Implicit Reasoning in Large Language Models: A Comprehensive Survey
Paper · 2025 · Jindong Li, Yali Fu, Li Fan et al.
Summary
Chain-of-Thought prompting makes LLMs write out every intermediate step, which inflates output length, latency and cost. This survey covers a growing alternative, implicit reasoning, in which a model carries out multi-step inference within its hidden states or layers instead of producing textual traces. Earlier reviews mostly concentrated on explicit reasoning or grouped latent methods by representation type. The authors instead propose an execution-centred taxonomy that asks how and where the internal computation actually happens. They sort the literature into three paradigms: latent optimization (at token, trajectory and internal-state granularity), signal-guided control (inserting special tokens of one or several kinds), and layer-recurrent execution (reusing transformer blocks in loops). They also collect structural, behavioral and representation-level evidence that LLMs genuinely reason silently, and they catalogue the metrics and benchmarks in use. No new model or dataset is introduced. The contribution is a unified map of a fragmented field plus a list of open problems, such as opacity, an accuracy gap versus explicit CoT, and inconsistent evaluation.
Key points
- Three paradigms, with representative methods:
- Latent optimization: Coconut, CODI, CCoT, LightThinker, SoftCoT.
- Signal-guided control: Pause Tokens, Filler Tokens, Planning Tokens, Quiet-STaR.
- Layer-recurrent execution: looped Transformer, CoTFormer, Huginn, ITT.
- Three kinds of evidence for silent reasoning:
- Layer-wise structural evidence, e.g. Jump to Conclusions and Internal Chain-of-Thought.
- Behavioral signatures, e.g. Grokked Transformer and step-skipping.
- Representation-based analysis, e.g. MechanisticProbe, steering vectors and backward chaining circuits.
- Benchmarks in five groups: commonsense, math/programming, language modeling and reading comprehension, multi-hop QA, and multimodal tasks. More than 70 datasets appear across studies, often as self-curated subsets, even though shared sets like GSM8K, CommonsenseQA and HotpotQA exist.
- Six listed challenges: opacity, weak controllability, a performance gap behind CoT, no standard evaluation, architecture and scale constraints (mostly small models), and reliance on explicit CoT supervision during training.
- Living resource: a maintained paper list at github.com/digailab/awesome-llm-implicit-reasoning.
Fields, topics and concepts
📚 Shelves 5The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 worksComputer Vision and Pattern Recognition · 2,869 works
🧭 Topics 2Research subjects and languages the work is about.Language models & pretraining · 3,320 worksReasoning · 1,426 works
Cite
Cite as Jindong Li, Yali Fu, Li Fan, Jiahong Liu, Yao Shu, Chengwei Qin, Menglin Yang, Irwin King and Rex Ying. 2025. Implicit Reasoning in Large Language Models: A Comprehensive Survey. arXiv:2509.02350.
@misc{li2025implicit,
title = {{Implicit Reasoning in Large Language Models: A Comprehensive Survey}},
author = {Jindong Li, Yali Fu, Li Fan, Jiahong Liu, Yao Shu, Chengwei Qin, Menglin Yang, Irwin King and Rex Ying},
year = {2025},
doi = {10.48550/arxiv.2509.02350},
eprint = {2509.02350},
archivePrefix = {arXiv},
url = {https://doi.org/10.48550/arxiv.2509.02350}
}References
- American invitational mathematics examination. — Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone https://artofproblemsolving.com/wiki/index.php/ American_Invitational_Mathematics_Examination. Marah Abdin, Jyoti Aneja, Hany Awadalla, Ahmed Awadallah, Ammar Ahmad Awan, Nguyen Bach, Amit Bahree, Arash Bakhtiari, Jianmin Bao, Harkirat Behl, et al. Phi-… ↗
- Janice Ahn, Rishu Verma, Renze Lou, Di Liu, Rui Zhang, and Wenpeng Yin. Large language models for mathematical reasoning: Progresses and challenges. In Proceedings of the 18th Conference of the European Chapter of the Association for Computational Linguistics: Student Research Workshop, pp. 225–237,…
- Aida Amini, Saadia Gabriel, Shanchuan Lin, Rik Koncel-Kedziorski, Yejin Choi, and Hannaneh Hajishirzi. Mathqa: Towards interpretable math word problem solving with operation-based formalisms. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Lin…
- Benjamin Arnav, Pablo Bernabeu-Pérez, Nathan Helm-Burger, Tim Kostolansky, Hannes Whittingham, and Mary Phuong. Cot red-handed: Stress testing chain-of-thought monitoring. arXiv preprint arXiv:2505.23575, 2025. — [arXiv:2505.23575](https://arxiv.org/abs/2505.23575) find
- Jacob Austin, Augustus Odena, Maxwell Nye, Maarten Bosma, Henryk Michalewski, David Dohan, Ellen Jiang, Carrie Cai, Michael Terry, Quoc Le, et al. Program synthesis with large language models. arXiv preprint arXiv:2108.07732, 2021.
- Jonathan Berant, Andrew Chou, Roy Frostig, and Percy Liang. Semantic parsing on freebase from question-answer pairs. In Proceedings of the 2013 conference on empirical methods in natural language processing, pp. 1533–1544, 2013.
- Bespoke Labs. Bespoke-stratos: The unreasonable effectiveness of reasoning distillation. https://www.bespokelabs.ai/blog/bespoke-stratos-the-unreasonable-effectiveness-of-reasoning-distillation, 2025. Accessed: 2025-06-25. ↗
- Stella Biderman, Hailey Schoelkopf, Quentin Gregory Anthony, Herbie Bradley, Kyle O’Brien, Eric Hallahan, Mohammad Aflah Khan, Shivanshu Purohit, USVSN Sai Prashanth, Edward Raff, et al. Pythia: A suite for analyzing large language models across training and scaling. In International Conference on M… find
- Yonatan Bisk, Rowan Zellers, Jianfeng Gao, Yejin Choi, et al. Piqa: Reasoning about physical commonsense in natural language. In Proceedings of the AAAI conference on artificial intelligence, volume 34, pp. 7432–7439, 2020.
- Jan A Botha, Manaal Faruqui, John Alex, Jason Baldridge, and Dipanjan Das. Learning to split and rephrase from wikipedia edit history. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pp. 732–737, 2018. find
- Jannik Brinkmann, Abhay Sheshadri, Victor Levoso, Paul Swoboda, and Christian Bartelt. A mechanistic analysis of a transformer trained on a symbolic multi-step reasoning task. In Findings of the Association for Computational Linguistics ACL 2024, pp. 4082–4102, 2024. find
- Ciprian Chelba, Tomas Mikolov, Mike Schuster, Qi Ge, Thorsten Brants, Phillipp Koehn, and Tony Robinson. One billion word benchmark for measuring progress in statistical language modeling. arXiv preprint arXiv:1312.3005, 2013.
