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# BFS-Prover
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## Model Details
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- Strategic filtering of problems solvable by beam search
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- Progressive focusing on harder theorems
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- Continuous policy improvement through iterative training
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2. **Direct Preference Optimization (DPO)**
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- Leverages compiler feedback for policy refinement
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- Uses positive and negative tactic pairs for learning
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- Improves sampling efficiency during proof search
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3. **Length-Normalized BFS**
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- Incorporates path length normalization
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- Enables effective exploration of deeper proof paths
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- Balances between shallow and deep reasoning
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## Performance
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- **Search Configuration**:
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- Temperature: 1.1
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- Expansion width: 2
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- Length normalization factor: 0.5
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## Usage
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```python
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from transformers import AutoModelForCausalLM, AutoTokenizer
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tokenizer = AutoTokenizer.from_pretrained(model_name)
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model = AutoModelForCausalLM.from_pretrained(model_name)
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# For memory-efficient loading
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model = AutoModelForCausalLM.from_pretrained(
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model_name,
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device_map="auto", # Automatic device mapping
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load_in_8bit=True # Or load_in_4bit=True for more memory savings
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)
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```
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- torch
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##
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- Trade-off between model size and inference speed in tree search
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## Citation
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```bibtex
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@article{
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title={BFS-Prover: Scalable Best-First Tree Search for LLM-based Automatic Theorem Proving},
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author={Xin, Ran and Xi, Chenguang and Yang, Jie and Chen, Feng and Wu, Hang and Xiao, Xia and Sun, Yifan and Zheng, Shen and Shen, Kai},
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}
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```
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##
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- Ran Xin (Seed Foundation Code, ByteDance)
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- Chenguang Xi (Seed Foundation Code, ByteDance)
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- Jie Yang (Applied Machine Learning, ByteDance)
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- Feng Chen (Stanford University)
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- Yifan Sun (Seed Foundation Code, ByteDance)
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- Shen Zheng (Seed Foundation Code, ByteDance)
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- Kai Shen (Seed Foundation Code, ByteDance)
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# BFS-Prover Tactic Generator
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This repository contains the latest tactic generator model checkpoint from BFS-Prover, a state-of-the-art theorem proving system. While the full BFS-Prover system integrates multiple components for scalable theorem proving, we are releasing the core tactic generation model that achieved competitive performance on formal mathematics tasks.
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## Model Details
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- Base Model: Qwen2.5-Math-7B
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- Training Approach:
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- Supervised Fine-Tuning (SFT) on state-tactic pairs
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- Direct Preference Optimization (DPO) using compiler feedback
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- Training Data Sources:
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- Mathlib (via LeanDojo)
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- Lean-Github repositories
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- Lean-Workbook
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- Autoformalized NuminaMath-CoT dataset
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## Performance
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When integrated into the full BFS-Prover system, this tactic generator model achieved
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72.54% success rate on MiniF2F test set accumulatively.
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## Usage
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```python
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# Example code for loading and using the tactic generator model
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from transformers import AutoModelForCausalLM, AutoTokenizer
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model = AutoModelForCausalLM.from_pretrained("path/to/bfsprover-tactic-generator")
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tokenizer = AutoTokenizer.from_pretrained("path/to/bfsprover-tactic-generator")
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# Input format example:
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prompt = f"{Lean4 TacticState}" + ":::"
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inputs = tokenizer(prompt, return_tensors="pt")
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outputs = model.generate(**inputs)
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tactic = tokenizer.decode(outputs[0])
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```
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## System Requirements
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- Compatible with Hugging Face Transformers library
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- Recommended: 16GB+ GPU memory for inference
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## Citation
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If you use this model in your research, please cite our paper:
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```bibtex
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@article{xin2025bfs,
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title={BFS-Prover: Scalable Best-First Tree Search for LLM-based Automatic Theorem Proving},
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author={Xin, Ran and Xi, Chenguang and Yang, Jie and Chen, Feng and Wu, Hang and Xiao, Xia and Sun, Yifan and Zheng, Shen and Shen, Kai},
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journal={arXiv preprint arXiv:2502.03438},
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year={2025}
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}
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```
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## License
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https://choosealicense.com/licenses/apache-2.0/
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## Contact
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For questions and feedback about the tactic generator model, please contact:
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- Ran Xin ([email protected])
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- Kai Shen ([email protected])
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