@article{yuan2023arithmetic,
  author    = {Yuan, Zheng and Yuan, Hongyi and Tan, Chuanqi and Wang, Wei and Huang, Songfang},
  title     = {How well do Large Language Models perform in Arithmetic tasks?},
  journal   = {arXiv preprint arXiv:2304.02015},
  year      = {2023}
}

@inproceedings{wei2022chain_of_thought,
  author    = {Wei, Jason and Wang, Xuezhi and Schuurmans, Dale and Bosma, Maarten and Ichter, Brian and Xia, Fei and Chi, Ed and Le, Quoc V. and Zhou, Denny},
  title     = {Chain-of-thought prompting elicits reasoning in large language models},
  booktitle = {Advances in Neural Information Processing Systems},
  volume    = {35},
  pages     = {24824--24837},
  year      = {2022}
}

@inproceedings{brown2020gpt3,
  author    = {Brown, Tom and Mann, Benjamin and Ryder, Nick and Subbiah, Melanie and Kaplan, Jared D. and Dhariwal, Prafulla and Neelakantan, Arvind and Shyam, Pranav and Sastry, Girish and Askell, Amanda and others},
  title     = {Language models are few-shot learners},
  booktitle = {Advances in Neural Information Processing Systems},
  volume    = {33},
  pages     = {1877--1901},
  year      = {2020}
}

@article{fedus2022switch_transformer,
  author    = {Fedus, William and Zoph, Barret and Shazeer, Noam},
  title     = {Switch transformer: Scaling to trillion parameter models with simple and efficient sparsity},
  journal   = {Journal of Machine Learning Research},
  volume    = {23},
  number    = {120},
  pages     = {1--39},
  year      = {2022}
}

@inproceedings{hendrycks2021math_dataset,
  author    = {Hendrycks, Dan and Burns, Collin and Kadavath, Saurav and Arora, Akul and Basart, Steven and Tang, Eric and Song, Dawn and Steinhardt, Jacob},
  title     = {Measuring mathematical problem solving with the MATH dataset},
  booktitle = {Advances in Neural Information Processing Systems},
  volume    = {34},
  pages     = {2539--2551},
  year      = {2021}
}

@inproceedings{wang2022self_consistency,
  author    = {Wang, Xuezhi and Wei, Jason and Schuurmans, Dale and Le, Quoc V. and Chi, Ed and Narang, Sharan and Chowdhery, Aakanksha and Zhou, Denny},
  title     = {Self-consistency improves chain of thought reasoning in language models},
  booktitle = {International Conference on Learning Representations},
  year      = {2023}
}

@article{ahn2024math_reasoning,
  author    = {Ahn, Janice and Verma, Rishu and Lou, Renze and Liu, Di and Zhang, Rui and Yin, Wenpeng},
  title     = {Large Language Models for Mathematical Reasoning: Progresses and Challenges},
  journal   = {arXiv preprint arXiv:2402.00157},
  year      = {2024}
}

@article{cobbe2021training_verifiers,
  author    = {Cobbe, Karl and Kosaraju, Vineet and Bavarian, Mohammad and Chen, Mark and Jun, Heewoo and Kaiser, Lukasz and Matthias, Plappert and Tworek, Jerry and Hilton, Jacob and Nakano, Reiichiro and Hesse, Christopher and Schulman, John},
  title     = {Training verifiers to solve math word problems},
  journal   = {arXiv preprint arXiv:2110.14168},
  year      = {2021}
}

@inproceedings{gou2024tora,
  author    = {Gou, Zhibin and Shao, Zhihong and Gong, Yeyun and Shen, Yelong and Yang, Yujiu and Huang, Minlie and Duan, Nan and Chen, Weizhu},
  title     = {ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving},
  booktitle = {International Conference on Learning Representations},
  year      = {2024}
}

@misc{openai2024learning_reason,
  author    = {{OpenAI}},
  title     = {Learning to reason with LLMs},
  year      = {2024},
  url       = {https://openai.com/index/learning-to-reason-with-llms/},
  note      = {Accessed: 2024-09-15}
}

@article{bi2024deepseekmath,
  author    = {Zhihong Shao and Peiyi Wang and Qihao Zhu and Runxin Xu and Junxiao Song and Mingchuan Zhang and Y.K. Li and Y. Wu and Daya Guo},
  title     = {DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models},
  journal   = {arXiv preprint arXiv:2402.03300},
  year      = {2024}
}

@article{yue2024mammoth,
  author    = {Xiang Yue and Xingwei Qu and Ge Zhang and Yao Fu and Wenhao Huang and Huan Sun and Yu Su and Wenhu Chen},
  title     = {MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning},
  journal   = {arXiv preprint arXiv:2309.05653},
  year      = {2023}
}

@article{pan2024mathqa,
  author    = {Amini, Aida and Gabriel, Saadia and Lin, Shanchuan and Koncel-Kedziorski, Rik and Choi, Yejin and Hajishirzi, Hannaneh},
  title     = {MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms},
  journal   = {Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics},
  year      = {2019}
}

@article{zhou2025moe_survey,
  author    = {Fanqi Wan and Ziyi Yang and Fanghua Ye and Longyue Wang and Xiaojun Quan and Deng Cai and Shuming Shi},
  title     = {A Survey on Mixture of Experts in Large Language Models},
  journal   = {IEEE Transactions on Knowledge and Data Engineering},
  year      = {2025}
}

