⛓️ Fractured Chain-of-Thought Reasoning ⛓️

🎉 News • 📢 Introduction • 🤝 Support

👷 Installation • 🔎 Evaluation • 📝 Citation

🎉News

• [2025.05.21] We release the first version that mainly supports the pass@k experiments.

📢Introduction

We introduce Fractured Sampling, a unified inference-time strategy that interpolates between full CoT and solution-only sampling along three orthogonal axes: (1) the number of reasoning trajectories (n dimension), (2) the number of final solutions per trajectory (m dimension), and (3) the depth at which reasoning traces are truncated (H dimension).

Main Takeaways

1. 📈 The long-reasoning LLM is able to use truncated CoT to derive a correct solution.
2. 🌟 We can sample in 3D: the full-CoT (n dimensin), the solution (m dimension) and the truncated CoT (H dimension). The H dimension shows the steepest log-linear scaling gains in Pass@k.
3. 🚀 Sampling over all 3 dimensions offers the highest Pass@k.
4. 📊 We can use a process reward model to select the best solution among all 3D samplings, a ~10% accuracy improvement compared to only sampling in the n dimension.
5. 🧠 We can use the self-consistency property within the H dimension to early stop the genration, saving 20% tokens without sacrifying accuracy.

🤝Support

• Pass@k for single dimension and multiple dimensions.
• Best-of-N accross multiple dimensions.
• Early stopping for efficient generation.

👷Installation

conda create -n frac_cot python=3.10
conda activate frac_cot
pip install -r requirements.txt

🔎Evaluation

1. Pass@k for single and multiple dimensions.

   # Generation
   bash ./scripts/gen.sh
   # Evaluate
   bash ./scriots/passk.sh

📝Citation

If you find our work useful, please cite as:

@article{liao2025fractured,
  title={Fractured Chain-of-Thought Reasoning},
  author={Liao, Baohao and Dong, Hanze and Xu, Yuhui and Sahoo, Doyen and Monz, Christof and Li, Junnan and Xiong, Caiming},
  journal={arXiv preprint arXiv:2505.12992},
  year={2025}
}