Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective

📝 Introduction

This project implements a novel Chain-of-Reasoning (CoR) framework to significantly enhance the mathematical reasoning capabilities of large language models. By integrating Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR), our model overcomes the limitations of single-paradigm approaches and achieves superior performance on a variety of mathematical tasks, including theorem proving and arithmetic calculations. The model is trained using a progressive paradigm training (PPT) strategy, leading to improved efficiency and strong zero-shot generalization capabilities. It aims to deal with the challenge that existing LLMs often depend on single reasoning paradigm, which resticts the model performance, and the model can achieve multi-paradigm cooperation.

📄 Table of Contents

🔧 Setup Environment

1. Install Lean 4

   Follow the instructions on the Lean Community to set up elan and Lean 4.

2. Clone the repository and submodules

   git clone --recurse-submodules https://github.com/yyyhz/CoR.git
   cd CoR
   

3. Install dependencies

   pip3 install -r requirements.txt
   

4. Build Mathlib4

   cd mathlib4
   lake build
   

📚 Create MPM dataset

1. Clone the Lean-Workbook dataset

   Clone the lean_workbook.json from Lean-Workbook, then change the path to the json file in ./utils/generate_informalproof.py, meanwhile set the save_dir to the path where you want to save the enhanced dataset.

2. Generate informal proofs

   Change the export OPENAI_API_KEY=... to your OpenAI API key, then run the following script to generate informal proofs for the Lean-Workbook dataset:

   bash ./script/leanwb_informalproof.sh
   

3. Clone the NuminaMath-TIR dataset

   Clone the data/train-00000-of-00001.parquet from NuminaMath-TIR and convert it to JSON format, then change the path to the json file in ./utils/generate_lean4.py, meanwhile set the save_dir to the path where you want to save the enhanced dataset.

4. Generate Lean4 proofs

   Change the export OPENAI_API_KEY=... to your OpenAI API key, then run the following script to generate Lean4 proofs for the NuminaMath-TIR dataset:

   bash ./script/numinatir_lean4.sh
   

5. Remove Data Leakage

   Change the target data path and your generated data path in discontaminate.sh, then run the following script to remove potential data leakage:

   bash discontaminate.sh
   

🏋️ Training

After creating the MPM dataset according to the above steps and the guidance in our paper, you can start training the model (you might need to change the leave blank or fake fields in the script according to your own situation):

bash ./script/train_CoR.sh

📊 Evaluation

We provide three scipts for evaluating the model on different benchmarks:

bash ./script/eval_CoR_math.sh
bash ./script/eval_CoR_aime2024.sh
bash ./script/eval_CoR_minif2f.sh

🏆 Results

📖 Citation

If you find this repository useful, please consider giving star and citing our paper:

@misc{yu2025chainofreasoningunifiedmathematicalreasoning,
      title={Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective}, 
      author={Yiyao Yu and Yuxiang Zhang and Dongdong Zhang and Xiao Liang and Hengyuan Zhang and Xingxing Zhang and Ziyi Yang and Mahmoud Khademi and Hany Awadalla and Junjie Wang and Yujiu Yang and Furu Wei},
      year={2025},
      eprint={2501.11110},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2501.11110}, 
}

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