- Haolin Chen, Yihao Feng, Zuxin Liu, Weiran Yao, Akshara Prabhakar, Shelby Heinecke, Ricky Ho, Phil Mui, Silvio Savarese, Caiming Xiong, et al. Language models are hidden reasoners: Unlocking latent reasoning capabilities via self-rewarding. arXiv preprint arXiv:2411.04282, 2024a. — [arXiv:2411.04282](https://arxiv.org/abs/2411.04282) find
- Lin Chen, Jinsong Li, Xiaoyi Dong, Pan Zhang, Yuhang Zang, Zehui Chen, Haodong Duan, Jiaqi Wang, Yu Qiao, Dahua Lin, et al. Are we on the right way for evaluating large vision-language models? In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024b.
- Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde De Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, et al. Evaluating large language models trained on code. arXiv preprint arXiv:2107.03374, 2021.
- Qiguang Chen, Libo Qin, Jinhao Liu, Dengyun Peng, Jiannan Guan, Peng Wang, Mengkang Hu, Yuhang Zhou, Te Gao, and Wanxiang Che. Towards reasoning era: A survey of long chain-of-thought for reasoning large language models. arXiv preprint arXiv:2503.09567, 2025a.
- Wenhu Chen, Ming Yin, Max Ku, Pan Lu, Yixin Wan, Xueguang Ma, Jianyu Xu, Xinyi Wang, and Tony Xia. Theoremqa: A theorem-driven question answering dataset. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pp. 7889–7901, 2023.
- Xinghao Chen, Anhao Zhao, Heming Xia, Xuan Lu, Hanlin Wang, Yanjun Chen, Wei Zhang, Jian Wang, Wenjie Li, and Xiaoyu Shen. Reasoning beyond language: A comprehensive survey on latent chain-of-thought reasoning. arXiv preprint arXiv:2505.16782, 2025b. — [arXiv:2505.16782](https://arxiv.org/abs/2505.16782) find
- Yilong Chen, Junyuan Shang, Zhenyu Zhang, Yanxi Xie, Jiawei Sheng, Tingwen Liu, Shuohuan Wang, Yu Sun, Hua Wu, and Haifeng Wang. Inner thinking transformer: Leveraging dynamic depth scaling to foster adaptive internal thinking. arXiv preprint arXiv:2502.13842, 2025c.
- Jeffrey Cheng and Benjamin Van Durme. Compressed chain of thought: Efficient reasoning through dense representations. arXiv preprint arXiv:2412.13171, 2024. find
- Eunsol Choi, He He, Mohit Iyyer, Mark Yatskar, Wen-tau Yih, Yejin Choi, Percy Liang, and Luke Zettlemoyer. Quac: Question answering in context. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pp. 2174–2184, 2018.
- Christopher Clark, Kenton Lee, Ming-Wei Chang, Tom Kwiatkowski, Michael Collins, and Kristina Toutanova. Boolq: Exploring the surprising difficulty of natural yes/no questions. In Proceedings of NAACL-HLT, pp. 2924–2936, 2019.
- Jonathan H Clark, Eunsol Choi, Michael Collins, Dan Garrette, Tom Kwiatkowski, Vitaly Nikolaev, and Jennimaria Palomaki. Tydi qa: A benchmark for information-seeking question answering in ty pologically di verse languages. Transactions of the Association for Computational Linguistics, 8:454–470, 202… find
- Peter Clark, Isaac Cowhey, Oren Etzioni, Tushar Khot, Ashish Sabharwal, Carissa Schoenick, and Oyvind Tafjord. Think you have solved question answering? try arc, the ai2 reasoning challenge. arXiv preprint arXiv:1803.05457, 2018.
- Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, et al. Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168, 2021.
- Arman Cohan, Franck Dernoncourt, Doo Soon Kim, Trung Bui, Seokhwan Kim, Walter Chang, and Nazli Goharian. A discourse-aware attention model for abstractive summarization of long documents. In Proceedings of NAACL-HLT, pp. 615–621, 2018.
- Foundational Contributors, Ahmed El-Kishky, Daniel Selsam, Francis Song, Giambattista Parascandolo, Hongyu Ren, Hunter Lightman, Hyung Won, Ilge Akkaya, Ilya Sutskever, Jason Wei, Jonathan Gordon, Karl Cobbe, Kevin Yu, Lukasz Kondraciuk, Max Schwarzer, Mostafa Rohaninejad, Noam Brown, Shengjia Zhao,… — OpenAI o1 System Card
- Russell Cooper and Andrew A John. Macroeconomics: Theory through applications. 2012 Book Archive, 2013. find
- Ganqu Cui, Lifan Yuan, Ning Ding, Guanming Yao, Wei Zhu, Yuan Ni, Guotong Xie, Zhiyuan Liu, and Maosong Sun. Ultrafeedback: Boosting language models with high-quality feedback. CoRR, 2023. find
- Hoagy Cunningham, Aidan Ewart, Logan Riggs, Robert Huben, and Lee Sharkey. Sparse autoencoders find highly interpretable features in language models. arXiv preprint arXiv:2309.08600, 2023. find
- DeepSeek-AI. Deepseek-v3.1 model card. Hugging Face model card, 2025. URL https://huggingface.co/deepseek-ai/DeepSeek-V3.1. Hybrid thinking/non-thinking inference, improved tool use and agent tasks, long-context extension (128 K), FP8 format. ↗
- Yuntian Deng, Kiran Prasad, Roland Fernandez, Paul Smolensky, Vishrav Chaudhary, and Stuart Shieber. Implicit chain of thought reasoning via knowledge distillation. arXiv preprint arXiv:2311.01460, 2023. find
- Yuntian Deng, Yejin Choi, and Stuart Shieber. From explicit cot to implicit cot: Learning to internalize cot step by step. arXiv preprint arXiv:2405.14838, 2024. find
- Alexander Yom Din, Taelin Karidi, Leshem Choshen, and Mor Geva. Jump to conclusions: Short-cutting transformers with linear transformations. In LREC/COLING, 2024. find
- Dheeru Dua, Yizhong Wang, Pradeep Dasigi, Gabriel Stanovsky, Sameer Singh, and Matt Gardner. Drop: A reading comprehension benchmark requiring discrete reasoning over paragraphs. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Hum…
- Scott Emmons, Erik Jenner, David K Elson, Rif A Saurous, Senthooran Rajamanoharan, Heng Chen, Irhum Shafkat, and Rohin Shah. When chain of thought is necessary, language models struggle to evade monitors. arXiv preprint arXiv:2507.05246, 2025. — [arXiv:2507.05246](https://arxiv.org/abs/2507.05246) find
- Gongfan Fang, Xinyin Ma, and Xinchao Wang. Thinkless: Llm learns when to think, 2025a. URL https://arxiv.org/abs/2505.13379. — [arXiv:2505.13379](https://arxiv.org/abs/2505.13379) ↗
- Xi Fang, Weijie Xu, Fiona Anting Tan, Ziqing Hu, Jiani Zhang, Yanjun Qi, Srinivasan H Sengamedu, and Christos Faloutsos. Large language models (llms) on tabular data: Prediction, generation, and understanding-a survey. Transactions on Machine Learning Research, 2025b. find
- Sicheng Feng, Gongfan Fang, Xinyin Ma, and Xinchao Wang. Efficient reasoning models: A survey. arXiv preprint arXiv:2504.10903, 2025.