@inproceedings{cobbe2021gsm8k,
  author    = {Cobbe, Karl and Kosaraju, Vineet and Bavarian, Mohammad and Chen, Mark and Jun, Heewoo and Kaiser, Lukasz and Plappert, Matthias and Tworek, Jerry and Hilton, Jacob and Nakano, Reiichiro and Hesse, Christopher and Schulman, John},
  title     = {Training Verifiers to Solve Math Word Problems},
  booktitle = {arXiv preprint arXiv:2110.14168},
  year      = {2021}
}

@article{mirzadeh2024gsm_symbolic,
  author    = {Aman Madaan and Amir Yazdanbakhsh and Denny Zhou and Bernd Bohnet and Arman Cohan and Maithra Raghu and Mehran Kazemi and Behnam Neyshabur and Hugo Larochelle and Katherine Lee},
  title     = {GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models},
  journal   = {arXiv preprint arXiv:2410.05229},
  year      = {2024}
}

@article{wang2024aime,
  author    = {Jonathan Yue and Daniel Klein},
  title     = {Benchmarking LLMs on Advanced Mathematical Reasoning},
  journal   = {UC Berkeley Technical Report EECS-2025-121},
  year      = {2025}
}

@inproceedings{wang2023scibench,
  author    = {Xiaoxuan Wang and Ziniu Hu and Pan Lu and Yanqiao Zhu and Jieyu Zhang and Satyen Subramaniam and Arjun R. Loomba and Shichang Zhang and Yizhou Sun and Wei Wang},
  title     = {SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models},
  booktitle = {International Conference on Machine Learning},
  year      = {2024}
}

@article{kaplan2020scaling,
  author    = {Jared Kaplan and Sam McCandlish and Tom Henighan and Tom B. Brown and Benjamin Chess and Rewon Child and Scott Gray and Alec Radford and Jeffrey Wu and Dario Amodei},
  title     = {Scaling Laws for Neural Language Models},
  journal   = {arXiv preprint arXiv:2001.08361},
  year      = {2020}
}

@article{dubey2024skywork_math,
  author    = {Liang Xiang and Zhining Liu and Tianwen Wei and Liang Zhao and Yuzhi Zhang and Ruijie Zhu and Zijun Yao and Qin Liu and Jingren Zhou and Lei Chen},
  title     = {Skywork-Math: Data Scaling Laws for Mathematical Reasoning in Large Language Models},
  journal   = {arXiv preprint arXiv:2407.08348},
  year      = {2024}
}

@inproceedings{mishra2024mathsensei,
  author    = {Debrup Das and Debopriyo Banerjee and Somak Aditya and Ashish Kulkarni},
  title     = {MATHSENSEI: A Tool-Augmented Large Language Model for Mathematical Reasoning},
  booktitle = {Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics},
  year      = {2024}
}

@article{chen2023pot,
  author    = {Wenhu Chen and Xueguang Ma and Xinyi Wang and William W. Cohen},
  title     = {Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks},
  journal   = {Transactions on Machine Learning Research},
  year      = {2023}
}

@inproceedings{kojima2022zero_shot,
  author    = {Takeshi Kojima and Shixiang Shane Gu and Machel Reid and Yutaka Matsuo and Yusuke Iwasawa},
  title     = {Large Language Models are Zero-Shot Reasoners},
  booktitle = {Advances in Neural Information Processing Systems},
  year      = {2022}
}

@article{li2024code_generation,
  author    = {Jiawei Liu and Chunqiu Steven Xia and Yuyao Wang and Lingming Zhang},
  title     = {Code Generation with Small Language Models: A Deep Evaluation on Codeforces},
  journal   = {arXiv preprint arXiv:2504.07343},
  year      = {2024}
}

@article{trask2018nalu,
  author    = {Andrew Trask and Felix Hill and Scott E. Reed and Jack Rae and Chris Dyer and Phil Blunsom},
  title     = {Neural Arithmetic Logic Units},
  journal   = {Advances in Neural Information Processing Systems},
  volume    = {31},
  year      = {2018}
}

@article{razeghi2022impact,
  author    = {Yasaman Razeghi and IV Robert L. Logan and Matt Gardner and Sameer Singh},
  title     = {Impact of Pretraining Term Frequencies on Few-Shot Reasoning},
  journal   = {arXiv preprint arXiv:2202.07206},
  year      = {2022}
}

@inproceedings{austin2021program,
  author    = {Jacob Austin and Augustus Odena and Maxwell Nye and Maarten Bosma and Henryk Michalewski and David Dohan and Ellen Jiang and Carrie Cai and Michael Terry and Quoc Le and Charles Sutton},
  title     = {Program Synthesis with Large Language Models},
  journal   = {arXiv preprint arXiv:2108.07732},
  year      = {2021}
}

@article{liang2024livecodebench,
  author    = {Naman Jain and King Han and Alex Gu and Wen-Ding Li and Fanjia Yan and Tianjun Zhang and Sida I. Wang and Armando Solar-Lezama and Koushik Sen and Ion Stoica},
  title     = {LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code},
  journal   = {arXiv preprint arXiv:2403.07974},
  year      = {2024}
}

@article{shao2024internlm_math,
  author    = {Huaiyuan Ying and Shuo Zhang and Linyang Li and Zhejian Zhou and Yunfan Shao and Zhaoye Fei and Yichuan Ma and Jiawei Hong and Kuikun Liu and Ziyi Wang and Yudong Wang and Zijian Wu and Shuaibin Li and Fengzhe Zhou and Hongwei Liu and Songyang Zhang and Wenwei Zhang and Hang Yan and Xipeng Qiu and Jiayu Wang and Kai Chen and Dahua Lin},
  title     = {InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning},
  journal   = {arXiv preprint arXiv:2402.06332},
  year      = {2024}
}