---
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
- sudoku
arxiv: 2605.10325
---

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

# VPR-Sudoku

[**🌐 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 Sudoku-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 **constraint-based VPR** on Sudoku, where a constraint oracle verifies whether each filled digit is consistent with the puzzle solution.

## 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 Sudoku, VPR uses a constraint-based verifier. The oracle rewards digit placements that are consistent with the valid solution, giving immediate feedback for intermediate reasoning steps.

## Results

### In-Domain Sudoku

| Method | Success Rate | Completion Rate |
|---|---:|---:|
| Base | 3.91 | 63.24 |
| OR | 48.43 | 82.80 |
| MC-PR | 34.72 | 77.39 |
| **VPR** | **56.25** | **85.13** |

### Zero-Shot Transfer

| Benchmark group | Metric | VPR-Sudoku |
|---|---:|---:|
| General reasoning | Average pass@1 | **62.34** |
| General reasoning | GPQA-Diamond | **50.17** |
| General reasoning | BBH | 88.82 |
| General reasoning | MMLU-Pro | 67.88 |
| Agentic reasoning | ALFWorld success rate | 25.62 |
| Agentic reasoning | WebShop score | **34.29** |
| Agentic reasoning | WebShop success rate | **2.20** |

## Usage

```python
from transformers import AutoModelForCausalLM, AutoTokenizer

model_id = "nics-efc/VPR-Sudoku"

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}
}
```