{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T02:25:13Z","timestamp":1781663113995,"version":"3.54.5"},"reference-count":68,"publisher":"MIT Press","license":[{"start":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T00:00:00Z","timestamp":1753142400000},"content-version":"vor","delay-in-days":202,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,7,18]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Decoding methods for large language models (LLMs) usually struggle with the tradeoff between ensuring factuality and maintaining diversity. In this paper, we propose REAL (Residual Entropy from Asymptotic Line) sampling,1 which predicts the step-wise hallucination likelihood of an LLM. When an LLM is likely to hallucinate, REAL lowers the p threshold in nucleus sampling. Otherwise, REAL sampling increases the p threshold to boost the diversity. To predict the step-wise hallucination likelihood without supervision, we construct a THF (Token-level Hallucination Forecasting) model, which predicts the asymptotic entropy (i.e., inherent uncertainty) of the next token by extrapolating the next-token entropies of an infinitely large language model from a series of LLMs with different sizes. If an LLM\u2019s entropy is higher than the asymptotic entropy (i.e., the LLM is more uncertain than it should be), the THF model predicts a high hallucination hazard, which leads to a lower p threshold in REAL sampling. In the FactualityPrompts benchmark (Lee et al., 2022), we demonstrate that REAL sampling based on a 70M THF model can substantially improve the factuality and diversity of 7B LLMs simultaneously. After combined with contrastive decoding, REAL sampling outperforms 13 sampling methods, and generates texts that are more factual than the greedy sampling and more diverse than the nucleus sampling with p = 0.5.<\/jats:p>","DOI":"10.1162\/tacl_a_00757","type":"journal-article","created":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T13:50:43Z","timestamp":1753192243000},"page":"760-783","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":1,"title":["REAL Sampling: Boosting Factuality and Diversity of Open-ended\n                    Generation by Extrapolating the Entropy of an Infinitely Large\n                    LM"],"prefix":"10.1162","volume":"13","author":[{"given":"Haw-Shiuan","family":"Chang","sequence":"first","affiliation":[{"name":"UMass Amherst CICS, USA. hschang@cs.umass.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nanyun","family":"Peng","sequence":"additional","affiliation":[{"name":"Amazon AGI Foundations, USA. pengnany@amazon.com"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohit","family":"Bansal","sequence":"additional","affiliation":[{"name":"Amazon AGI Foundations, USA. mobansal@amazon.com"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anil","family":"Ramakrishna","sequence":"additional","affiliation":[{"name":"Amazon AGI Foundations, USA. aniramak@amazon.com"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tagyoung","family":"Chung","sequence":"additional","affiliation":[{"name":"Amazon AGI Foundations, USA. tagyoung@amazon.com"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","published-online":{"date-parts":[[2025,7,18]]},"reference":[{"key":"2025072209503517000_bib1","article-title":"Do language models know when they\u2019re\n                        hallucinating references?","author":"Agrawal","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib2","article-title":"Characterizing attribution and fluency tradeoffs for\n                        retrieval-augmented large language models","volume":"abs\/2302.05578","author":"Aksitov","year":"2023","journal-title":"ArXiv\n                        preprint"},{"key":"2025072209503517000_bib3","article-title":"The stable entropy hypothesis and\n                        entropy-aware decoding: An analysis and algorithm for robust natural\n                        language generation","author":"Arora","year":"2023","journal-title":"arXiv preprint\n                        arXiv:2302.06784"},{"key":"2025072209503517000_bib4","doi-asserted-by":"publisher","DOI":"10.18653\/v1\/2023.findings-emnlp.68","article-title":"The internal state of an llm knows when\n                        its lying","author":"Azaria","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib5","article-title":"Mirostat: A neural text decoding algorithm\n                        that directly controls perplexity","volume-title":"Proceedings of\n                        the 9th International Conference on Learning Representations\n                    (ICLR)","author":"Basu","year":"2021"},{"key":"2025072209503517000_bib6","doi-asserted-by":"publisher","first-page":"108","DOI":"10.18653\/v1\/2023.bigpicture-1.9","article-title":"It\u2019s MBR all the way down: Modern\n                        generation techniques through the lens of minimum bayes\n                    risk","volume-title":"Proceedings of the Big Picture\n                        Workshop","author":"Bertsch","year":"2023"},{"key":"2025072209503517000_bib7","article-title":"Emergent and predictable memorization in large language\n                        models","author":"Biderman","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib8","first-page":"2397","article-title":"Pythia: A suite for analyzing large language\n                        models across training and scaling","volume-title":"International\n                        Conference on Machine Learning","author":"Biderman","year":"2023"},{"key":"2025072209503517000_bib9","article-title":"Discovering latent knowledge in language\n                        models without supervision","volume-title":"The Eleventh\n                        International Conference on Learning\n                    Representations","author":"Burns","year":"2022"},{"key":"2025072209503517000_bib10","article-title":"Do androids know they\u2019re only\n                        dreaming of electric sheep?","author":"CH-Wang","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib11","article-title":"Kl- divergence guided temperature sampling","author":"Chang","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib12","doi-asserted-by":"publisher","DOI":"10.18653\/v1\/2024.emnlp-main.484","article-title":"Explaining and improving contrastive decoding\n                        by extrapolating the probabilities of a huge and hypothetical\n                        lm","volume-title":"Proceedings of the 2024 Conference on\n                        Empirical Methods in Natural Language Processing","author":"Chang","year":"2024"},{"key":"2025072209503517000_bib13","doi-asserted-by":"publisher","first-page":"1749","DOI":"10.1007\/s10994-020-05897-1","article-title":"Using error decay prediction to overcome\n                        practical issues of deep active learning for named entity\n                        recognition","volume":"109","author":"Chang","year":"2020","journal-title":"Machine Learning"},{"key":"2025072209503517000_bib14","article-title":"Fidelity- enriched contrastive search: Reconciling the\n                        faithfulness-diversity trade-off in text generation","author":"Chen","year":"2023","journal-title":"arXiv preprint arXiv:2310.14981"},{"key":"2025072209503517000_bib15","doi-asserted-by":"publisher","DOI":"10.18653\/v1\/2023.findings-emnlp.599","article-title":"A closer look into automatic evaluation using large language\n                        models","volume-title":"EMNLP 2023 Findings","author":"Chiang","year":"2023"},{"key":"2025072209503517000_bib16","article-title":"DoLa: Decoding by contrasting layers improves factuality in\n                        large language models","author":"Chuang","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib17","article-title":"Entropy guided extrapolative decoding to\n                        improve factuality in large language models","author":"Das","year":"2024","journal-title":"arXiv\n                        preprint arXiv:2404.09338"},{"key":"2025072209503517000_bib18","doi-asserted-by":"publisher","DOI":"10.1002\/9781118625590","volume-title":"Applied Regression Analysis","author":"Draper","year":"1998"},{"key":"2025072209503517000_bib19","doi-asserted-by":"publisher","first-page":"2197","DOI":"10.18653\/v1\/2021.emnlp-main.168","article-title":"Neural path hunter: Reducing hallucination in dialogue\n                        systems via path grounding","volume-title":"Proceedings of the\n                        2021 Conference on Empirical Methods in Natural Language\n                    Processing","author":"Dziri","year":"2021"},{"key":"2025072209503517000_bib20","doi-asserted-by":"crossref","first-page":"889","DOI":"10.18653\/v1\/P18-1082","article-title":"Hierarchical neural story\n                        generation","volume-title":"Proceedings of the 56th Annual\n                        Meeting of the Association for Computational Linguistics (Volume 1: Long\n                        Papers)","author":"Fan","year":"2018"},{"key":"2025072209503517000_bib21","doi-asserted-by":"publisher","first-page":"94","DOI":"10.18653\/v1\/W17-4912","article-title":"Controlling linguistic style aspects in\n                        neural