---
license: llama3.1
base_model:
- meta-llama/Llama-3.1-8B
datasets:
- nvidia/OpenMathInstruct-2
language:
- en
tags:
- nvidia
- math
---

# OpenMath2-Llama3.1-8B

OpenMath2-Llama3.1-8B is obtained by finetuning [Llama3.1-8B-Base](https://huggingface.co/meta-llama/Llama-3.1-8B) with [OpenMathInstruct-2](https://huggingface.co/datasets/nvidia/OpenMathInstruct-2).

The model outperforms [Llama3.1-8B-Instruct](https://huggingface.co/meta-llama/Llama-3.1-8B-Instruct) on all the popular math benchmarks we evaluate on, especially on [MATH](https://github.com/hendrycks/math) by 15.9%. 

<!-- <p align="center">
  <img src="scaling_plot.jpg" width="350"><img src="math_level_comp.jpg" width="350">
</p> -->

  <style>
      .image-container {
          display: flex;
          justify-content: center;
          align-items: center;
          gap: 20px;
      }
      .image-container img {
          width: 350px;
          height: auto;
      }
  </style>

<div class="image-container">
        <img src="scaling_plot.jpg" title="Performance of Llama-3.1-8B-Instruct as it is trained on increasing proportions of OpenMathInstruct-2">
        <img src="math_level_comp.jpg" title="Comparison of OpenMath2-Llama3.1-8B vs. Llama-3.1-8B-Instruct across MATH levels">
    </div>

| Model | GSM8K | MATH | AMC 2023 | AIME 2024 | Omni-MATH |
|:---|:---:|:---:|:---:|:---:|:---:|
| Llama3.1-8B-Instruct | 84.5 | 51.9 | 9/40 | 2/30 | 12.7 |
| **OpenMath2-Llama3.1-8B** ([nemo](https://huggingface.co/nvidia/OpenMath2-Llama3.1-8B-nemo) \| [HF](https://huggingface.co/nvidia/OpenMath2-Llama3.1-8B)) | 91.7 | 67.8 | 16/40 | 3/30 | 22.0 |
| + majority@256 | 94.1 | 76.1 | 23/40 | 3/30 | 24.6 |
| Llama3.1-70B-Instruct | 95.8 | 67.9 | 19/40 | 6/30 | 19.0 |
| OpenMath2-Llama3.1-70B ([nemo](https://huggingface.co/nvidia/OpenMath2-Llama3.1-70B-nemo) \| [HF](https://huggingface.co/nvidia/OpenMath2-Llama3.1-70B)) | 94.9 | 71.9 | 20/40 | 4/30 | 23.1 |
| + majority@256 | 96.0 | 79.6 | 24/40 | 6/30 | 27.6 |

The pipeline we used to produce the data and models is fully open-sourced!

- [Code](https://github.com/Kipok/NeMo-Skills)
- [Models](https://huggingface.co/collections/nvidia/openmath-2-66fb142317d86400783d2c7b)
- [Dataset](https://huggingface.co/datasets/nvidia/OpenMathInstruct-2)


# How to use the models?

Our models are fully compatible with Llama3.1-instruct format, so you should be able to just replace an existing Llama3.1 checkpoint and use it in the same way. 
Please note that these models have not been instruction tuned and might not provide good answers outside of math domain. 

If you don't know how to use Llama3.1 models, we provide convenient [instructions in our repo](https://github.com/Kipok/NeMo-Skills/blob/main/docs/inference.md).

# Reproducing our results

We provide [all instructions](https://github.com/Kipok/NeMo-Skills/blob/main/docs/reproducing-results.md) to fully reproduce our results.

## Citation

If you find our work useful, please consider citing us!

```bibtex
@article{toshniwal2024openmath2,
  title   = {OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data},
  author  = {Shubham Toshniwal and Wei Du and Ivan Moshkov and  Branislav Kisacanin and Alexan Ayrapetyan and Igor Gitman},
  year    = {2024},
  journal = {arXiv preprint arXiv:2410.01560}
}
```

## Terms of use

By accessing this model, you are agreeing to the LLama 3.1 terms and conditions of the [license](https://github.com/meta-llama/llama-models/blob/main/models/llama3_1/LICENSE), [acceptable use policy](https://github.com/meta-llama/llama-models/blob/main/models/llama3_1/USE_POLICY.md) and [Meta’s privacy policy](https://www.facebook.com/privacy/policy/)