- Leo Gao, Stella Biderman, Sid Black, Laurence Golding, Travis Hoppe, Charles Foster, Jason Phang, Horace He, Anish Thite, Noa Nabeshima, et al. The pile: An 800gb dataset of diverse text for language modeling. arXiv preprint arXiv:2101.00027, 2020. find
- Luyu Gao, Aman Madaan, Shuyan Zhou, Uri Alon, Pengfei Liu, Yiming Yang, Jamie Callan, and Graham Neubig. Pal: Program-aided language models. In International Conference on Machine Learning, pp. 10764–10799. PMLR, 2023. find
- Jonas Geiping, Sean McLeish, Neel Jain, John Kirchenbauer, Siddharth Singh, Brian R Bartoldson, Bhavya Kailkhura, Abhinav Bhatele, and Tom Goldstein. Scaling up test-time compute with latent reasoning: A recurrent depth approach. arXiv preprint arXiv:2502.05171, 2025. find
- Mor Geva, Daniel Khashabi, Elad Segal, Tushar Khot, Dan Roth, and Jonathan Berant. Did aristotle use a laptop? a question answering benchmark with implicit reasoning strategies. Transactions of the Association for Computational Linguistics, 9:346–361, 2021. find
- Aaron Gokaslan and Vanya Cohen. OpenWebTextCorpus, 2019. find
- Openwebtext corpus. http://skylion007.github.io/Zhuocheng Gong, Jian Guan, Wei Wu, Huishuai Zhang, and Dongyan Zhao. Latent preference coding: Aligning large language models via discrete latent codes. arXiv preprint arXiv:2505.04993, 2025. — [arXiv:2505.04993](https://arxiv.org/abs/2505.04993) ↗
- Sachin Goyal, Ziwei Ji, Ankit Singh Rawat, Aditya Krishna Menon, Sanjiv Kumar, and Vaishnavh Nagarajan. Think before you speak: Training language models with pause tokens. In The Twelfth International Conference on Learning Representations, 2024. find
- Halil Alperen Gozeten, M Emrullah Ildiz, Xuechen Zhang, Hrayr Harutyunyan, Ankit Singh Rawat, and Samet Oymak. Continuous chain of thought enables parallel exploration and reasoning. arXiv preprint arXiv:2505.23648, 2025. — [arXiv:2505.23648](https://arxiv.org/abs/2505.23648) find
- Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, et al. The llama 3 herd of models. arXiv preprint arXiv:2407.21783, 2024.
- Alex Graves and Alex Graves. Long short-term memory. Supervised sequence labelling with recurrent neural networks, pp. 37–45, 2012. find
- Tianrui Guan, Fuxiao Liu, Xiyang Wu, Ruiqi Xian, Zongxia Li, Xiaoyu Liu, Xijun Wang, Lichang Chen, Furong Huang, Yaser Yacoob, et al. Hallusionbench: an advanced diagnostic suite for entangled language hallucination and visual illusion in large vision-language models. In Proceedings of the IEEE/CVF…
- Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, et al. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning. arXiv preprint arXiv:2501.12948, 2025.
- Thilo Hagendorff and Sarah Fabi. Beyond chains of thought: Benchmarking latent-space reasoning abilities in large language models. arXiv preprint arXiv:2504.10615, 2025. — [arXiv:2504.10615](https://arxiv.org/abs/2504.10615) find
- Shibo Hao, Sainbayar Sukhbaatar, DiJia Su, Xian Li, Zhiting Hu, Jason Weston, and Yuandong Tian. Training large language models to reason in a continuous latent space. arXiv preprint arXiv:2412.06769, 2024. find
- Chaoqun He, Renjie Luo, Yuzhuo Bai, Shengding Hu, Zhen Thai, Junhao Shen, Jinyi Hu, Xu Han, Yujie Huang, Yuxiang Zhang, et al. Olympiadbench: A challenging benchmark for promoting agi with olympiad-level bilingual multimodal scientific problems. In Proceedings of the 62nd Annual Meeting of the Assoc…
- Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Jacob Steinhardt. Measuring massive multitask language understanding. In International Conference on Learning Representations, 2021a.
- Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. Measuring mathematical problem solving with the math dataset. In Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 2), 2021b.
- David Herel and Tomas Mikolov. Thinking tokens for language modeling. arXiv preprint arXiv:2405.08644, 2024. — [arXiv:2405.08644](https://arxiv.org/abs/2405.08644) find
- Tuomo Hiippala, Malihe Alikhani, Jonas Haverinen, Timo Kalliokoski, Evanfiya Logacheva, Serafina Orekhova, Aino Tuomainen, Matthew Stone, and John A Bateman. Ai2d-rst: a multimodal corpus of 1000 primary school science diagrams. Language Resources and Evaluation, 55:661–688, 2021. find
- Xanh Ho, Anh-Khoa Duong Nguyen, Saku Sugawara, and Akiko Aizawa. Constructing a multi-hop qa dataset for comprehensive evaluation of reasoning steps. In Proceedings of the 28th International Conference on Computational Linguistics, pp. 6609–6625, 2020.
- Jialiang Hong, Taihang Zhen, Kai Chen, Jiaheng Liu, Wenpeng Zhu, Jing Huo, Yang Gao, Depeng Wang, Haitao Wan, Xi Yang, et al. Reconsidering overthinking: Penalizing internal and external redundancy in cot reasoning. arXiv preprint arXiv:2508.02178, 2025. — [arXiv:2508.02178](https://arxiv.org/abs/2508.02178) find
- Mohammad Javad Hosseini, Hannaneh Hajishirzi, Oren Etzioni, and Nate Kushman. Learning to solve arithmetic word problems with verb categorization. In Proceedings of the 2014 conference on empirical methods in natural language processing (EMNLP), pp. 523–533, 2014.
- Yifan Hou, Jiaoda Li, Yu Fei, Alessandro Stolfo, Wangchunshu Zhou, Guangtao Zeng, Antoine Bosselut, and Mrinmaya Sachan. Towards a mechanistic interpretation of multi-step reasoning capabilities of language models. arXiv preprint arXiv:2310.14491, 2023. find
- Yupeng Hou, Jiacheng Li, Zhankui He, An Yan, Xiusi Chen, and Julian McAuley. Bridging language and items for retrieval and recommendation. arXiv preprint arXiv:2403.03952, 2024. — [arXiv:2403.03952](https://arxiv.org/abs/2403.03952) find
- Aaron Hurst, Adam Lerer, Adam P Goucher, Adam Perelman, Aditya Ramesh, Aidan Clark, AJ Ostrow, Akila Welihinda, Alan Hayes, Alec Radford, et al. Gpt-4o system card. arXiv preprint arXiv:2410.21276, 2024.
