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Scaling inference compute enhances reasoning in large language models (LLMs), with long chains-of-thought (CoTs) enabling strategies like backtracking and error correction.
On the resemblance and containment of documents
Broder, A · 1997
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Min-wise independent permutations
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Common crawl – building an open web-scale crawl using hadoop, 2010
Rana, A · 2010
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Professor forcing: A new algorithm for training recurrent networks
Lamb, A. M., ALIAS PARTH GOYAL, A. G., Zhang, Y., Zhang, S., Courville, A. C., and Bengio, Y · 2016
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Sgdr: Stochastic gradient descent with warm restarts, 2017
Loshchilov, I. and Hutter, F · 2017
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Proximal policy optimization algorithms, 2017
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Reinforcement Learning: An Introduction
Sutton, R. S. and Barto, A. G · 2018
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Language models are few-shot learners
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Zero: Memory optimizations toward training trillion parameter models
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Deepspeed: System optimizations enable training deep learning models with over 100 billion parameters
Rasley, J., Rajbhandari, S., Ruwase, O., and He, Y · 2020
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Evaluating large language models trained on code, 2021
Chen, M., Tworek, J., Jun, H., Yuan, Q., de Oliveira Pinto, H. P., Kaplan, J., Edwards, H., Burda, Y., Joseph, N., Brockman, G., Ray, A., Puri, R., Krueger, G., Petrov, M., Khlaaf, H., Sastry, G., Mishkin, P., Chan, B., Gray, S., Ryder, N., Pavlov, M., Power, A., Kaiser, L., Bavarian, M., Winter, C., Tillet, P., Such, F. P., Cummings, D., Plappert, M., Chantzis, F., Barnes, E., Herbert-Voss, A., Guss, W. H., Nichol, A., Paino, A., Tezak, N., Tang, J., Babuschkin, I., Balaji, S., Jain, S., Saunders, W., Hesse, C., Carr, A. N., Leike, J., Achiam, J., Misra, V., Morikawa, E., Radford, A., Knight, M., Brundage, M., Murati, M., Mayer, K., Welinder, P., McGrew, B., Amodei, D., McCandlish, S., Sutskever, I., and Zaremba, W · 2021
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Training verifiers to solve math word problems
Cobbe, K., Kosaraju, V., Bavarian, M., Chen, M., Jun, H., Kaiser, L., Plappert, M., Tworek, J., Hilton, J., Nakano, R., et al · 2021
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The neural basis of delayed gratification
Gao, Z., Wang, H., Lu, C., Lu, T., Froudist-Walsh, S., Chen, M., Wang, X.-J., Hu, J., and Sun, W · 2021
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Measuring mathematical problem solving with the math dataset
Hendrycks, D., Burns, C., Kadavath, S., Arora, A., Basart, S., Tang, E., Song, D., and Steinhardt, J · 2021
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Training language models to follow instructions with human feedback, 2022
Ouyang, L., Wu, J., Jiang, X., Almeida, D., Wainwright, C. L., Mishkin, P., Zhang, C., Agarwal, S., Slama, K., Ray, A., Schulman, J., Hilton, J., Kelton, F., Miller, L., Simens, M., Askell, A., Welinder, P., Christiano, P., Leike, J., and Lowe, R · 2022
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Chain-of-thought prompting elicits reasoning in large language models
Wei, J., Wang, X., Schuurmans, D., Bosma, M., ichter, b., Xia, F., Chi, E., Le, Q. V., and Zhou, D · 2022
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Star: Bootstrapping reasoning with reasoning
Zelikman, E., Wu, Y., Mu, J., and Goodman, N · 2022
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Introducing claude, 2023
Anthropic · 2023
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TheoremQA: A theorem-driven question answering dataset
Chen, W., Yin, M., Ku, M., Lu, P., Wan, Y., Ma, X., Xu, J., Wang, X., and Xia, T · 2023
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Raft: Reward ranked finetuning for generative foundation model alignment
Dong, H., Xiong, W., Goyal, D., Zhang, Y., Chow, W., Pan, R., Diao, S., Zhang, J., KaShun, S., and Zhang, T · 2023
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Alphazero-like tree-search can guide large language model decoding and training, 2023
Feng, X., Wan, Z., Wen, M., McAleer, S. M., Wen, Y., Zhang, W., and Wang, J · 2023
