---
base_model:
- deepseek-ai/DeepSeek-Prover-V2-7B
license: mit
library_name: transformers
pipeline_tag: text-generation
tags:
- math
- lean
- theorem-proving
- reinforcement-learning
---

# GAR: Generative Adversarial Reinforcement Learning for Formal Theorem Proving

This is the official model for **GAR: Generative Adversarial Reinforcement Learning**, a framework that jointly trains a problem composer and solver in an adversarial loop for formal theorem proving.

- **Paper:** [GAR: Generative Adversarial Reinforcement Learning for Formal Theorem Proving](https://huggingface.co/papers/2510.11769)
- **Repository:** [GAR-Official](https://github.com/RickySkywalker/GAR-Official)
- **Authors:** Ruida Wang, Jiarui Yao, [Rui Pan](https://huggingface.co/research4pan), Shizhe Diao, Tong Zhang

## Introduction

![main plot](main_plot.png)

We introduce **GAR: Generative Adversarial Reinforcement Learning**, an RL training method that intends to solve inefficiency and suboptimial performance in formal theorem prover training caused by fixed problem sets. GAR jointly trains the problem composer and solver in an adversarial loop, which introduces an implicit curriculum learning mechanism, aligning the task difficulty with the prover's evolving capability to improve training efficiency and enabling stronger model performance. 

Experiments indicates that GAR trained models (such as Goedel-Prover-V2-8B and DeepSeek-Prover-V2-7B) achieve an average of 4.20% of enhancement on MiniF2F-Test under pass@32, and improve the DeepSeek-Prover-V2's pass@32 performance on ProofNet-Test from 22.58% to 25.81%.

## Related Artifacts

### Trained Models
* **GAR_Goedel-Prover-V2:** [RickyDeSkywalker/GAR_Goedel-Prover-V2](https://huggingface.co/RickyDeSkywalker/GAR_Goedel-Prover-V2)
* **GAR_DeepSeek-Prover-V2 (this repo):** [RickyDeSkywalker/GAR_DeepSeek-Prover-V2](https://huggingface.co/RickyDeSkywalker/GAR_DeepSeek-Prover-V2/)

### Base Datasets
* **Original base dataset:** [RickyDeSkywalker/GAR_baseDataset](https://huggingface.co/datasets/RickyDeSkywalker/GAR_baseDataset)
* **Base dataset under Numina-Math:** [RickyDeSkywalker/GAR_baseDataset_NuminaMath](https://huggingface.co/datasets/RickyDeSkywalker/GAR_baseDataset_NuminaMath)

## Training Guide

### Clone repository

Clone the repo using the following command:

```bash
git clone --recurse-submodules git@github.com:RickySkywalker/GAR-Official.git
```

### Init Lean server

We apply KiminaLeanServer as the Lean verification server. It can be initialized by:
```bash
cd KiminaLeanServer
cp .env.template .env
docker compose up -d
```

### Setup environment

The environment can be set up by running the following command:

```bash
conda env create -f environment.yaml
```

### Clone base dataset

Clone and transform the dataset into JSON form:

```python
from datasets import load_dataset
ds = load_dataset("RickyDeSkywalker/GAR_baseDataset_NuminaMath")
ds["train"].to_json("./base_data/GAR_base_data_Numina-Math.json")
```

### Run training

The GAR training can be initialized through the following command, detailed training config can be found in `./main.py`.

```bash
python -u ./main.py \
    --training_name GAR-Prover \
    --base_data_path ./base_data/GAR_base_data_Numina-Math.json
```

## Citation
```bibtex
@article{wang2025gar,
  title={GAR: Generative Adversarial Reinforcement Learning for Formal Theorem Proving},
  author={Wang, Ruida and Yao, Jiarui and Pan, Rui and Diao, Shizhe and Zhang, Tong},
  journal={arXiv preprint arXiv:2510.11769},
  year={2025}
}
```

## Acknowledgement
This material is based upon work supported partially by NSF under Grant No. 2416897, Grant No. 2505932, and by ORN under Grant No. N000142512318. This research used both Delta (NSF award OAC 2005572) and DeltaAI (NSF award OAC 2320345) advanced computing systems, and computing resources provided by NAIRR Pilot NAIRR250157.