- Naman Jain, King Han, Alex Gu, Wen-Ding Li, Fanjia Yan, Tianjun Zhang, Sida Wang, Armando Solar-Lezama, Koushik Sen, and Ion Stoica. Livecodebench: Holistic and contamination free evaluation of large language models for code. In The Thirteenth International Conference on Learning Representations, 20…
- Mojan Javaheripi, Sébastien Bubeck, Marah Abdin, Jyoti Aneja, Sebastien Bubeck, Caio César Teodoro Mendes, Weizhu Chen, Allie Del Giorno, Ronen Eldan, Sivakanth Gopi, et al. Phi-2: The surprising power of small language models. Microsoft Research Blog, 1(3):3, 2023. find
- 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
- Mingyu Jin, Weidi Luo, Sitao Cheng, Xinyi Wang, Wenyue Hua, Ruixiang Tang, William Yang Wang, and Yongfeng Zhang. Disentangling memory and reasoning ability in large language models. arXiv preprint arXiv:2411.13504, 2024.
- Mandar Joshi, Eunsol Choi, Daniel S Weld, and Luke Zettlemoyer. 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), pp. 1601–1611, 2017.
- Andrej Karpathy. nanogpt: The simplest, fastest repository for training/finetuning medium-sized gpts. https://github.com/karpathy/nanoGPT, 2023. Accessed: 2025-06-28. ↗
- Aniruddha Kembhavi, Mike Salvato, Eric Kolve, Minjoon Seo, Hannaneh Hajishirzi, and Ali Farhadi. A diagram is worth a dozen images. In European conference on computer vision, pp. 235–251. Springer, 2016.
- Eunki Kim, Sangryul Kim, and James Thorne. Learning to insert [pause] tokens for better reasoning. arXiv preprint arXiv:2506.03616, 2025. find
- Tomáš Kočiskỳ, Jonathan Schwarz, Phil Blunsom, Chris Dyer, Karl Moritz Hermann, Gábor Melis, and Edward Grefenstette. The narrativeqa reading comprehension challenge. Transactions of the Association for Computational Linguistics, 6:317–328, 2018.
- Rik Koncel-Kedziorski, Hannaneh Hajishirzi, Ashish Sabharwal, Oren Etzioni, and Siena Dumas Ang. Parsing algebraic word problems into equations. Transactions of the Association for Computational Linguistics, 3:585–597, 2015. find
- Rik Koncel-Kedziorski, Subhro Roy, Aida Amini, Nate Kushman, and Hannaneh Hajishirzi. Mawps: A math word problem repository. In Proceedings of the 2016 conference of the north american chapter of the association for computational linguistics: human language technologies, pp. 1152–1157, 2016. find
- Deqian Kong, Minglu Zhao, Dehong Xu, Bo Pang, Shu Wang, Edouardo Honig, Zhangzhang Si, Chuan Li, Jianwen Xie, Sirui Xie, et al. Scalable language models with posterior inference of latent thought vectors. arXiv preprint arXiv:2502.01567, 2025. — [arXiv:2502.01567](https://arxiv.org/abs/2502.01567) find
- Andreas Köpf, Yannic Kilcher, Dimitri Von Rütte, Sotiris Anagnostidis, Zhi Rui Tam, Keith Stevens, Abdullah Barhoum, Duc Nguyen, Oliver Stanley, Richárd Nagyfi, et al. Openassistant conversations-democratizing large language model alignment. Advances in Neural Information Processing Systems, 36: 476… — OpenAssistant Conversations — Democratizing Large Language Model Alignment
- Keito Kudo, Yoichi Aoki, Tatsuki Kuribayashi, Shusaku Sone, Masaya Taniguchi, Ana Brassard, Keisuke Sakaguchi, and Kentaro Inui. Think-to-talk or talk-to-think? when llms come up with an answer in multi-step reasoning. arXiv preprint arXiv:2412.01113, 2024. find
- Nate Kushman, Yoav Artzi, Luke Zettlemoyer, and Regina Barzilay. Learning to automatically solve algebra word problems. In Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 271–281, 2014. find
- Tom Kwiatkowski, Jennimaria Palomaki, Olivia Redfield, Michael Collins, Ankur Parikh, Chris Alberti, Danielle Epstein, Illia Polosukhin, Jacob Devlin, Kenton Lee, et al. Natural questions: a benchmark for question answering research. Transactions of the Association for Computational Linguistics, 7:4…
- Guokun Lai, Qizhe Xie, Hanxiao Liu, Yiming Yang, and Eduard Hovy. Race: Large-scale reading comprehension dataset from examinations. In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pp. 785–794, 2017.
- Hengli Li, Chenxi Li, Tong Wu, Xuekai Zhu, Yuxuan Wang, Zhaoxin Yu, Eric Hanchen Jiang, Song-Chun Zhu, Zixia Jia, Ying Nian Wu, et al. Seek in the dark: Reasoning via test-time instance-level policy gradient in latent space. arXiv preprint arXiv:2505.13308, 2025a. — [arXiv:2505.13308](https://arxiv.org/abs/2505.13308) find
- Xinzhe Li. A survey on llm test-time compute via search: Tasks, llm profiling, search algorithms, and relevant frameworks. arXiv preprint arXiv:2501.10069, 2025. — [arXiv:2501.10069](https://arxiv.org/abs/2501.10069) find
- Yinheng Li, Shaofei Wang, Han Ding, and Hang Chen. Large language models in finance: A survey. In Proceedings of the fourth ACM international conference on AI in finance, pp. 374–382, 2023a. find
- Yuanzhi Li, Sébastien Bubeck, Ronen Eldan, Allie Del Giorno, Suriya Gunasekar, and Yin Tat Lee. Textbooks are all you need ii: phi-1.5 technical report. arXiv preprint arXiv:2309.05463, 2023b.
- Zhong-Zhi Li, Duzhen Zhang, Ming-Liang Zhang, Jiaxin Zhang, Zengyan Liu, Yuxuan Yao, Haotian Xu, Junhao Zheng, Pei-Jie Wang, Xiuyi Chen, et al. From system 1 to system 2: A survey of reasoning large language models. arXiv preprint arXiv:2502.17419, 2025b.
- Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let’s verify step by step. In The Twelfth International Conference on Learning Representations, 2024. — Let's Verify Step by Step
- Stephanie Lin, Jacob Hilton, and Owain Evans. Truthfulqa: Measuring how models mimic human falsehoods. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 3214–3252, 2022.