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Reinforced self-training (rest) for language modeling
Gulcehre, C., Paine, T. L., Srinivasan, S., Konyushkova, K., Weerts, L., Sharma, A., Siddhant, A., Ahern, A., Wang, M., Gu, C., et al · 2023
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Let’s verify step by step
Lightman, H., Kosaraju, V., Burda, Y., Edwards, H., Baker, B., Lee, T., Leike, J., Schulman, J., Sutskever, I., and Cobbe, K · 2024
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Introducing meta llama 3: The most capable openly available llm to date., 2024
Meta · 2024
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Learning to reason with llms, 2024
OpenAI · 2024
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GPQA: A graduate-level google-proof q&a benchmark
Rein, D., Hou, B. L., Stickland, A. C., Petty, J., Pang, R. Y., Dirani, J., Michael, J., and Bowman, S. R · 2024
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Scaling llm test-time compute optimally can be more effective than scaling model parameters, 2024
Snell, C., Lee, J., Xu, K., and Kumar, A · 2024
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Roformer: Enhanced transformer with rotary position embedding
Su, J., Ahmed, M., Lu, Y., Pan, S., Bo, W., and Liu, Y · 2024
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The flan collection: Designing data and methods for effective instruction tuning
Longpre, S., Hou, L., Vu, T., Webson, A., Chung, H. W., Tay, Y., Zhou, D., Le, Q. V., Zoph, B., Wei, J., and Roberts, A · 2023
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OpenAI · 2023
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Openwebmath: An open dataset of high-quality mathematical web text, 2023
Paster, K., Santos, M. D., Azerbayev, Z., and Ba, J · 2023
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Beyond human data: Scaling self-training for problem-solving with language models
Singh, A., Co-Reyes, J. D., Agarwal, R., Anand, A., Patil, P., Liu, P. J., Harrison, J., Lee, J., Xu, K., Parisi, A., et al · 2023
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Llama: Open and efficient foundation language models, 2023
Touvron, H., Lavril, T., Izacard, G., Martinet, X., Lachaux, M.-A., Lacroix, T., Rozière, B., Goyal, N., Hambro, E., Azhar, F., Rodriguez, A., Joulin, A., Grave, E., and Lample, G · 2023
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Scaling relationship on learning mathematical reasoning with large language models
Yuan, Z., Yuan, H., Li, C., Dong, G., Tan, C., and Zhou, C · 2023
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Don’t teach. incentivize
Chung, H. W · 2024
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DART-math: Difficulty-aware rejection tuning for mathematical problem-solving
Tong, Y., Zhang, X., Wang, R., Wu, R., and He, J · 2024
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Metamath: Bootstrap your own mathematical questions for large language models
Yu, L., Jiang, W., Shi, H., YU, J., Liu, Z., Zhang, Y., Kwok, J., Li, Z., Weller, A., and Liu, W · 2024
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Mammoth2: Scaling instructions from the web
Yue, X., Zheng, T., Zhang, G., and Chen, W · 2024
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SGLang: Efficient execution of structured language model programs
Zheng, L., Yin, L., Xie, Z., Sun, C., Huang, J., Yu, C. H., Cao, S., Kozyrakis, C., Stoica, I., Gonzalez, J. E., Barrett, C., and Sheng, Y · 2024
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Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning, 2025
DeepSeek-AI · 2025
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Advancing language model reasoning through reinforcement learning and inference scaling, 2025
Hou, Z., Lv, X., Lu, R., Zhang, J., Li, Y., Yao, Z., Li, J., Tang, J., and Dong, Y · 2025
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Reinforce++: A simple and efficient approach for aligning large language models
Hu, J · 2025
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Kimi k1.5: Scaling reinforcement learning with llms, 2025
Kimi Team · 2025
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Tinyzero, 2025
Pan, J., Zhang, J., Wang, X., and Yuan, L · 2025
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7b model and 8k examples: Emerging reasoning with reinforcement learning is both effective and efficient
Zeng, W., Huang, Y., Liu, W., He, K., Liu, Q., Ma, Z., and He, J · 2025
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