language generation","volume-title":"Proceedings of the\n                        Workshop on Stylistic Variation","author":"Ficler","year":"2017"},{"issue":"1","key":"2025072209503517000_bib22","doi-asserted-by":"publisher","first-page":"87","DOI":"10.2307\/2340521","article-title":"On the interpretation of\n                            \u03c7 2 from contingency tables, and the calculation\n                        of p","volume":"85","author":"Fisher","year":"1922","journal-title":"Journal of the Royal Statistical\n                        Society"},{"key":"2025072209503517000_bib23","article-title":"OpenLLaMA: An open reproduction of\n                    LLaMA","author":"Geng","year":"2023"},{"key":"2025072209503517000_bib24","article-title":"Language models hallucinate, but may excel at fact\n                        verification","author":"Guan","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib25","doi-asserted-by":"publisher","first-page":"103","DOI":"10.18653\/v1\/W18-5516","article-title":"UKP-athene: Multi-sentence textual\n                        entailment for claim verification","volume-title":"Proceedings of\n                        the First Workshop on Fact Extraction and VERification (FEVER)","author":"Hanselowski","year":"2018"},{"key":"2025072209503517000_bib26","doi-asserted-by":"publisher","first-page":"3414","DOI":"10.18653\/v1\/2022.findings-emnlp.249","article-title":"Truncation sampling as language model\n                        desmoothing","volume-title":"Findings of the Association for\n                        Computational Linguistics: EMNLP 2022","author":"Hewitt","year":"2022"},{"key":"2025072209503517000_bib27","article-title":"The curious case of neural text degeneration","volume-title":"8th International Conference on Learning Representations, ICLR 2020,\n                        Addis Ababa, Ethiopia, April 26\u201330, 2020","author":"Holtzman","year":"2020"},{"key":"2025072209503517000_bib28","article-title":"A survey on hallucination in large language models:\n                        Principles, taxonomy, challenges, and open questions","author":"Huang","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib29","article-title":"Scaling laws for neural language\n                        models","author":"Kaplan","year":"2020","journal-title":"arXiv preprint\n                    arXiv:2001.08361"},{"key":"2025072209503517000_bib30","first-page":"34586","article-title":"Factuality enhanced language models for\n                        open-ended text generation","volume":"35","author":"Lee","year":"2022","journal-title":"Advances in Neural\n                        Information Processing Systems"},{"key":"2025072209503517000_bib31","first-page":"110","article-title":"A diversity-promoting objective function for\n                        neural conversation models","volume-title":"Proceedings of the\n                        2016 Conference of the North American Chapter of the Association for\n                        Computational Linguistics: Human Language Technologies","author":"Li","year":"2016"},{"key":"2025072209503517000_bib32","article-title":"Inference-time intervention: Eliciting\n                        truthful answers from a language model","author":"Li","year":"2023","journal-title":"ArXiv\n                        preprint"},{"key":"2025072209503517000_bib33","article-title":"Contrastive decoding: Open-ended text\n                        generation as optimization","author":"Li","year":"2022","journal-title":"ArXiv preprint"},{"issue":"6624","key":"2025072209503517000_bib34","doi-asserted-by":"publisher","first-page":"1092","DOI":"10.1126\/science.abq1158","article-title":"Competition-level code generation with\n                        alphacode","volume":"378","author":"Li","year":"2022","journal-title":"Science"},{"key":"2025072209503517000_bib35","doi-asserted-by":"crossref","first-page":"6723","DOI":"10.18653\/v1\/2022.acl-long.464","article-title":"A token-level reference-free hallucination\n                        detection benchmark for free-form text generation","volume-title":"Proceedings of the 60th Annual Meeting of the Association for\n                        Computational Linguistics (Volume 1: Long Papers)","author":"Liu","year":"2022"},{"key":"2025072209503517000_bib36","article-title":"Open-domain text evaluation via contrastive distribution\n                        methods","volume-title":"Forty-first International Conference on\n                        Machine Learning","author":"Sidi","year":"2024"},{"key":"2025072209503517000_bib37","article-title":"Odysseus navigates the