- Tianhe Lin, Jian Xie, Siyu Yuan, and Deqing Yang. Implicit reasoning in transformers is reasoning through shortcuts. arXiv preprint arXiv:2503.07604, 2025. find
- Wang Ling, Dani Yogatama, Chris Dyer, and Phil Blunsom. Program induction by rationale generation: Learning to solve and explain algebraic word problems. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 158–167, 2017. find
- Aixin Liu, Bei Feng, Bing Xue, Bingxuan Wang, Bochao Wu, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chenyu Zhang, Chong Ruan, et al. Deepseek-v3 technical report. arXiv preprint arXiv:2412.19437, 2024a. find
- Jiahong Liu, Zexuan Qiu, Zhongyang Li, Quanyu Dai, Jieming Zhu, Minda Hu, Menglin Yang, and Irwin King. A survey of personalized large language models: Progress and future directions. arXiv preprint arXiv:2502.11528, 2025a. — [arXiv:2502.11528](https://arxiv.org/abs/2502.11528) find
- Jian Liu, Leyang Cui, Hanmeng Liu, Dandan Huang, Yile Wang, and Yue Zhang. Logiqa: a challenge dataset for machine reading comprehension with logical reasoning. In Proceedings of the Twenty-Ninth International Conference on International Joint Conferences on Artificial Intelligence, pp. 3622–3628, 2…
- Tengxiao Liu, Qipeng Guo, Xiangkun Hu, Cheng Jiayang, Yue Zhang, Xipeng Qiu, and Zheng Zhang. Can language models learn to skip steps? In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024b. find
- Tianqiao Liu, Zui Chen, Zitao Liu, Mi Tian, and Weiqi Luo. Expediting and elevating large language model reasoning via hidden chain-of-thought decoding. arXiv preprint arXiv:2409.08561, 2024c. — [arXiv:2409.08561](https://arxiv.org/abs/2409.08561) find
- Yuan Liu, Haodong Duan, Yuanhan Zhang, Bo Li, Songyang Zhang, Wangbo Zhao, Yike Yuan, Jiaqi Wang, Conghui He, Ziwei Liu, et al. Mmbench: Is your multi-modal model an all-around player? In European conference on computer vision, pp. 216–233. Springer, 2024d.
- Yue Liu, Jiaying Wu, Yufei He, Hongcheng Gao, Hongyu Chen, Baolong Bi, Jiaheng Zhang, Zhiqi Huang, and Bryan Hooi. Efficient inference for large reasoning models: A survey. arXiv preprint arXiv:2503.23077, 2025b. — [arXiv:2503.23077](https://arxiv.org/abs/2503.23077) find
- Anton Lozhkov, Loubna Ben Allal, Elie Bakouch, Leandro von Werra, and Wolf. Finemath: the finest collection of mathematical content, 2024. https://huggingface.co/datasets/HuggingFaceTB/finemath. ↗
- Thomas URL Pan Lu, Swaroop Mishra, Tanglin Xia, Liang Qiu, Kai-Wei Chang, Song-Chun Zhu, Oyvind Tafjord, Peter Clark, and Ashwin Kalyan. Learn to explain: Multimodal reasoning via thought chains for science question answering. Advances in Neural Information Processing Systems, 35:2507–2521, 2022. find
- Pan Lu, Hritik Bansal, Tony Xia, Jiacheng Liu, Chunyuan Li, Hannaneh Hajishirzi, Hao Cheng, Kai-Wei Chang, Michel Galley, and Jianfeng Gao. Mathvista: Evaluating mathematical reasoning of foundation models in visual contexts. In The Twelfth International Conference on Learning Representations, 2024.
- Xinyin Ma, Guangnian Wan, Runpeng Yu, Gongfan Fang, and Xinchao Wang. compressible chain-of-thought tuning. arXiv preprint arXiv:2502.09601, 2025. — [arXiv:2502.09601](https://arxiv.org/abs/2502.09601) find
- Cot-valve: Length-Mitch Marcus, Beatrice Santorini, and Mary Ann Marcinkiewicz. Building a large annotated corpus of english: The penn treebank. Computational linguistics, 19(2):313–330, 1993.
- MathAI. Aime2024 dataset. https://huggingface.co/datasets/math-ai/aime24, 2024a. ↗
- MathAI. Aime2025 dataset. https://huggingface.co/datasets/math-ai/aime25, 2024b. ↗
- Stephen Merity, Caiming Xiong, James Bradbury, and Richard Socher. Pointer sentinel mixture models. In International Conference on Learning Representations, 2017.
- AI Meta. Llama 3.2: Revolutionizing edge ai and vision with open, customizable models. https://ai.meta.com/blog/llama-3-2-connect-2024-vision-edge-mobile-devices/, 2024. ↗
- Meta AI. LLaMA: Open and efficient foundation language models. https://www.llama.com/, 2023. Accessed: 2024-06-25. ↗
- Shen-Yun Miao, Chao-Chun Liang, and Keh-Yih Su. 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, pp. 975–984, 2020. find
- Todor Mihaylov, Peter Clark, Tushar Khot, and Ashish Sabharwal. Can a suit of armor conduct electricity? a new dataset for open book question answering. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pp. 2381–2391, 2018. find
- Amirkeivan Mohtashami, Matteo Pagliardini, and Martin Jaggi. CoTFormer: A chain of thought driven architecture with budget-adaptive computation cost at inference. In The Thirteenth International Conference on Learning Representations, 2025. find
- OpenAI. Introducing gpt-5. https://openai.com/index/introducing-gpt-5/, 2025. Accessed: 2025-08-29. ↗
- José I Orlicki. Beyond words: A latent memory approach to internal reasoning in llms. arXiv preprint arXiv:2502.21030, 2025. — [arXiv:2502.21030](https://arxiv.org/abs/2502.21030) find
- Denis Paperno, Germán Kruszewski, Angeliki Lazaridou, Ngoc-Quan Pham, Raffaella Bernardi, Sandro Pezzelle, Marco Baroni, Gemma Boleda, and Raquel Fernández. The lambada dataset: Word prediction requiring a broad discourse context. In Proceedings of the 54th Annual Meeting of the Association for Comp…
- Keiran Paster, Marco Dos Santos, Zhangir Azerbayev, and Jimmy Ba. Openwebmath: An open dataset of high-quality mathematical web text. In The Twelfth International Conference on Learning Representations, 2024.
- Arkil Patel, Satwik Bhattamishra, and Navin Goyal. 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, pp. 2080–2094, 2021.
- Jacob Pfau, William Merrill, and Samuel R. Bowman. Let’s think dot by dot: Hidden computation in transformer language models. In First Conference on Language Modeling, 2024. find
- Ofir Press, Muru Zhang, Sewon Min, Ludwig Schmidt, Noah A Smith, and Mike Lewis. Measuring and narrowing the compositionality gap in language models. In Findings of the Association for Computational Linguistics: EMNLP 2023, pp. 5687–5711, 2023. find
- Jianing Qiu, Kyle Lam, Guohao Li, Amish Acharya, Tien Yin Wong, Ara Darzi, Wu Yuan, and Eric J Topol. Llm-based agentic systems in medicine and healthcare. Nature Machine Intelligence, 6(12):1418– 1420, 2024. find
- Xiaoye Qu, Yafu Li, Zhaochen Su, Weigao Sun, Jianhao Yan, Dongrui Liu, Ganqu Cui, Daizong Liu, Shuxian Liang, Junxian He, et al. A survey of efficient reasoning for large reasoning models: Language, multimodality, and beyond. arXiv preprint arXiv:2503.21614, 2025.
- Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, et al. Language models are unsupervised multitask learners. OpenAI blog, 1(8):9, 2019. find
- Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J Liu. Exploring the limits of transfer learning with a unified text-to-text transformer. Journal of machine learning research, 21(140):1–67, 2020.
- Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. Squad: 100,000+ questions for machine comprehension of text. In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, pp. 2383–2392, 2016.
- Pranav Rajpurkar, Robin Jia, and Percy Liang. Know what you don’t know: Unanswerable questions for squad. In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pp. 784–789, 2018. — Know What You Don't Know: Unanswerable Questions for SQuAD
- Siva Reddy, Danqi Chen, and Christopher D Manning. Coqa: A conversational question answering challenge. Transactions of the Association for Computational Linguistics, 7:249–266, 2019.
- David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Dirani, Julian Michael, and Samuel R Bowman. Gpqa: A graduate-level google-proof q&a benchmark. In First Conference on Language Modeling, 2024.
- Subhro Roy and Dan Roth. Solving general arithmetic word problems. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pp. 1743–1752, 2015.
- Subhro Roy, Tim Vieira, and Dan Roth. Reasoning about quantities in natural language. Transactions of the Association for Computational Linguistics, 3:1–13, 2015. find
- Yangjun Ruan, Neil Band, Chris J Maddison, and Tatsunori Hashimoto. Reasoning to learn from latent thoughts. arXiv preprint arXiv:2503.18866, 2025. — [arXiv:2503.18866](https://arxiv.org/abs/2503.18866) find
- Keisuke Sakaguchi, Ronan Le Bras, Chandra Bhagavatula, and Yejin Choi. Winogrande: An adversarial winograd schema challenge at scale. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pp. 8732–8740. Association for the Advancement of Artificial Intelligence (AAAI), 2020. find
- Maarten Sap, Hannah Rashkin, Derek Chen, Ronan Le Bras, and Yejin Choi. Social iqa: Commonsense reasoning about social interactions. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EM… find
- Abulhair Saparov and He He. Language models are greedy reasoners: A systematic formal analysis of chain-of-thought. In The Eleventh International Conference on Learning Representations, 2023.
- Nikunj Saunshi, Nishanth Dikkala, Zhiyuan Li, Sanjiv Kumar, and Sashank J Reddi. Reasoning with latent thoughts: On the power of looped transformers. arXiv preprint arXiv:2502.17416, 2025. find
- David Saxton, Edward Grefenstette, Felix Hill, and Pushmeet Kohli. Analysing mathematical reasoning abilities of neural models. In International Conference on Learning Representations, 2019.
- Yuval Shalev, Amir Feder, and Ariel Goldstein. Distributional reasoning in llms: Parallel reasoning processes in multi-hop reasoning. arXiv preprint arXiv:2406.13858, 2024. — [arXiv:2406.13858](https://arxiv.org/abs/2406.13858) find
- Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Y Wu, et al. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300, 2024.
- Xuan Shen, Yizhou Wang, Xiangxi Shi, Yanzhi Wang, Pu Zhao, and Jiuxiang Gu. Efficient reasoning with hidden thinking. arXiv preprint arXiv:2501.19201, 2025a. — [arXiv:2501.19201](https://arxiv.org/abs/2501.19201) find
- Zhenyi Shen, Hanqi Yan, Linhai Zhang, Zhanghao Hu, Yali Du, and Yulan He. Codi: Compressing chain-of-thought into continuous space via self-distillation. arXiv preprint arXiv:2502.21074, 2025b.
- Aarohi Srivastava, Abhinav Rastogi, Abhishek Rao, Abu Awal Md Shoeb, Abubakar Abid, Adam Fisch, Adam R Brown, Adam Santoro, Aditya Gupta, Adrià Garriga-Alonso, et al. Beyond the imitation game: quantifying and extrapolating the capabilities of language models. Transactions on Machine Learning Resear…
- DiJia Su, Hanlin Zhu, Yingchen Xu, Jiantao Jiao, Yuandong Tian, and Qinqing Zheng. Token assorted: Mixing latent and text tokens for improved language model reasoning. arXiv preprint arXiv:2502.03275, 2025. — [arXiv:2502.03275](https://arxiv.org/abs/2502.03275) find
- Yang Sui, Yu-Neng Chuang, Guanchu Wang, Jiamu Zhang, Tianyi Zhang, Jiayi Yuan, Hongyi Liu, Andrew Wen, Shaochen Zhong, Hanjie Chen, et al. Stop overthinking: A survey on efficient reasoning for large language models. arXiv preprint arXiv:2503.16419, 2025.
- Jiankai Sun, Chuanyang Zheng, Enze Xie, Zhengying Liu, Ruihang Chu, Jianing Qiu, Jiaqi Xu, Mingyu Ding, Hongyang Li, Mengzhe Geng, et al. A survey of reasoning with foundation models. arXiv preprint arXiv:2312.11562, 2023. — [arXiv:2312.11562](https://arxiv.org/abs/2312.11562) find
- Yuchang Sun, Yanxi Chen, Yaliang Li, and Bolin Ding. Enhancing latent computation in transformers with latent tokens. arXiv preprint arXiv:2505.12629, 2025. — [arXiv:2505.12629](https://arxiv.org/abs/2505.12629) find
- Mirac Suzgun, Nathan Scales, Nathanael Schärli, Sebastian Gehrmann, Yi Tay, Hyung Won Chung, Aakanksha Chowdhery, Quoc Le, Ed Chi, Denny Zhou, et al. Challenging big-bench tasks and whether chain-of-thought can solve them. In Findings of the Association for Computational Linguistics: ACL 2023, pp. 1…
- Jihoon Tack, Jack Lanchantin, Jane Yu, Andrew Cohen, Ilia Kulikov, Janice Lan, Shibo Hao, Yuandong Tian, Jason Weston, and Xian Li. Llm pretraining with continuous concepts. arXiv preprint arXiv:2502.08524, 2025. — [arXiv:2502.08524](https://arxiv.org/abs/2502.08524) find
- Alon Talmor and Jonathan Berant. The web as a knowledge-base for answering complex questions. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers), pp. 641–651, 2018.
- Alon Talmor, Jonathan Herzig, Nicholas Lourie, and Jonathan Berant. Commonsenseqa: A question answering challenge targeting commonsense knowledge. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume…
- Wenhui Tan, Jiaze Li, Jianzhong Ju, Zhenbo Luo, Jian Luan, and Ruihua Song. Think silently, think fast: Dynamic latent compression of llm reasoning chains. arXiv preprint arXiv:2505.16552, 2025.
