained atomic evaluation of factual precision in long form text generation. In Proceedings of the 2023 Conference on Empirical Methods in Natural L…
  36. Shashi Narayan, Shay B. Cohen, and Mirella Lapata. 2018. Don’t give me the details, just the summary! topic-aware convolutional neural networks for extreme summarization. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, Brussels, Belgium, October 31 -Novembe…
  37. Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. 2017. Simple and scalable predictive uncertainty estimation using deep ensembles. In Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc. find
  38. Alexander Nikitin, Jannik Kossen, Yarin Gal, and Pekka Marttinen. 2024. Kernel language entropy: Fine-grained uncertainty quantification for llms from semantic similarities. arXiv preprint arXiv:2405.20003. — [arXiv:2405.20003](https://arxiv.org/abs/2405.20003) find
  39. Kimin Lee, Kibok Lee, Honglak Lee, and Jinwoo Shin. 2018. A simple unified framework for detecting out-of-distribution samples and adversarial attacks. In Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3-8… find
  40. OpenAI, Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, Red Avila, Igor Babuschkin, Suchir Balaji, Valerie Balcom, Paul Baltescu, Haiming Bao, Mohammad Bavarian, Jeff Belgum, Irwan Bello, Ja… — GPT-4 Technical Report
  41. Morgane Rivière, Shreya Pathak, Pier Giuseppe Sessa, Cassidy Hardin, Surya Bhupatiraju, Léonard Hussenot, Thomas Mesnard, Bobak Shahriari, Alexandre Ramé, Johan Ferret, Peter Liu, Pouya Tafti, Abe Friesen, Michelle Casbon, Sabela Ramos, Ravin Kumar, Charline Le Lan, Sammy Jerome, Anton Tsitsulin, Ni… find
  42. Alexander Podolskiy, Dmitry Lipin, Andrey Bout, Ekaterina Artemova, and Irina Piontkovskaya. 2021. Revisiting mahalanobis distance for transformer-based out-of-domain detection. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 13675– 13682. find
  43. Abigail See, Peter J. Liu, and Christopher D. Manning. 2017. Get to the point: Summarization with pointer-generator networks. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 1073– 1083, Vancouver, Canada. Association for Compu… find
  44. Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J. Liu. 2020. Exploring the limits of transfer learning with a unified text-to-text transformer. J. Mach. Learn. Res., 21:140:1–140:67.
  45. Siva Reddy, Danqi Chen, and Christopher D. Manning. 2019. CoQA: A conversational question answering challenge. Transactions of the Association for Computational Linguistics, 7:249–266.
  46. Jie Ren, Jiaming Luo, Yao Zhao, Kundan Krishna, Mohammad Saleh, Balaji Lakshminarayanan, and Peter J Liu. 2023. Out-of-distribution detection and selective generation for conditional language models. In The Eleventh International Conference on Learning Representations.
  47. Peter J Rousseeuw. 1984. Least median of squares regression. Journal of the American statistical association, 79(388):871–880. find
  48. Artem Shelmanov, Evgenii Tsymbalov, Dmitri Puzyrev, Kirill Fedyanin, Alexander Panchenko, and Maxim Panov. 2021. How certain is your transformer? In Proceedings of the 16th Conference of the European Chapter of the Association for Computational Linguistics: Main Volume, pages 1833–1840, Online. Asso… find
  49. Noora Shrestha. 2020. Detecting multicollinearity in regression analysis. American Journal of Applied Mathematics and Statistics, 8:39–42. find
  50. Evgenii Tsymbalov, Maxim Panov, and Alexander Shapeev. 2018. Dropout-based active learning for regression. In Analysis of Images, Social Networks and Texts: 7th International Conference, AIST 2018, Moscow, Russia, July 5–7, 2018, pages 247–258. find
  51. Joost van Amersfoort, Lewis Smith, Yee Whye Teh, and Yarin Gal. 2020. Uncertainty estimation using a single deep deterministic neural network. In Proceedings of the 37th International Conference on Machine Learning, ICML 2020, 13-18 July 2020, Virtual Event, volume 119 of Proceedings of Machine Lear… find
