🧩 ReForm: Reflective Autoformalization with Prospective Bounded Sequence Optimization

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.

🚀 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).

_{Figure: ReForm consistently outperforms Goedel-V2 and Kimina-Autoformalizer on all benchmarks.}

💡 Quick Start

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.

📚 Citation

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

@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}, 
}