- Jiakai Tang, Sunhao Dai, Teng Shi, Jun Xu, Xu Chen, Wen Chen, Wu Jian, and Yuning Jiang. Think before recommend: Unleashing the latent reasoning power for sequential recommendation. arXiv preprint arXiv:2503.22675, 2025. — [arXiv:2503.22675](https://arxiv.org/abs/2503.22675) find
- Zhengyang Tang, Xingxing Zhang, Benyou Wang, and Furu Wei. Mathscale: Scaling instruction tuning for mathematical reasoning. In International Conference on Machine Learning, pp. 47885–47900. PMLR, 2024. find
- Qwen Team. Qwq: Reflect deeply on the boundaries of the unknown. https://qwenlm.github.io/blog/ qwq-32b-preview, 2024. ↗
- Qwen Team. Qwq-32b: Embracing the power of reinforcement learning, 2025. find
- Yuxuan Tong, Xiwen Zhang, Rui Wang, Ruidong Wu, and Junxian He. Dart-math: Difficulty-aware rejection tuning for mathematical problem-solving. Advances in Neural Information Processing Systems, 37:7821– 7846, 2024. find
- Hugo Touvron, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timothée Lacroix, Baptiste Rozière, Naman Goyal, Eric Hambro, Faisal Azhar, et al. Llama: Open and efficient foundation language models. arXiv preprint arXiv:2302.13971, 2023a.
- Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open foundation and fine-tuned chat models. arXiv preprint arXiv:2307.09288, 2023b.
- Boshi Wang, Xiang Yue, Yu Su, and Huan Sun. Grokked transformers are implicit reasoners: A mechanistic journey to the edge of generalization. arXiv preprint arXiv:2405.15071, 2024a. find
- Jianwei Wang, Ziming Wu, Fuming Lai, Shaobing Lian, and Ziqian Zeng. Synadapt: Learning adaptive reasoning in large language models via synthetic continuous chain-of-thought. arXiv preprint arXiv:2508.00574, 2025a. — [arXiv:2508.00574](https://arxiv.org/abs/2508.00574) find
- Qi Wang, Jindong Li, Shiqi Wang, Qianli Xing, Runliang Niu, He Kong, Rui Li, Guodong Long, Yi Chang, and Chengqi Zhang. Towards next-generation llm-based recommender systems: A survey and beyond. arXiv preprint arXiv:2410.19744, 2024b. — [arXiv:2410.19744](https://arxiv.org/abs/2410.19744) find
- Rui Wang, Hongru Wang, Boyang Xue, Jianhui Pang, Shudong Liu, Yi Chen, Jiahao Qiu, Derek Fai Wong, Heng Ji, and Kam-Fai Wong. Harnessing the reasoning economy: A survey of efficient reasoning for large language models. arXiv preprint arXiv:2503.24377, 2025b.
- Xiaoqiang Wang, Suyuchen Wang, Yun Zhu, and Bang Liu. System-1.5 reasoning: Traversal in language and latent spaces with dynamic shortcuts. arXiv preprint arXiv:2505.18962, 2025c. — [arXiv:2505.18962](https://arxiv.org/abs/2505.18962) find
- Xinyi Wang, Lucas Caccia, Oleksiy Ostapenko, Xingdi Yuan, William Yang Wang, and Alessandro Sordoni. Guiding language model reasoning with planning tokens. In First Conference on Language Modeling, 2024c. find
- Yiming Wang, Pei Zhang, Baosong Yang, Derek F Wong, and Rui Wang. Latent space chain-of-embedding enables output-free llm self-evaluation. arXiv preprint arXiv:2410.13640, 2024d. — [arXiv:2410.13640](https://arxiv.org/abs/2410.13640) find
- Maurice Weber, Dan Fu, Quentin Anthony, Yonatan Oren, Shane Adams, Anton Alexandrov, Xiaozhong Lyu, Huu Nguyen, Xiaozhe Yao, Virginia Adams, et al. Redpajama: an open dataset for training large language models. Advances in neural information processing systems, 37:116462–116492, 2024.
- Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems, 35:24824–24837, 2022.
- Johannes Welbl, Nelson F Liu, and Matt Gardner. Crowdsourcing multiple choice science questions. In Proceedings of the 3rd Workshop on Noisy User-generated Text, pp. 94–106, 2017.
- Ruibin Xiong, Yunchang Yang, Di He, Kai Zheng, Shuxin Zheng, Chen Xing, Huishuai Zhang, Yanyan Lan, Liwei Wang, and Tieyan Liu. On layer normalization in the transformer architecture. In International conference on machine learning, pp. 10524–10533. PMLR, 2020. find
- Guowei Xu, Peng Jin, Li Hao, Yibing Song, Lichao Sun, and Li Yuan. Llava-o1: Let vision language models reason step-by-step. arXiv preprint arXiv:2411.10440, 2024. find
- Kevin Xu and Issei Sato. To cot or to loop? a formal comparison between chain-of-thought and looped transformers. arXiv preprint arXiv:2505.19245, 2025. — [arXiv:2505.19245](https://arxiv.org/abs/2505.19245) find
- Yige Xu, Xu Guo, Zhiwei Zeng, and Chunyan Miao. Softcot++: Test-time scaling with soft chain-of-thought reasoning. arXiv preprint arXiv:2505.11484, 2025a. — [arXiv:2505.11484](https://arxiv.org/abs/2505.11484) find
- Yige Xu, Xu Guo, Zhiwei Zeng, and Chunyan Miao. Softcot: Soft chain-of-thought for efficient reasoning with llms. arXiv preprint arXiv:2502.12134, 2025b.
- Yibo Yan, Shen Wang, Jiahao Huo, Jingheng Ye, Zhendong Chu, Xuming Hu, Philip S Yu, Carla Gomes, Bart Selman, and Qingsong Wen. Position: Multimodal large language models can significantly advance scientific reasoning. arXiv preprint arXiv:2502.02871, 2025. find
- An Yang, Baosong Yang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Zhou, Chengpeng Li, Chengyuan Li, Dayiheng Liu, Fei Huang, Guanting Dong, Haoran Wei, Huan Lin, Jialong Tang, Jialin Wang, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Ma, Jianxin Yang, Jin Xu, Jingren Zhou, Jinze Bai, Jinzheng He, Juny… find
- An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Haoran Wei, Huan Lin, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Yang, Jiaxi Yang, Jingren Zhou, Junyang Lin, Kai Dang, Keming Lu, Keqin Bao, Kexin Yang, Le Yu, Mei Li, Mingfeng Xue, Pei… find
- An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, et al. Qwen3 technical report. arXiv preprint arXiv:2505.09388, 2025a.
- Sohee Yang, Elena Gribovskaya, Nora Kassner, Mor Geva, and Sebastian Riedel. Do large language models latently perform multi-hop reasoning? In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 10210–10229, 2024c. find
- Zhilin Yang, Peng Qi, Saizheng Zhang, Yoshua Bengio, William Cohen, Ruslan Salakhutdinov, and Christopher D Manning. Hotpotqa: A dataset for diverse, explainable multi-hop question answering. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pp. 2369–2380, 20…
- Zhipeng Yang, Junzhuo Li, Siyu Xia, and Xuming Hu. Internal chain-of-thought: Empirical evidence for layer-wise subtask scheduling in llms. arXiv preprint arXiv:2505.14530, 2025b.
