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Intermediate token generation (ITG), where a model produces output before the solution, has become a standard method to improve the performance of language models on reasoning tasks.
A formal basis for the heuristic determination of minimum cost paths
Hart, P. E., Nilsson, N. J., and Raphael, B · 1968
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Artificial intelligence meets natural stupidity
McDermott, D · 1976
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Telling more than we can know: Verbal reports on mental processes
Nisbett, R. E. and Wilson, T. D · 1977
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Artificial Intelligence: A Modern Approach
Russell, S. J. and Norvig, P · 2010
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The gardener and the carpenter: What the new science of child development tells us about the relationship between parents and children
Gopnik, A · 2016
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Adaptive computation time for recurrent neural networks
Graves, A · 2016
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Show your work: Scratchpads for intermediate computation with language models
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
Earlier work this paper cites.
Large language models are zero-shot reasoners
Kojima, T., Gu, S. S., Reid, M., Matsuo, Y., and Iwasawa, Y · 2022
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Chain-of-thought prompting elicits reasoning in large language models
Wei, J., Wang, X., Schuurmans, D., Bosma, M., Xia, F., Chi, E., Le, Q. V., Zhou, D., et al · 2022
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Star: Bootstrapping reasoning with reasoning
Zelikman, E., Wu, Y., Mu, J., and Goodman, N · 2022
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Automatic chain of thought prompting in large language models
Zhang, Z., Zhang, A., Li, M., and Smola, A · 2022
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Learning and leveraging verifiers to improve planning capabilities of pre-trained language models
Arora, D. and Kambhampati, S · 2023
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Sparks of artificial general intelligence: Early experiments with gpt-4
Bubeck, S., Chandrasekaran, V., Eldan, R., Gehrke, J., Horvitz, E., Kamar, E., Lee, P., Lee, Y. T., Li, Y., Lundberg, S., et al · 2023
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Minillm: Knowledge distillation of large language models
Gu, Y., Dong, L., Wei, F., and Huang, M · 2023
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Hsieh, C.-Y., Li, C.-L., Yeh, C.-K., Nakhost, H., Fujii, Y., Ratner, A., Krishna, R., Lee, C.-Y., and Pfister, T · 2023
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Let’s verify step by step, 2023
Lightman, H., Kosaraju, V., Burda, Y., Edwards, H., Baker, B., Lee, T., Leike, J., Schulman, J., Sutskever, I., and Cobbe, K · 2023
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Mathematical discoveries from program search with large language models
Romera-Paredes, B., Barekatain, M., Novikov, A., Balog, M., Kumar, M. P., Dupont, E., Ruiz, F. J., Ellenberg, J. S., Wang, P., Fawzi, O., et al · 2023
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Tree of thoughts: Deliberate problem solving with large language models
Yao, S., Yu, D., Zhao, J., Shafran, I., Griffiths, T. L., Cao, Y., and Narasimhan, K. R · 2023
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Universal and transferable adversarial attacks on aligned language models, 2023
Zou, A., Wang, Z., Carlini, N., Nasr, M., Kolter, J. Z., and Fredrikson, M · 2023
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Talking nonsense: Probing large language models’ understanding of adversarial gibberish inputs, 2024
Cherepanova, V. and Zou, J · 2024
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Stream of Search (SoS): Learning to Search in Language
Gandhi, K., Lee, D., Grand, G., Liu, M., Cheng, W., Sharma, A., and Goodman, N. D · 2024
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On designing effective rl reward at training time for llm reasoning
Gao, J., Xu, S., Ye, W., Liu, W., He, C., Fu, W., Mei, Z., Wang, G., and Wu, Y · 2024
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Alignment faking in large language models, 2024
Greenblatt, R., Denison, C., Wright, B., Roger, F., MacDiarmid, M., Marks, S., Treutlein, J., Belonax, T., Chen, J., Duvenaud, D., Khan, A., Michael, J., Mindermann, S., Perez, E., Petrini, L., Uesato, J., Kaplan, J., Shlegeris, B., Bowman, S. R., and Hubinger, E · 2024
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Training large language models to reason in a continuous latent space, 2024
Hao, S., Sukhbaatar, S., Su, D., Li, X., Hu, Z., Weston, J., and Tian, Y · 2024
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Hughes, J., Price, S., Lynch, A., Schaeffer, R., Barez, F., Koyejo, S., Sleight, H., Jones, E., Perez, E., and Sharma, M · 2024
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Position: LLMs can’t plan, but can help planning in LLM-modulo frameworks
Kambhampati, S., Valmeekam, K., Guan, L., Verma, M., Stechly, K., Bhambri, S., Saldyt, L. P., and Murthy, A. B · 2024
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Tulu 3: Pushing frontiers in open language model post-training
Lambert, N., Morrison, J., Pyatkin, V., Huang, S., Ivison, H., Brahman, F., Miranda, L. J. V., Liu, A., Dziri, N., Lyu, S., et al · 2024
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Flipattack: Jailbreak llms via flipping
Liu, Y., He, X., Xiong, M., Fu, J., Deng, S., and Hooi, B · 2024
Cited alongside, same era.
