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.
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-previewat 44.6%) - Competitive MATH-500 scores; Minerva lags behind 7B models.
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)
Citation
If this project aids your work, please cite it as:
@inproceedings{
dang2026reinforcement,
title={Reinforcement Learning for Reasoning in Small {LLM}s: What Works and What Doesn{\textquoteright}t},
author={Quy-Anh Dang and Chris Ngo},
booktitle={Logical and Symbolic Reasoning in Language Models @ AAAI 2026},
year={2026},
url={https://openreview.net/forum?id=3pWL6Zxc4A}
}