  52. Roman Vashurin, Ekaterina Fadeeva, Artem Vazhentsev, Lyudmila Rvanova, Akim Tsvigun, Daniil Vasilev, Rui Xing, Abdelrahman Boda Sadallah, Kirill Grishchenkov, Sergey Petrakov, Alexander Panchenko, Timothy Baldwin, Preslav Nakov, Maxim Panov, and Artem Shelmanov. 2024. Benchmarking uncertainty quanti…
  53. Roman Vashurin, Maiya Goloburda, Preslav Nakov, Artem Shelmanov, and Maxim Panov. 2025. Cocoa: A generalized approach to uncertainty quantification by integrating confidence and consistency of llm outputs. arXiv preprint arXiv:2502.04964. — [arXiv:2502.04964](https://arxiv.org/abs/2502.04964) find
  54. Artem Vazhentsev, Ekaterina Fadeeva, Rui Xing, Alexander Panchenko, Preslav Nakov, Timothy Baldwin, Maxim Panov, and Artem Shelmanov. 2024. Unconditional truthfulness: Learning conditional dependency for uncertainty quantification of large language models. arXiv preprint arXiv:2408.10692. — [arXiv:2408.10692](https://arxiv.org/abs/2408.10692) find
  55. Artem Vazhentsev, Gleb Kuzmin, Artem Shelmanov, Akim Tsvigun, Evgenii Tsymbalov, Kirill Fedyanin, Maxim Panov, Alexander Panchenko, Gleb Gusev, Mikhail Burtsev, Manvel Avetisian, and Leonid Zhukov. 2022. Uncertainty estimation of transformer predictions for misclassification detection. In Proceeding… find
  56. Artem Vazhentsev, Gleb Kuzmin, Akim Tsvigun, Alexander Panchenko, Maxim Panov, Mikhail Burtsev, and Artem Shelmanov. 2023a. Hybrid uncertainty quantification for selective text classification in ambiguous tasks. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguisti… find
  57. Johannes Welbl, Nelson F. Liu, and Matt Gardner. 2017. Crowdsourcing multiple choice science questions. In Proceedings of the 3rd Workshop on Noisy User-generated Text, pages 94–106, Copenhagen, Denmark. Association for Computational Linguistics.
  58. Yijun Xiao and William Yang Wang. 2021. On hallucination and predictive uncertainty in conditional language generation. In Proceedings of the 16th Conference of the European Chapter of the Association for Computational Linguistics: Main Volume, pages 2734–2744, Online. Association for Computational…
  59. Ji Xin, Raphael Tang, Yaoliang Yu, and Jimmy Lin. 2021. The art of abstention: Selective prediction and error regularization for natural language processing. In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natu… find
  60. KiYoon Yoo, Jangho Kim, Jiho Jang, and Nojun Kwak. 2022. Detection of adversarial examples in text classification: Benchmark and baseline via robust density estimation. In Findings of the Association for Computational Linguistics: ACL 2022, pages 3656–3672, Dublin, Ireland. Association for Computati… find
  61. Yuheng Zha, Yichi Yang, Ruichen Li, and Zhiting Hu. 2023. AlignScore: Evaluating factual consistency with a unified alignment function. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 11328–11348, Toronto, Canada. Association…
  62. Xuchao Zhang, Fanglan Chen, Chang-Tien Lu, and Naren Ramakrishnan. 2019. Mitigating uncertainty in document classification. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Pape… find
  63. Artem Vazhentsev, Akim Tsvigun, Roman Vashurin, Sergey Petrakov, Daniil Vasilev, Maxim Panov, Alexander Panchenko, and Artem Shelmanov. 2023b. Efficient out-of-domain detection for sequence to sequence models. In Findings of the Association for Computational Linguistics: ACL 2023, pages 1430– 1454,… find
  64. Yuxia Wang, Daniel Beck, Timothy Baldwin, and Karin Verspoor. 2022. Uncertainty estimation and reduction of pre-trained models for text regression. Transactions of the Association for Computational Linguistics, 10:680–696.

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