{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T12:12:51Z","timestamp":1783426371111,"version":"3.54.6"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T00:00:00Z","timestamp":1763942400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T00:00:00Z","timestamp":1763942400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. King Saud Univ. Comput. Inf. Sci."],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s44443-025-00353-3","type":"journal-article","created":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T10:46:25Z","timestamp":1763981185000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Adaptive heterogeneous multi-agent debate for enhanced educational and factual reasoning in large language models"],"prefix":"10.1007","volume":"37","author":[{"given":"Yan","family":"Zhou","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanguang","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,11,24]]},"reference":[{"key":"353_CR1","unstructured":"Brown T, Mann B, Ryder N, Subbiah M, Kaplan J.D, Dhariwal P, Neelakantan A, Shyam P, Sastry G, Askell A et al (2020) Language models are few-shot learners. Adv Neural Inf Process Syst 33:1877\u20131901"},{"key":"353_CR2","first-page":"1877","volume":"33","author":"T Brown","year":"2020","unstructured":"Brown T, Mann B, Ryder N, Subbiah M, Kaplan JD, Dhariwal P, Neelakantan A, Shyam P, Sastry G, Askell A et al (2020) Language models are few-shot learners. Adv Neural Inf Process Syst 33:1877\u20131901","journal-title":"Adv Neural Inf Process Syst"},{"key":"353_CR3","unstructured":"Kojima T, Gu SS, Reid M, Matsuo Y, Iwasawa Y (2022) Large language models are zero-shot reasoners. Adv Neural Inf Process Syst 35:22199\u201322213"},{"key":"353_CR4","doi-asserted-by":"crossref","unstructured":"Lin S, Hilton J, Evans O (2021) Truthfulqa: Measuring how models mimic human falsehoods. arXiv preprint arXiv:2109.07958","DOI":"10.18653\/v1\/2022.acl-long.229"},{"key":"353_CR5","doi-asserted-by":"crossref","unstructured":"Ji Z, Lee N, Frieske R, Yu T, Su D, Xu Y, Ishii E, Bang YJ, Madotto A, Fung P (2023) Survey of hallucination in natural language generation. ACM Comput Surv 55(12):1\u201338","DOI":"10.1145\/3571730"},{"key":"353_CR6","unstructured":"Ouyang L, Wu J, Jiang X, Almeida D, Wainwright C, Mishkin P, Zhang C, Agarwal S, Slama K, Ray A et al (2022) Training language models to follow instructions with human feedback. Adv Neural Inf Process Syst 35:27730\u201327744"},{"key":"353_CR7","unstructured":"Ziegler DM, Stiennon N, Wu J, Brown TB, Radford A, Amodei D, Christiano P, Irving G (2019) Fine-tuning language models from human preferences. arXiv preprint arXiv:1909.08593"},{"key":"353_CR8","unstructured":"Lee N, Ping W, Xu P, Patwary M, Fung P.N, Shoeybi M, Catanzaro B (2022) Factuality enhanced language models for open-ended text generation. Adv Neural Inf Process Syst 35:34586\u201334599"},{"key":"353_CR9","unstructured":"Kadavath S, Conerly T, Askell A, Henighan T, Drain D, Perez E, Schiefer N, Hatfield-Dodds Z, DasSarma N, Tran-Johnson E et al (2022) Language models (mostly) know what they know. arXiv preprint arXiv:2207.05221"},{"key":"353_CR10","unstructured":"Wei J, Wang X, Schuurmans D, Bosma M, Xia F, Chi E, Le QV, Zhou D et al (2022) Chain-of-thought prompting elicits reasoning in large language models. Adv Neural Inf Process Syst 35:24824\u201324837"},{"key":"353_CR11","unstructured":"Wang X, Wei J, Schuurmans D, Le Q, Chi E, Narang S, Chowdhery A, Zhou D (2022) Self-consistency improves chain of thought reasoning in language models. arXiv preprint arXiv:2203.11171"},{"key":"353_CR12","unstructured":"Nye M, Andreassen A.J, Gur-Ari G, Michalewski H, Austin J, Bieber D, Dohan D, Lewkowycz A, Bosma M, Luan D et al (2021) Show your work: Scratchpads for intermediate computation with language models"},{"key":"353_CR13","unstructured":"Yao S, Zhao J, Yu D, Du N, Shafran I, Narasimhan K, Cao Y (2023) React: Synergizing reasoning and acting in language models. In: International conference on learning representations (ICLR)"},{"key":"353_CR14","unstructured":"Schick T, Dwivedi-Yu J, Dess\u00ec R, Raileanu R, Lomeli M, Hambro E, Zettlemoyer L, Cancedda N, Scialom T (2023) Toolformer: Language models can teach themselves to use tools. Adv Neural Inf Process Syst 36:68539\u201368551"},{"issue":"12","key":"353_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3571730","volume":"55","author":"Z