---
license: apache-2.0
language:
- en
base_model:
- Qwen/Qwen3-4B
pipeline_tag: text-generation
library_name: transformers
tags:
- qwen3
- reinforcement-learning
- verifiable-rewards
- process-rewards
- agentic-reasoning
- reasoning
- tic-tac-toe
arxiv: 2605.10325
---

![VPR overview](https://thu-nics.github.io/VPR/static/images/overview.png)

# VPR-Tic-Tac-Toe

[**🌐 Project Page**](https://thu-nics.github.io/VPR/) | [**📝 Paper**](https://arxiv.org/abs/2605.10325) | [**💻 Code**](https://github.com/thu-nics/VPR)

## Model Description

This is the Tic-Tac-Toe-trained checkpoint from **VPR: Verifiable Process Rewards for Agentic Reasoning**, initialized from Qwen3-4B.

VPR turns verifiable oracles into dense turn-level rewards for long-horizon agentic reasoning. This checkpoint is trained with **search-based VPR** on Tic-Tac-Toe, where MCTS lookahead identifies strategically optimal moves and provides turn-level feedback.

## Overview

Reinforcement learning from verifiable rewards usually rewards only final success. In long-horizon agentic tasks, this creates a credit assignment problem: a trajectory may fail after many correct steps, or succeed despite flawed intermediate decisions.

VPR studies densely-verifiable agentic reasoning problems, where each intermediate action can be checked by a task-specific oracle. Instead of learning a noisy process reward model or estimating step values through extra rollouts, VPR uses task structure itself to provide reliable turn-level supervision.

## Method

![VPR method](https://thu-nics.github.io/VPR/static/images/vpr.png)

VPR converts sparse trajectory-level feedback into dense process rewards:

```text
r_t^VPR = V(s_t, a_t)
```

For Tic-Tac-Toe, VPR uses a search-based verifier. MCTS lookahead evaluates legal moves and rewards strategically strong actions according to the estimated search value.

## Results

### In-Domain Tic-Tac-Toe

Tic-Tac-Toe reports average return against a strong MCTS opponent.

| Method | First Player | Second Player |
|---|---:|---:|
| Base | -0.31 | -0.35 |
| OR | -0.18 | -0.21 |
| MC-PR | -0.11 | -0.20 |
| **VPR** | **-0.09** | **-0.11** |

### Zero-Shot Transfer

| Benchmark group | Metric | VPR-Tic-Tac-Toe |
|---|---:|---:|
| General reasoning | Average pass@1 | **62.16** |
| General reasoning | AIME24 | **33.33** |
| General reasoning | AIME25 | **21.33** |
| General reasoning | BBH | **88.96** |
| Agentic reasoning | ALFWorld success rate | 27.34 |
| Agentic reasoning | WebShop score | 30.88 |
| Agentic reasoning | WebShop success rate | 1.83 |

## Usage

```python
from transformers import AutoModelForCausalLM, AutoTokenizer

model_id = "nics-efc/VPR-Tic-Tac-Toe"

tokenizer = AutoTokenizer.from_pretrained(model_id, trust_remote_code=True)
model = AutoModelForCausalLM.from_pretrained(
    model_id,
    torch_dtype="auto",
    device_map="auto",
    trust_remote_code=True,
)

messages = [
    {"role": "user", "content": "Solve this step by step: If a train travels 180 miles in 3 hours, what is its average speed?"}
]
text = tokenizer.apply_chat_template(
    messages,
    tokenize=False,
    add_generation_prompt=True,
    enable_thinking=True,
)
inputs = tokenizer([text], return_tensors="pt").to(model.device)
outputs = model.generate(**inputs, max_new_tokens=1024)
print(tokenizer.decode(outputs[0], skip_special_tokens=True))
```

## Intended Use

This checkpoint is intended for research on verifiable rewards, process supervision, reinforcement learning for LLM agents, and transfer from game-like agentic training environments to broader reasoning tasks.

The released checkpoint contains the trained language model. Environment simulators, verifiers, and training code are provided in the project repository.

## Citation

If you find this model helpful, please cite:

```bibtex
@misc{yuan2026verifiable,
  title={Verifiable Process Rewards for Agentic Reasoning},
  author={Huining Yuan and Zelai Xu and Huaijie Wang and Xiangmin Yi and Jiaxuan Gao and Xiao-Ping Zhang and Yu Wang and Chao Yu and Yi Wu},
  year={2026},
  eprint={2605.10325},
  archivePrefix={arXiv},
  primaryClass={cs.AI},
  url={https://arxiv.org/abs/2605.10325}
}
```