The CLRS-Text Algorithmic Reasoning Language Benchmark
Markeeva, L., Mcleish, S., Ibarz, B., Bounsi, W., Kozlova, O., Vitvitskyi, A., Blundell, C., Goldstein, T., Schwarzschild, A., and Veličkovi´veličkovi´c, P · 2024
Cited alongside, same era.
Parthasarathy, V. B., Zafar, A., Khan, A., and Shahid, A · 2024
Cited alongside, same era.
Making reasoning matter: Measuring and improving faithfulness of chain-of-thought reasoning, 2024
Paul, D., West, R., Bosselut, A., and Faltings, B · 2024
Cited alongside, same era.
Let’s think dot by dot: Hidden computation in transformer language models
(how) do reasoning models reason?
Kambhampati, S., Stechly, K., and Valmeekam, K · 2025
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Natural emergent misalignment from reward hacking in production rl, 2025
MacDiarmid, M., Wright, B., Uesato, J., Benton, J., Kutasov, J., Price, S., Bouscal, N., Bowman, S., Bricken, T., Cloud, A., Denison, C., Gasteiger, J., Greenblatt, R., Leike, J., Lindsey, J., Mikulik, V., Perez, E., Rodrigues, A., Thomas, D., Webson, A., Ziegler, D., and Hubinger, E · 2025
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Deepseek-r1 thoughtology: Let’s think about llm reasoning, 2025
Marjanović, S. V., Patel, A., Adlakha, V., Aghajohari, M., BehnamGhader, P., Bhatia, M., Khandelwal, A., Kraft, A., Krojer, B., Lù, X. H., Meade, N., Shin, D., Kazemnejad, A., Kamath, G., Mosbach, M., Stańczak, K., and Reddy, S · 2025
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Muennighoff, N., Yang, Z., Shi, W., Li, X. L., Fei-Fei, L., Hajishirzi, H., Zettlemoyer, L., Liang, P., Candès, E., and Hashimoto, T · 2025
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Pfau, J., Merrill, W., and Bowman, S. R · 2024
Cited alongside, same era.
Mastering board games by external and internal planning with language models, 2024
Schultz, J., Adamek, J., Jusup, M., Lanctot, M., Kaisers, M., Perrin, S., Hennes, D., Shar, J., Lewis, C., Ruoss, A., Zahavy, T., Veličković, P., Prince, L., Singh, S., Malmi, E., and Tomašev, N · 2024
Cited alongside, same era.
Chain of Thoughtlessness: An Analysis of CoT in Planning
Stechly, K., Valmeekam, K., and Kambhampati, S · 2024
Cited alongside, same era.
Dualformer: Controllable fast and slow thinking by learning with randomized reasoning traces
Su, D., Sukhbaatar, S., Rabbat, M., Tian, Y., and Zheng, Q · 2024
Cited alongside, same era.
On the hardness of faithful chain-of-thought reasoning in large language models, 2024
Tanneru, S. H., Ley, D., Agarwal, C., and Lakkaraju, H · 2024
Cited alongside, same era.
Solving olympiad geometry without human demonstrations
Trinh, T. H., Wu, Y., Le, Q. V., He, H., and Luong, T · 2024
Cited alongside, same era.
How interpretable are reasoning explanations from prompting large language models?
Wei Jie, Y., Satapathy, R., Goh, R., and Cambria, E · 2024
Cited alongside, same era.
Generative verifiers: Reward modeling as next-token prediction, 2024
Zhang, L., Hosseini, A., Bansal, H., Kazemi, M., Kumar, A., and Agarwal, R · 2024
Cited alongside, same era.