sirens\u2019 song: Dynamic focus\n                        decoding for factual and diverse open-ended text generation","author":"Luo","year":"2025","journal-title":"arXiv preprint arXiv:2503.08057"},{"key":"2025072209503517000_bib38","article-title":"SelfCheckGPT: Zero-resource black-box\n                        hallucination detection for generative large language\n                    models","author":"Manakul","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib39","doi-asserted-by":"publisher","first-page":"248","DOI":"10.18653\/v1\/2022.gem-1.21","article-title":"Unsupervised token-level hallucination\n                        detection from summary generation by-products","volume-title":"Proceedings of the 2nd Workshop on Natural Language Generation,\n                        Evaluation, and Metrics (GEM)","author":"Marfurt","year":"2022"},{"key":"2025072209503517000_bib40","article-title":"Typical decoding for natural language\n                        generation","author":"Meister","year":"2022","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib41","article-title":"A corpus and evaluation framework for deeper\n                        understanding of commonsense stories","author":"Mostafazadeh","year":"2016","journal-title":"ArXiv\n                        preprint"},{"key":"2025072209503517000_bib42","article-title":"Generating benchmarks for factuality\n                        evaluation of language models","author":"Muhlgay","year":"2023","journal-title":"ArXiv\n                        preprint"},{"key":"2025072209503517000_bib43","article-title":"Diversity of thought improves reasoning\n                        abilities of large language models","author":"Naik","year":"2023","journal-title":"arXiv preprint\n                        arXiv:2310.07088"},{"key":"2025072209503517000_bib44","unstructured":"OpenAI. 2023. GPT-4 technical\n                        report. arXiv preprint\n                    arXiv:2303.08774."},{"key":"2025072209503517000_bib45","article-title":"LLMs know more than they show: On the\n                        intrinsic representation of LLM hallucinations","author":"Orgad","year":"2024","journal-title":"arXiv preprint arXiv:2410.02707"},{"key":"2025072209503517000_bib46","article-title":"Language models are unsupervised multitask\n                        learners","author":"Radford","year":"2019"},{"key":"2025072209503517000_bib47","article-title":"The troubling emergence of hallucination in large language\n                        models\u2013an extensive definition, quantification, and prescriptive\n                        remediations","author":"Rawte","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib48","article-title":"Trusting your evidence: Hallucinate less with context-aware\n                        decoding","author":"Shi","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib49","article-title":"The curious case of hallucinatory\n                        unanswerablity: Finding truths in the hidden states of over-confident large\n                        language models","author":"Slobodkin","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib50","article-title":"Contrastive search is what you need for\n                        neural text generation","author":"Yixuan","year":"2022","journal-title":"arXiv preprint\n                        arXiv:2210.14140"},{"key":"2025072209503517000_bib51","article-title":"TrustLLM: Trustworthiness in large language\n                        models","author":"Sun","year":"2024"},{"key":"2025072209503517000_bib52","doi-asserted-by":"publisher","first-page":"809","DOI":"10.18653\/v1\/N18-1074","article-title":"FEVER: A large-scale dataset for fact\n                        extraction and VERification","volume-title":"Proceedings of the\n                        2018 Conference of the North American Chapter of the Association for\n                        Computational Linguistics: Human Language Technologies, Volume 1 (Long\n                        Papers)","author":"Thorne","year":"2018"},{"key":"2025072209503517000_bib53","article-title":"A comprehensive survey of hallucination mitigation techniques\n                        in large language models","author":"Tonmoy","year":"2024","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib54","article-title":"Unlocking anticipatory text generation: A constrained\n                        approach for faithful decoding with large language models","author":"Lifu","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib55","doi-asserted-by":"publisher","first-page":"5956","DOI":"10.18653\/v1\/2022.emnlp-main.399","article-title":"Mutual