Ji","year":"2023","unstructured":"Ji Z, Lee N, Frieske R, Yu T, Su D, Xu Y, Ishii E, Bang YJ, Madotto A, Fung P (2023) Survey of hallucination in natural language generation. ACM Comput Surv 55(12):1\u201338","journal-title":"ACM Comput Surv"},{"key":"353_CR16","unstructured":"Stiennon N, Ouyang L, Wu J, Ziegler D, Lowe R, Voss C, Radford A, Amodei D, Christiano PF (2020) Learning to summarize with human feedback. Adv Neural Inf Process Syst 33:3008\u20133021"},{"key":"353_CR17","doi-asserted-by":"crossref","unstructured":"Siddiky MNA, Rahman ME, Hossen M, Rahman MR, Jaman MS (2025) Optimizing ai language models: a study of chatgpt-4 vs. chatgpt-4o. Preprints. org","DOI":"10.20944\/preprints202502.0066.v1"},{"key":"353_CR18","first-page":"568","volume-title":"International Conference on Advanced Robotics","author":"K Kawamura","year":"2003","unstructured":"Kawamura K, Noelle D, Hambuchen K, Rogers T, Turkay E (2003) A multi-agent approach to self-reflection for cognitive robotics. International Conference on Advanced Robotics. Coimbra, Portugal, pp 568\u2013575"},{"key":"353_CR19","unstructured":"Kawamura K, Noelle D, Hambuchen K, Rogers T, Turkay E (2003) A multi-agent approach to self-reflection for cognitive robotics. In: International Conference on Advanced Robotics, Coimbra, Portugal, pp 568\u2013575"},{"key":"353_CR20","first-page":"22199","volume":"35","author":"T Kojima","year":"2022","unstructured":"Kojima T, Gu SS, Reid M, Matsuo Y, Iwasawa Y (2022) Large language models are zero-shot reasoners. Adv Neural Inf Process Syst 35:22199\u201322213","journal-title":"Adv Neural Inf Process Syst"},{"key":"353_CR21","first-page":"34586","volume":"35","author":"N Lee","year":"2022","unstructured":"Lee N, Ping W, Xu P, Patwary M, Fung PN, Shoeybi M, Catanzaro B (2022) Factuality enhanced language models for open-ended text generation. Adv Neural Inf Process Syst 35:34586\u201334599","journal-title":"Adv Neural Inf Process Syst"},{"key":"353_CR22","unstructured":"Lewis P, Perez E, Piktus A, Petroni F, Karpukhin V, Goyal N, K\u00fcttler H, Lewis M, Yih W.-t, Rockt\u00e4schel T et al (2020) Retrieval-augmented generation for knowledge-intensive nlp tasks. Adv Neural Inf Process Syst 33:9459\u20139474"},{"key":"353_CR23","first-page":"51991","volume":"36","author":"G Li","year":"2023","unstructured":"Li G, Hammoud H, Itani H, Khizbullin D, Ghanem B (2023) Camel: Communicative agents for \u201cmind\u2019\u2019 exploration of large language model society. Adv Neural Inf Process Syst 36:51991\u201352008","journal-title":"Adv Neural Inf Process Syst"},{"key":"353_CR24","unstructured":"Khan A, Hughes J, Valentine D, Ruis L, Sachan K, Radhakrishnan A, Grefenstette E, Bowman SR, Rockt\u00e4schel T, Perez E (2024) Debating with more persuasive llms leads to more truthful answers. arXiv preprint arXiv:2402.06782"},{"key":"353_CR25","unstructured":"Li G, Hammoud H, Itani H, Khizbullin D, Ghanem B (2023) Camel: Communicative agents for \u201cmind\" exploration of large language model society. Adv Neural Inf Process Syst 36:51991\u201352008"},{"key":"353_CR26","first-page":"46534","volume":"36","author":"A Madaan","year":"2023","unstructured":"Madaan A, Tandon N, Gupta P, Hallinan S, Gao L, Wiegreffe S, Alon U, Dziri N, Prabhumoye S, Yang Y et al (2023) Self-refine: Iterative refinement with self-feedback. Adv Neural Inf Process Syst 36:46534\u201346594","journal-title":"Adv Neural Inf Process Syst"},{"key":"353_CR27","doi-asserted-by":"crossref","unstructured":"Parrish A, Trivedi H, Nangia N, Padmakumar V, Phang J, Saimbhi AS, Bowman SR (2022) Two-turn debate doesn\u2019t help humans answer hard reading comprehension questions. arXiv preprint arXiv:2210.10860","DOI":"10.18653\/v1\/2022.lnls-1.3"},{"key":"353_CR28","volume-title":"Society of mind","author":"M Minsky","year":"1986","unstructured":"Minsky M (1986) Society of mind. Simon and Schuster"},{"key":"353_CR29","unstructured":"Du Y, Li S, Torralba A, Tenenbaum JB, Mordatch I (2023) Improving factuality and reasoning in language models through multiagent debate. In: 41st international conference on machine learning"},{"key":"353_CR30","first-page":"27730","volume":"35","author":"L Ouyang","year":"2022","unstructured":"Ouyang L, Wu J, Jiang X, Almeida D, Wainwright C, Mishkin P, Zhang C, Agarwal S, Slama K, Ray A et al (2022) Training language models to follow instructions with human feedback. Adv Neural Inf Process Syst 35:27730\u201327744","journal-title":"Adv