- Jiaran Ye, Zijun Yao, Zhidian Huang, Liangming Pan, Jinxin Liu, Yushi Bai, Amy Xin, Liu Weichuan, Xiaoyin Che, Lei Hou, et al. How does transformer learn implicit reasoning? arXiv preprint arXiv:2505.23653, 2025a. — [arXiv:2505.23653](https://arxiv.org/abs/2505.23653) find
- Yixin Ye, Zhen Huang, Yang Xiao, Ethan Chern, Shijie Xia, and Pengfei Liu. Limo: Less is more for reasoning. arXiv preprint arXiv:2502.03387, 2025b.
- Yelp. Yelp open dataset. Accessed: 2025-06-29, 2024. https://business.yelp.com/data/resources/ open-dataset/. ↗
- Zihao Yi, Jiarui Ouyang, Yuwen Liu, Tianhao Liao, Zhe Xu, and Ying Shen. A survey on recent advances in llm-based multi-turn dialogue systems. arXiv preprint arXiv:2402.18013, 2024.
- Longhui Yu, Weisen Jiang, Han Shi, YU Jincheng, Zhengying Liu, Yu Zhang, James Kwok, Zhenguo Li, Adrian Weller, and Weiyang Liu. Metamath: Bootstrap your own mathematical questions for large language models. In The Twelfth International Conference on Learning Representations, 2024a.
- Ping Yu, Jing Xu, Jason E Weston, and Ilia Kulikov. Distilling system 2 into system 1. In The First Workshop on System-2 Reasoning at Scale, NeurIPS’24, 2024b. find
- Qifan Yu, Zhenyu He, Sijie Li, Xun Zhou, Jun Zhang, Jingjing Xu, and Di He. Enhancing auto-regressive chain-of-thought through loop-aligned reasoning. arXiv preprint arXiv:2502.08482, 2025a.
- Qiying Yu, Zheng Zhang, Ruofei Zhu, Yufeng Yuan, Xiaochen Zuo, Yu Yue, Weinan Dai, Tiantian Fan, Gaohong Liu, Lingjun Liu, et al. Dapo: An open-source llm reinforcement learning system at scale. arXiv preprint arXiv:2503.14476, 2025b.
- Weihao Yu, Zhengyuan Yang, Linjie Li, Jianfeng Wang, Kevin Lin, Zicheng Liu, Xinchao Wang, and Lijuan Wang. Mm-vet: Evaluating large multimodal models for integrated capabilities. In International Conference on Machine Learning, pp. 57730–57754. PMLR, 2024c.
- Yijiong Yu. Do llms really think step-by-step in implicit reasoning? arXiv preprint arXiv:2411.15862, 2024.
- Linan Yue, Yichao Du, Yizhi Wang, Weibo Gao, Fangzhou Yao, Li Wang, Ye Liu, Ziyu Xu, Qi Liu, Shimin Di, et al. Don’t overthink it: A survey of efficient r1-style large reasoning models. arXiv preprint arXiv:2508.02120, 2025a. find
- Zhenrui Yue, Bowen Jin, Huimin Zeng, Honglei Zhuang, Zhen Qin, Jinsung Yoon, Lanyu Shang, Jiawei Han, and Dong Wang. Hybrid latent reasoning via reinforcement learning. arXiv preprint arXiv:2505.18454, 2025b. — [arXiv:2505.18454](https://arxiv.org/abs/2505.18454) find
- Eric Zelikman, Georges Raif Harik, Yijia Shao, Varuna Jayasiri, Nick Haber, and Noah Goodman. Quiet-STar: Language models can teach themselves to think before speaking. In First Conference on Language Modeling, 2024.
- Rowan Zellers, Ari Holtzman, Yonatan Bisk, Ali Farhadi, and Yejin Choi. Hellaswag: Can a machine really finish your sentence? In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pp. 4791–4800, 2019. find
- Boyi Zeng, Shixiang Song, Siyuan Huang, Yixuan Wang, He Li, Ziwei He, Xinbing Wang, Zhiyu Li, and Zhouhan Lin. Pretraining language models to ponder in continuous space. arXiv preprint arXiv:2505.20674, 2025. — [arXiv:2505.20674](https://arxiv.org/abs/2505.20674) find
- Jason Zhang and Scott W Viteri. Uncovering latent chain of thought vectors in large language models. In Workshop on Neural Network Weights as a New Data Modality, 2025. find
- Jintian Zhang, Yuqi Zhu, Mengshu Sun, Yujie Luo, Shuofei Qiao, Lun Du, Da Zheng, Huajun Chen, and Ningyu Zhang. Lightthinker: Thinking step-by-step compression. arXiv preprint arXiv:2502.15589, 2025a.
- Peiyuan Zhang, Guangtao Zeng, Tianduo Wang, and Wei Lu. Tinyllama: An open-source small language model. arXiv preprint arXiv:2401.02385, 2024.
- Qiyuan Zhang, Fuyuan Lyu, Zexu Sun, Lei Wang, Weixu Zhang, Wenyue Hua, Haolun Wu, Zhihan Guo, Yufei Wang, Niklas Muennighoff, et al. A survey on test-time scaling in large language models: What, how, where, and how well? arXiv preprint arXiv:2503.24235, 2025b. find
- Xiang Zhang, Junbo Zhao, and Yann LeCun. Character-level convolutional networks for text classification. Advances in neural information processing systems, 28, 2015.
- Zhen Zhang, Xuehai He, Weixiang Yan, Ao Shen, Chenyang Zhao, Shuohang Wang, Yelong Shen, and Xin Eric Wang. Soft thinking: Unlocking the reasoning potential of llms in continuous concept space. arXiv preprint arXiv:2505.15778, 2025c.
- Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li, Dacheng Li, Eric Xing, et al. Judging llm-as-a-judge with mt-bench and chatbot arena. Advances in Neural Information Processing Systems, 36:46595–46623, 2023.
- Guanghao Zhou, Panjia Qiu, Cen Chen, Jie Wang, Zheming Yang, Jian Xu, and Minghui Qiu. Reinforced mllm: A survey on rl-based reasoning in multimodal large language models. arXiv preprint arXiv:2504.21277, 2025. — [arXiv:2504.21277](https://arxiv.org/abs/2504.21277) find
- Hanlin Zhu, Shibo Hao, Zhiting Hu, Jiantao Jiao, Stuart Russell, and Yuandong Tian. Reasoning by superposition: A theoretical perspective on chain of continuous thought. arXiv preprint arXiv:2505.12514, 2025a. — [arXiv:2505.12514](https://arxiv.org/abs/2505.12514) find
- Rui-Jie Zhu, Tianhao Peng, Tianhao Cheng, Xingwei Qu, Jinfa Huang, Dawei Zhu, Hao Wang, Kaiwen Xue, Xuanliang Zhang, Yong Shan, et al. A survey on latent reasoning. arXiv preprint arXiv:2507.06203, 2025b. zwhe99. Amc23 dataset. https://huggingface.co/datasets/zwhe99/amc23, 2024. ↗
Updated
This page in Markdown → https://md.research.elamur.ai/free/en/papers/li-2025-implicit-reasoning-large-language-models/