• [2025-03-04] 🚀 Released SoS-7B model on Hugging Face
• [2025-03-04] 📰 Featured in Hugging Face's Daily Paper Report
• [2024-03-04] 📜 Paper Released: SoS1: O1 and R1-Like Reasoning LLMs are Sum-of-Square Solvers

• 📜 Paper
• 🤗 SoS-7B Model

Large Language Models (LLMs) have achieved human-level proficiency across diverse tasks, but their ability to perform rigorous mathematical problem solving remains an open challenge. In this work, we investigate a fundamental yet computationally intractable problem: determining whether a given multivariate polynomial is nonnegative. This problem, closely related to Hilbert's Seventeenth Problem, plays a crucial role in global polynomial optimization and has applications in various fields. First, we introduce SoS-1K, a meticulously curated dataset of approximately 1,000 polynomials, along with expert-designed reasoning instructions based on five progressively challenging criteria. Evaluating multiple state-of-the-art LLMs, we find that without structured guidance, all models perform only slightly above the random guess baseline 50%. However, high-quality reasoning instructions significantly improve accuracy, boosting performance up to 81%. Furthermore, our 7B model, SoS-7B, fine-tuned on SoS-1K for just 4 hours, outperforms the 671B DeepSeek-V3 and GPT-4o-mini in accuracy while only requiring 1.8% and 5% of the computation time needed, respectively. Our findings highlight the potential of LLMs to push the boundaries of mathematical reasoning and tackle NP-hard problems.

First, create and activate a Conda environment:

conda create --name sos python=3.10
conda activate sos

To install the required Python packages, use the requirements.txt file. Run the following command in the root directory of your project:

pip install -r requirements.txt

Before running the evaluation, ensure that you have configured the necessary settings in the code:

1. API Key Configuration:

   • Open the sos/evals/sos_api_caller.py file.
   • Configure your API keys for the models you intend to use. This includes setting the keys for deepseek_key, siliconflow_key, qwen_key, chatgpt_key, and volc_key as needed.

2. Model and Channel Selection:

   • Open the sos/evals/experiment_controller.py file.
   • In the configuration section, specify the models and channels you wish to use for the evaluation. You can adjust the model_configs list to include the desired models and their respective channels.
   • Set the sample_size to determine the number of data samples to use for the evaluation. If sample_size is set to None, all available data will be used.

Once the configuration is complete, you can start the evaluation by running the experiment_controller.py script. This will execute the evaluation process using the specified models and datasets.

python sos/evals/experiment_controller.py

This command will initiate the evaluation, and the results will be processed and saved as specified in the script.

The evaluation datasets are located in the /data directory. We provide two main datasets for evaluation:

1. SoS Dataset (Length ~4k): This dataset is designed for evaluating the performance of models on polynomial non-negativity determination tasks. It contains polynomials with a length of approximately 4,000 tokens.

2. Comparison Dataset: This dataset is used for comparing the performance of our models with traditional solvers. It includes a variety of polynomial instances that are also used in the benchmarks presented in our paper.

The training scripts are located in the /sos/train directory. We utilize LlamaFactory for training our models. The provided scripts allow you to replicate the training process used to fine-tune our SoS-7B model on the SoS-1K dataset.

To train the model, navigate to the /sos/train directory and follow the instructions in the training scripts. Ensure that your environment is set up with the necessary dependencies as outlined in the installation section.

If you find this project helpful, please consider citing our paper:

@misc{sos1_2024,
  title={SoS1: O1 and R1-Like Reasoning LLMs are Sum-of-Square Solvers},
  author={Li, Kechen and Zhu, Wenqi and Cartis, Coralia and Ji, Tianbo and Liu, Shiwei},
  howpublished={arXiv preprint arXiv:2502.20545 [cs.LG]},
  year={2025}
}

We thank all contributors for their efforts! Special thanks to:

• Project team members
• All code contributors
• Peers who provided feedback and suggestions

This project is licensed under the Apache 2.0 License - see the LICENSE file for details