---
pipeline_tag: text-generation
inference: true
license: mit
datasets:
  - knoveleng/open-rs
  - knoveleng/open-s1
  - knoveleng/open-deepscaler
base_model:
  - deepseek-ai/DeepSeek-R1-Distill-Qwen-1.5B
---

# Model Summary

This repository hosts model for the **Open RS** project, accompanying the paper *Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn’t*. The project explores enhancing reasoning capabilities in small large language models (LLMs) using reinforcement learning (RL) under resource-constrained conditions.

We focus on a 1.5-billion-parameter model, `DeepSeek-R1-Distill-Qwen-1.5B`, trained on 4 NVIDIA A40 GPUs (48 GB VRAM each) within 24 hours. By adapting the Group Relative Policy Optimization (GRPO) algorithm and leveraging a curated, compact mathematical reasoning dataset, we conducted three experiments to assess performance and behavior. Key findings include:

- Significant reasoning improvements, e.g., AMC23 accuracy rising from 63% to 80% and AIME24 reaching 46.7%, outperforming `o1-preview`.
- Efficient training with just 7,000 samples at a cost of $42, compared to thousands of dollars for baseline models.
- Challenges like optimization instability and length constraints with extended training.

These results showcase RL-based fine-tuning as a cost-effective approach for small LLMs, making reasoning capabilities accessible in resource-limited settings. We open-source our code, models, and datasets to support further research.

For more details, please refer our [github](https://github.com/knoveleng/open-rs).

## Evaluation
### Performance Highlights
- **Open-RS1**: 53.0% avg. score
- **Open-RS2**: 55.7% avg. score, 80.0% on AMC23
- **Open-RS3**: 56.3% avg. score, 46.7% on AIME24 (outperforms `o1-preview` at 44.6%)
- Competitive MATH-500 scores; Minerva lags behind 7B models.

![Performance Metrics](assets/performances.png)

### Cost Efficiency
Our approach uses 7,000 samples (42,000 total outputs) and costs ~$42 on 4x A40 GPUs in 24 hours, compared to:
- 7B models: `Qwen2.5-7B-SimpleRL` ($1,633), `Eurus-2-7B-PRIME` ($1,088)
- 1.5B models: `DeepScaleR-1.5B-Preview` ($3,629), `Still-3-1.5B-Preview` ($2,268)

![7B Model Costs](assets/costs-7b.png)  
![1.5B Model Costs](assets/costs-1.5b.png)


## Citation
If this project aids your work, please cite it as:
```
@misc{dang2025reinforcementlearningreasoningsmall,
      title={Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn't}, 
      author={Quy-Anh Dang and Chris Ngo},
      year={2025},
      eprint={2503.16219},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2503.16219}, 
}
```