OpenAI, :, Agarwal, S., Ahmad, L., Ai, J., Altman, S., Applebaum, A., Arbus, E., Arora, R. K., Bai, Y., Baker, B., Bao, H., Barak, B., Bennett, A., Bertao, T., Brett, N., Brevdo, E., Brockman, G., Bubeck, S., Chang, C., Chen, K., Chen, M., Cheung, E., Clark, A., Cook, D., Dukhan, M., Dvorak, C., Fives, K., Fomenko, V., Garipov, T., Georgiev, K., Glaese, M., Gogineni, T., Goucher, A., Gross, L., Guzman, K. G., Hallman, J., Hehir, J., Heidecke, J., Helyar, A., Hu, H., Huet, R., Huh, J., Jain, S., Johnson, Z., Koch, C., Kofman, I., Kundel, D., Kwon, J., Kyrylov, V., Le, E. Y., Leclerc, G., Lennon, J. P., Lessans, S., Lezcano-Casado, M., Li, Y., Li, Z., Lin, J., Liss, J., Lily, Liu, Liu, J., Lu, K., Lu, C., Martinovic, Z., McCallum, L., McGrath, J., McKinney, S., McLaughlin, A., Mei, S., Mostovoy, S., Mu, T., Myles, G., Neitz, A., Nichol, A., Pachocki, J., Paino, A., Palmie, D., Pantuliano, A., Parascandolo, G., Park, J., Pathak, L., Paz, C., Peran, L., Pimenov, D., Pokrass, M., Proehl, E., Qiu, H., Raila, G., Raso, F., Ren, H., Richardson, K., Robinson, D., Rotsted, B., Salman, H., Sanjeev, S., Schwarzer, M., Sculley, D., Sikchi, H., Simon, K., Singhal, K., Song, Y., Stuckey, D., Sun, Z., Tillet, P., Toizer, S., Tsimpourlas, F., Vyas, N., Wallace, E., Wang, X., Wang, M., Watkins, O., Weil, K., Wendling, A., Whinnery, K., Whitney, C., Wong, H., Yang, L., Yang, Y., Yasunaga, M., Ying, K., Zaremba, W., Zhan, W., Zhang, C., Zhang, B., Zhang, E., and Zhao, S · 2025
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Performative thinking? the brittle correlation between cot length and problem complexity
Palod, V., Valmeekam, K., Stechly, K., and Kambhampati, S · 2025
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To backtrack or not to backtrack: When sequential search limits model reasoning
Qin, T., Alvarez-Melis, D., Jelassi, S., and Malach, E · 2025
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Rl in name only? analyzing the structural assumptions in rl post-training for llms
Samineni, S. R., Kalwar, D., Valmeekam, K., Stechly, K., and Kambhampati, S · 2025
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On the Self-Verification Limitations of Large Language Models on Reasoning and Planning Tasks
Stechly, K., Valmeekam, K., and Kambhampati, S · 2025
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Su, J., Healey, J., Nakov, P., and Cardie, C · 2025
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Invisible tokens, visible bills: The urgent need to audit hidden operations in opaque LLM services
Sun, G., Wang, Z., Zhao, X., Tian, B., Shen, Z., He, Y., Xing, J., and Li, A · 2025
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A systematic evaluation of the planning and scheduling abilities of the reasoning model o1
Valmeekam, K., Stechly, K., Gundawar, A., and Kambhampati, S · 2025
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Reinforcement learning for reasoning in large language models with one training example
Wang, Y., Yang, Q., Zeng, Z., Ren, L., Liu, L., Peng, B., Cheng, H., He, X., Wang, K., Gao, J., et al · 2025
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Understanding aha moments: from external observations to internal mechanisms
Yang, S., Wu, J., Chen, X., Xiao, Y., Yang, X., Wong, D. F., and Wang, D · 2025
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Dapo: An open-source llm reinforcement learning system at scale
Yu, Q., Zhang, Z., Zhu, R., Yuan, Y., Zuo, X., Yue, Y., Fan, T., Liu, G., Liu, L., Liu, X., et al · 2025
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R1-zero’s” aha moment” in visual reasoning on a 2b non-sft model
Zhou, H., Li, X., Wang, R., Cheng, M., Zhou, T., and Hsieh, C.-J · 2025
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Interpretable traces, unexpected outcomes: Investigating the disconnect in trace-based knowledge distillation
Bhambri, S., Biswas, U., and Kambhampati, S · 2026
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interwhen: A generalizable framework for verifiable reasoning with test-time monitors
Bhat, V. K., Chanda, P., Khandelwal, A., Swaroop, M., Kambhampati, S., Balasubramanian, V. N., Natarajan, N., and Sharma, A · 2026
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“thinking traces” in large reasoning models: Cognitive cost or performative scaffolding?
Hu, Y · 2026
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Masked distillation: Internalizing chain-of-thought in small language models
Kalwar, D., Palod, V., and Kambhampati, S · 2026
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Reasoning models generate societies of thought
Kim, J., Lai, S., Scherrer, N., Evans, J., et al · 2026
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Evaluating the false trust engendered by llm explanations, 2026
Palod, V., Biswas, U., and Kambhampati, S · 2026
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Ai scientists produce results without reasoning scientifically, 2026
Ríos-García, M., Alampara, N., Gupta, C., Mandal, I., Mannan, S., Aghajani, A. A., Krishnan, N. M. A., and Jablonka, K. M · 2026
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Sample more to think less: Group filtered policy optimization for concise reasoning
Shrivastava, V., Awadallah, A. H., Balachandran, V., Garg, S., Behl, H., and Papailiopoulos, D · 2026
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Beyond semantics: The unreasonable effectiveness of reasonless intermediate tokens
Valmeekam, K., Palod, V., Stechly, K., Gundawar, A., and Kambhampati, S · 2026
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Correlations without causation do not support claims of human–llm reasoning alignment
Vankov, I. I., Adolfi, F., Heaton, R. F., Puebla, G., and Bowers, J. S · 2026
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