Neural Inf Process Syst"},{"key":"353_CR31","unstructured":"Zhang H, Du W, Shan J, Zhou Q, Du Y, Tenenbaum J.B, Shu T, Gan C (2023) Building cooperative embodied agents modularly with large language models. arXiv preprint arXiv:2307.02485"},{"key":"353_CR32","unstructured":"Wu Q, Bansal G, Zhang J, Wu Y, Li B, Zhu E, Jiang L, Zhang X, Zhang S, Liu J et al (2024) Autogen: Enabling next-gen llm applications via multi-agent conversations. In: 1st conference on language modeling"},{"key":"353_CR33","unstructured":"Zelikman E, Wu Y, Mu J, Goodman N (2022) Star: Bootstrapping reasoning with reasoning. Adv Neural Inf Process Syst 35:15476\u201315488"},{"key":"353_CR34","first-page":"68539","volume":"36","author":"T Schick","year":"2023","unstructured":"Schick T, Dwivedi-Yu J, Dess\u00ec R, Raileanu R, Lomeli M, Hambro E, Zettlemoyer L, Cancedda N, Scialom T (2023) Toolformer: Language models can teach themselves to use tools. Adv Neural Inf Process Syst 36:68539\u201368551","journal-title":"Adv Neural Inf Process Syst"},{"key":"353_CR35","unstructured":"Guu K, Lee K, Tung Z, Pasupat P, Chang M (2020) Realm: Retrieval-augmented language model pre. Training"},{"key":"353_CR36","unstructured":"Lewis P, Perez E, Piktus A, Petroni F, Karpukhin V, Goyal N, K\u00fcttler H, Lewis M, Yih W.-t, Rockt\u00e4schel T et al (2020) Retrieval-augmented generation for knowledge-intensive nlp tasks. Adv Neural Inf Process Syst 33:9459\u20139474"},{"key":"353_CR37","first-page":"3008","volume":"33","author":"N Stiennon","year":"2020","unstructured":"Stiennon N, Ouyang L, Wu J, Ziegler D, Lowe R, Voss C, Radford A, Amodei D, Christiano PF (2020) Learning to summarize with human feedback. Adv Neural Inf Process Syst 33:3008\u20133021","journal-title":"Adv Neural Inf Process Syst"},{"key":"353_CR38","unstructured":"Hendrycks D, Burns C, Kadavath S, Arora A, Basart S, Tang E, Song D, Steinhardt J (2021) Measuring mathematical problem solving with the math dataset. arXiv preprint arXiv:2103.03874"},{"key":"353_CR39","unstructured":"Minsky M (1986) Society of mind. Simon and Schuster"},{"key":"353_CR40","unstructured":"Wei J, Wang X, Schuurmans D, Bosma M, Xia F, Chi E, Le QV, Zhou D et al (2022) Chain-of-thought prompting elicits reasoning in large language models. Adv Neural Inf Process Syst 35:24824\u201324837"},{"key":"353_CR41","unstructured":"Wei J, Wang X, Schuurmans D, Bosma M, Xia F, Chi E, Le QV, Zhou D et al (2022) Chain-of-thought prompting elicits reasoning in large language models. Adv Neural Inf Process Syst 35:24824\u201324837"},{"key":"353_CR42","unstructured":"Li S, Du Y, Tenenbaum JB, Torralba A, Mordatch I (2022) Composing ensembles of pre-trained models via iterative consensus. arXiv preprint arXiv:2210.11522"},{"key":"353_CR43","unstructured":"Sabour S, Frosst N, Hinton GE (2017) Dynamic routing between capsules. Adv Neural Inf Process Syst 30"},{"key":"353_CR44","unstructured":"Hendrycks D, Burns C, Basart S, Zou A, Mazeika M, Song D, Steinhardt J (2020) Measuring massive multitask language understanding. arXiv preprint arXiv:2009.03300"},{"key":"353_CR45","unstructured":"Hurst A, Lerer A, Goucher AP, Perelman A, Ramesh A, Clark A, Ostrow A, Welihinda A, Hayes A, Radford A et al (2024) Gpt-4o system card. arXiv preprint arXiv:2410.21276"},{"key":"353_CR46","unstructured":"Irving G, Christiano P, Amodei D (2018) Ai safety via debate. arXiv preprint arXiv:1805.00899"}],"container-title":["Journal of King Saud University Computer and Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44443-025-00353-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s44443-025-00353-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44443-025-00353-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T18:47:34Z","timestamp":1767638854000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s44443-025-00353-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,24]]},"references-count":46,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["353"],"URL":"https:\/\/doi.org\/10.1007\/s44443-025-00353-3","relation":{},"ISSN":["1319-1578","2213-1248"],"issn-type":[{"value":"1319-1578","type":"print"},{"value":"2213-1248","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,24]]},"assertion":[{"value":"14 August 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 October 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 November 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"330"}}