We introduce an iterative self-checking approach that significantly improves the verification accuracy of mathematical solutions for language models. Our method achieves remarkable performance with Deepseek R1 distilled models, enabling 7B/8B models to surpass all 70B/72B models and GPT-4o on ProcessBench. For example, with DeepSeek-R1-Distill-Qwen-7B, our method achieves 71.3% accuracy on ProcessBench, while with DeepSeek- 79AF R1-Distill-Llama-8B it achieves 67.2% accuracy. In the Iterative Self-checking method, each LLM iteratively checks its own identifications, and the final output is only produced when multiple LLMs demonstrate consistent self-checking over time.
git clone https://github.com/jcguo123/Iterative-self-checking.git
cd Iterative-self-checking
pip install -r requirements.txt For data in a JSON file. First, run the following code to generate the results for the first verification.
python ./code/generation/initial_verification.py --model_path <MODEL_PATH> --dataset_path <DATASET_PATH> --output_dic <OUTPUT_DIR>Then, run the following code for the self-checking rounds.
python ./code/generation/self_checking.py --model_path <MODEL_PATH> --output_dic <OUTPUT_DIRECTORY>To run our evaluation scripts, run:
python ./code/evaluation/evaluation.py --model <MODEL_NAME> --output_dic <OUTPUT_DIRECTORY>To evaluate the error detection capabilities, we choose three annotated mathematical step datasets, PRM800K, ProcessBench, and MathCheck. These benchmarks contain problems from GSM8K, MATH dataset, OlympiadBench, and Omni-MATH.
| Model | Mathcheck* | ProcessBench | PRM800K |
|---|---|---|---|
| GPT-4o mini | 78.8 | 52.9 | 34.0 |
| + Iterative Self-checking | 84.8 | 58.2 | 39.0 |
| GPT-40 | 87.3 | 62.5 | 41.6 |
| + Iterative Self-checking | 91.8 | 69.1 | 51.6 |
| Llama 3.1 8B Instruct | 13.3 | 6.4 | 2.4 |
| + Iterative Self-checking | 60.2 | 35.5 | 22.1 |
| Mistral 7B Instruct v0.3 | 26.4 | 20.3 | 13.0 |
| + Iterative Self-checking | 37.4 | 22.5 | 13.3 |
| Deepseek-R1-Qwen-7B | 86.0 | 54.8 | 46.2 |
| + Iterative Self-checking | 89.5 | 71.3 | 57.7 |
| Deepseek-R1-Llama-8B | 35.9 | 29.3 | 21.2 |
| + Iterative Self-checking | 82.5 | 67.2 | 50.2 |
| Deepseek-R1-Qwen-14B | 91.1 | 71.6 | 54.6 |
| + Iterative Self-checking | 94.8 | 82.2 | 63.2 |
| Deepseek-R1 | 93.5 | 83.3 | 62.9 |