information alleviates\n                        hallucinations in abstractive summarization","volume-title":"Proceedings of the 2022 Conference on Empirical Methods in Natural\n                        Language Processing","author":"van der Poel","year":"2022"},{"key":"2025072209503517000_bib56","article-title":"A stitch in time saves nine: Detecting and\n                        mitigating hallucinations of llms by validating low-confidence\n                        generation","author":"Varshney","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib57","doi-asserted-by":"publisher","first-page":"2864","DOI":"10.18653\/v1\/2023.eacl-main.210","article-title":"Faithfulness-aware decoding strategies for\n                        abstractive summarization","volume-title":"Proceedings of the\n                        17th Conference of the European Chapter of the Association for Computational\n                        Linguistics","author":"Wan","year":"2023"},{"key":"2025072209503517000_bib58","article-title":"Self-consistency improves chain of thought reasoning in\n                        language models","volume-title":"The Eleventh International\n                        Conference on Learning Representations","author":"Wang","year":"2022"},{"key":"2025072209503517000_bib59","article-title":"Tree of thoughts: Deliberate problem\n                        solving with large language models","author":"Yao","year":"2023","journal-title":"ArXiv\n                        preprint"},{"key":"2025072209503517000_bib60","article-title":"Flow of reasoning: Training llms for divergent problem\n                        solving with minimal examples","author":"Fangxu","year":"2024","journal-title":"arXiv preprint\n                        arXiv:2406.05673"},{"key":"2025072209503517000_bib61","article-title":"How language model hallucinations can\n                        snowball","author":"Zhang","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib62","article-title":"EDT: Improving large language models\u2019\n                        generation by entropy-based dynamic temperature sampling","author":"Zhang","year":"2024","journal-title":"arXiv preprint arXiv:2403.14541"},{"key":"2025072209503517000_bib63","article-title":"OPT: Open pre-trained transformer language\n                        models","author":"Zhang","year":"2022"},{"key":"2025072209503517000_bib64","article-title":"MixCE: Training autoregressive language\n                        models by mixing forward and reverse cross-entropies","author":"Zhang","year":"2023","journal-title":"ArXiv preprint"},{"key":"2025072209503517000_bib65","article-title":"Weak-to-strong extrapolation expedites\n                        alignment","author":"Zheng","year":"2024","journal-title":"arXiv preprint\n                    arXiv:2404.16792"},{"key":"2025072209503517000_bib66","article-title":"Why does chatgpt fall short in providing\n                        truthful answers","author":"Zheng","year":"2023","journal-title":"ArXiv preprint,\n                        abs\/2304.10513"},{"key":"2025072209503517000_bib67","doi-asserted-by":"publisher","first-page":"1393","DOI":"10.18653\/v1\/2021.findings-acl.120","article-title":"Detecting hallucinated content in\n                        conditional neural sequence generation","volume-title":"Findings\n                        of the Association for Computational Linguistics: ACL-IJCNLP 2021","author":"Zhou","year":"2021"},{"key":"2025072209503517000_bib68","article-title":"Improving open-ended text generation via adaptive\n                        decoding","volume-title":"Forty-first International Conference on\n                        Machine Learning","author":"Zhu","year":"2024"}],"container-title":["Transactions of the Association for Computational Linguistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/direct.mit.edu\/tacl\/article-pdf\/doi\/10.1162\/tacl_a_00757\/2538234\/tacl_a_00757.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/direct.mit.edu\/tacl\/article-pdf\/doi\/10.1162\/tacl_a_00757\/2538234\/tacl_a_00757.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T13:50:50Z","timestamp":1753192250000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/tacl\/article\/doi\/10.1162\/tacl_a_00757\/131836\/REAL-Sampling-Boosting-Factuality-and-Diversity-of"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":68,"URL":"https:\/\/doi.org\/10.1162\/tacl_a_00757","relation":{},"ISSN":["2307-387X"],"issn-type":[{"value":"2307-387X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025]]},"published":{"date-parts":[[2025]]}}}