README.md

---
library_name: transformers
license: apache-2.0
license_link: https://huggingface.co/Qwen/Qwen3-32B/blob/main/LICENSE
pipeline_tag: text-generation
---
<div align="center">

# 🧩 ReForm: Reflective Autoformalization with Prospective Bounded Sequence Optimization

<a href="https://arxiv.org/pdf/2510.24592"><img src="https://img.shields.io/badge/Paper-arXiv-d63031?logo=arxiv&logoColor=white"></a>
<a href="https://huggingface.co/collections/GuoxinChen/reform"><img src="https://img.shields.io/badge/%F0%9F%A4%97%20Hugging%20Face-Models-0984e3"></a>
<a href="https://github.com/Chen-GX/ReForm"><img src="https://img.shields.io/badge/GitHub-ReForm-black?logo=github"></a>

</div>

**ReForm** is a reflective **Autoformalization** framework that enables large language models to *generate → verify → refine* formal mathematical statements in an integrated self-corrective loop. 
It introduces **Prospective Bounded Sequence Optimization (PBSO)** — a novel reinforcement learning algorithm designed for heterogeneous rewards at different sequence positions — enabling stable, reflective training and substantial gains in semantic fidelity.

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## 🚀 Highlights

- 🪞 **Reflective Autoformalization Paradigm**  
  Turns single-pass translation into an iterative “generate–validate–refine” cycle, allowing the model to autonomously detect and correct semantic errors.

- ⚖️ **Prospective Bounded Sequence Optimization (PBSO)**  
  A reinforcement learning algorithm with position-specific rewards for both task accuracy and critique quality, ensuring stable and interpretable optimization.

- 📈 **State-of-the-art Semantic Consistency**  
  ReForm achieves an **average +22.6pp improvement** over the strongest baseline across four formalization benchmarks (miniF2F, ProofNet, Putnam, and AIME 2025).

---

<div align="center">
  <img src="https://github.com/Chen-GX/ReForm/raw/main/images/benchmark_comparison.png" width="100%">
  <br>
  <sub><b>Figure:</b> ReForm consistently outperforms Goedel-V2 and Kimina-Autoformalizer on all benchmarks.</sub>
</div>

---

## 💡 Quick Start

```python
from transformers import AutoTokenizer, AutoModelForCausalLM

model_name = "GuoxinChen/ReForm-8B"  # or "GuoxinChen/ReForm-32B"
tokenizer = AutoTokenizer.from_pretrained(model_name)
model = AutoModelForCausalLM.from_pretrained(model_name, torch_dtype="auto", device_map="auto")

prompt = "Think step by step to translate the mathematical problem in natural language to Lean 4, and verify the consistency.\nLet $a_1, a_2,\\cdots, a_n$ be real constants, $x$ a real variable, and $f(x)=\\cos(a_1+x)+\\frac{1}{2}\\cos(a_2+x)+\\frac{1}{4}\\cos(a_3+x)+\\cdots+\\frac{1}{2^{n-1}}\\cos(a_n+x).$ Given that $f(x_1)=f(x_2)=0,$ prove that $x_2-x_1=m\\pi$ for some integer $m.$"

inputs = tokenizer(prompt, return_tensors="pt").to(model.device)
outputs = model.generate(**inputs, max_new_tokens=32768)
print(tokenizer.decode(outputs[0], skip_special_tokens=True))
```


More Details please refer to our [Github Repo](https://github.com/Chen-GX/ReForm).

# 📚 Citation

If you find ReForm useful for your research, please cite:

```bibtex
@misc{chen2025reform,
      title={ReForm: Reflective Autoformalization with Prospective Bounded Sequence Optimization}, 
      author={Guoxin Chen and Jing Wu and Xinjie Chen and Wayne Xin Zhao and Ruihua Song and Chengxi Li and Kai Fan and Dayiheng Liu and Minpeng Liao},
      year={2025},
      eprint={2510.24592},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2510.24592}, 
}
```