OpenMathInstruct-2

OpenMathInstruct-2 is a math instruction tuning dataset with 14M problem-solution pairs generated using the Llama3.1-405B-Instruct model.

The training set problems of GSM8K and MATH are used for constructing the dataset in the following ways:

• Solution augmentation: Generating chain-of-thought solutions for training set problems in GSM8K and MATH.
• Problem-Solution augmentation: Generating new problems, followed by solutions for these new problems.

OpenMathInstruct-2 dataset contains the following fields:

• problem: Original problem from either the GSM8K or MATH training set or augmented problem from these training sets.
• generated_solution: Synthetically generated solution.
• expected_answer: For problems in the training set, it is the ground-truth answer provided in the datasets. For augmented problems, it is the majority-voting answer.
• problem_source: Whether the problem is taken directly from GSM8K or MATH or is an augmented version derived from either dataset.

We also release the 1M, 2M, and 5M, fair-downsampled versions of the entire training set corresponding to points in the above scaling plot. These splits are referred to as train_1M, train_2M, and train_5M. To use these subsets, just specify one of these subsets as split while downloading the data:

from datasets import load_dataset
<h1 class="text-2xl font-bold mt-8 mb-4 text-gray-900 dark:text-white">Download only the 1M training split</h1>
dataset = load_dataset('nvidia/OpenMathInstruct-2', split='train_1M', streaming=True)

To download the entire training set and to convert it into the jsonl format, use the following code snippet. This might take 20-30 minutes (or more depending on your network connection) and will use ~20Gb of RAM.

import json
from datasets import load_dataset
from tqdm import tqdm
dataset = load_dataset('nvidia/OpenMathInstruct-2', split='train')
print("Converting dataset to jsonl format")
output_file = "openmathinstruct2.jsonl"
with open(output_file, 'w', encoding='utf-8') as f:
    for item in tqdm(dataset):
        f.write(json.dumps(item, ensure_ascii=False) + '\n')
print(f"Conversion complete. Output saved as {output_file}")

Apart from the dataset, we also release the contamination explorer for looking at problems in the OpenMathInstruct-2 dataset that are similar to the GSM8K, MATH, AMC 2023, AIME 2024, and Omni-MATH test set problems.

See our paper to learn more details!

Note

OpenMath2 models

To demonstrate the quality of this dataset, we release a series of OpenMath2 models trained on this data.

| 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 \| HF) | 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 \| HF) | 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
• Models
• Dataset

Reproducing our results

We provide all instructions to fully reproduce our results, including data generation.

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}
}