OpenMath2-Llama3.1-8B

OpenMath2-Llama3.1-8B

OpenMath2-Llama3.1-8B is obtained by finetuning Llama3.1-8B-Base with OpenMathInstruct-2.

The model outperforms Llama3.1-8B-Instruct on all the popular math benchmarks we evaluate on, especially on 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>

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

• Code
• Models
• Dataset

See our paper to learn more details!

How to use the models?

Our models are trained with the same "chat format" as Llama3.1-instruct models (same system/user/assistant tokens). Please note that these models have not been instruction tuned on general data and thus might not provide good answers outside of math domain.

We recommend using instructions in our repo to run inference with these models, but here is an example of how to do it through transformers api:

import transformers
import torch

model_id = "nvidia/OpenMath2-Llama3.1-8B"

pipeline = transformers.pipeline(
    "text-generation",
    model=model_id,
    model_kwargs={"torch_dtype": torch.bfloat16},
    device_map="auto",
)

messages = [
    {
        "role": "user", 
        "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\n" + 
        "What is the minimum value of $a^2+6a-7$?"},
]

outputs = pipeline(
    messages,
    max_new_tokens=4096,
)
print(outputs[0]["generated_text"][-1]['content'])

Reproducing our results

We provide all instructions to fully reproduce our results.

Citation

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

@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, acceptable use policy and Meta’s privacy policy