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# MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models
[](CODE_LICENSE)
[](MetaMath/LICENSE)
[](https://www.python.org/downloads/release/python-390/)
<p align="center">
🤗 <a href="https://huggingface.co/meta-math" target="_blank">HF Repo</a> • 📃 <a href="https://arxiv.org/abs/2309.12284" target="_blank">[MetaMath]</a><br>
</p>
<p align="center" width="100%">
<a ><img src="./imgs/metamath.svg" alt="MetaMath" style="width: 80%; min-width: 300px; display: block; margin: auto;"></a>
</p>
## News
- 🔥 Our **MetaMath-Llemma-7B** model achieves **30.0 pass@1** on the MATH Benchmarks, surpassing all the SOTA open-source LLM in 7B-13B scales! All the training scripts and the model are opened.
- 🔥 Our **MetaMath-Mistral-7B** model achieves **77.7 pass@1** on the [GSM8k Benchmarks](https://github.com/openai/grade-school-math), surpassing all the SOTA open-source LLM! All the training scripts and the model are opened.
- 🔥 The full **MetaMathQA** dataset is now released in the huggingface [MetaMathQA](https://huggingface.co/datasets/meta-math/MetaMathQA/tree/main)!
- 🔥 We released the GSM8K_Backward dataset is also released in the huggingface [GSM8K_Backward](https://huggingface.co/datasets/meta-math/GSM8K_Backward) to evaluate the reversal mathematical reasoning ability!
- 🔥 Although the data augmentation for **MetaMathQA** is sourced from **ChatGPT 3.5**, Our **MetaMath-70B** model outperforms the closed-source LLMs **ChatGPT 3.5** on the GSM8K!
- 🔥 Our **MetaMath-7B** model achieves **66.5 pass@1** on the [GSM8k Benchmarks](https://github.com/openai/grade-school-math), **11.6** points higher than the SOTA open-source LLM!
- 🔥 Our **MetaMath-7B** model achieves **19.8 pass@1** on the [MATH Benchmarks](https://github.com/hendrycks/math), **9.1** points higher than the SOTA open-source LLM!
| Model | Checkpoint | Paper | GSM8k | MATH | License|
| ----- |------| ---- |------|-------| ----- |
| MetaMath-70B-V1.0 | 🤗 <a href="https://huggingface.co/meta-math/MetaMath-70B-V1.0" target="_blank">HF Link</a> | 📃 <a href="https://arxiv.org/abs/2309.12284" target="_blank">[MetaMath]</a>| **82.3** | **26.6** | <a href="https://ai.meta.com/resources/models-and-libraries/llama-downloads/" target="_blank">Llama 2 </a> |
| MetaMath-13B-V1.0 | 🤗 <a href="https://huggingface.co/meta-math/MetaMath-13B-V1.0" target="_blank">HF Link</a> | 📃 <a href="https://arxiv.org/abs/2309.12284" target="_blank">[MetaMath]</a>| **72.3** | **22.4** | <a href="https://ai.meta.com/resources/models-and-libraries/llama-downloads/" target="_blank">Llama 2 </a> |
| MetaMath-7B-V1.0 | 🤗 <a href="https://huggingface.co/meta-math/MetaMath-7B-V1.0" target="_blank">HF Link</a> | 📃 <a href="https://arxiv.org/abs/2309.12284" target="_blank">[MetaMath]</a>| **66.5** | **19.8** | <a href="https://ai.meta.com/resources/models-and-libraries/llama-downloads/" target="_blank">Llama 2 </a>|
| MetaMath-Mistral-7B | 🤗 <a href="https://huggingface.co/meta-math/MetaMath-Mistral-7B" target="_blank">HF Link</a> | 📃 <a href="https://arxiv.org/abs/2309.12284" target="_blank">[MetaMath]</a>| **77.7** | **28.2** | <a href="http://www.apache.org/licenses/" target="_blank">Apache License 2.0 </a>|
| MetaMath-Llemma-7B | 🤗 <a href="https://huggingface.co/meta-math/MetaMath-Llemma-7B" target="_blank">HF Link</a> | 📃 <a href="https://arxiv.org/abs/2309.12284" target="_blank">[MetaMath]</a>| **69.2** | **30.0** | <a href="http://www.apache.org/licenses/" target="_blank">Apache License 2.0 </a>|
## Comparing MetaMath with the LLM models.
🔥 Comprehensive Results
| Model | GSM8k Pass@1 | MATH Pass@1 |
|---------------------|--------------|-------------|
| MPT-7B | 6.8 | 3.0 |
| Falcon-7B | 6.8 | 2.3 |
| LLaMA-1-7B | 11.0 | 2.9 |
| LLaMA-2-7B | 14.6 | 2.5 |
| MPT-30B | 15.2 | 3.1 |
| LLaMA-1-13B | 17.8 | 3.9 |
| GPT-Neo-2.7B | 19.5 | -- |
| Falcon-40B | 19.6 | 2.5 |
| Baichuan-chat-13B | 23.9 | -- |
| Vicuna-v1.3-13B | 27.6 | -- |
| LLaMA-2-13B | 28.7 | 3.9 |
| InternLM-7B | 31.2 | -- |
| ChatGLM-2-6B | 32.4 | -- |
| GPT-J-6B | 34.9 | -- |
| LLaMA-1-33B | 35.6 | 3.9 |
| LLaMA-2-34B | 42.2 | 6.24 |
| RFT-7B | 50.3 | -- |
| LLaMA-1-65B | 50.9 | 10.6 |
| Qwen-7B | 51.6 | -- |
| WizardMath-7B | 54.9 | 10.7 |
| LLaMA-2-70B | 56.8 | 13.5 |
| WizardMath-13B | 63.9 | 14.0 |
| 🔥 MetaMath-7B | **66.5** | **19.8** |
| 🔥 MetaMath-13B | **72.3** | **22.4** |
| 🔥 MetaMath-Mistral-7B | **77.7** | **28.2** |
| 🔥 MetaMath-Llemma-7B | **69.2** | **30.0** |
| WizardMath-70B | 81.6 | 22.7 |
| 🔥 MetaMath-70B | **82.3** | **26.6** |
<h2 id="env">Quick Start</h2>
Clone Metamath and install the required packages:
```bash
git clone https://github.com/meta-math/MetaMath.git
cd MetaMath
pip install -r requirements.txt
```
If you encounter a Ray installation problem, please run:
```bash
pip install --upgrade ray
pip install --upgrade pyarrow
pip install pandas
```
<h2 id="Inference">Dataset Usage</h2>
Run the following command to load the data:
```python
from datasets import load_dataset
dataset = load_dataset("meta-math/MetaMathQA")
```
<h2 id="train">Training</h2>
you need to prepare the llama-2 base model and our **MetaMathQA** dataset huggingface [MetaMathQA](https://huggingface.co/datasets/meta-math/MetaMathQA/tree/main)
```
bash run.sh
```
or
```
CUDA_VISIBLE_DEVICES=0,1,2,3,4,5,6,7 python3 -m torch.distributed.launch --master_addr ${MASTER_ADDR} --master_port ${MASTER_PORT} --nproc_per_node=8 --use_env train_math.py \
--model_name_or_path "meta-llama/Llama-2-7b-hf" \
--data_path "path/to/metamathqa" \
--data_length 10000000 \
--bf16 True \
--output_dir "path/to/save" \
--num_train_epochs 3 \
--per_device_train_batch_size 4 \
--per_device_eval_batch_size 4 \
--gradient_accumulation_steps 4 \
--evaluation_strategy "no" \
--save_strategy "steps" \
--save_steps 1000 \
--save_total_limit 2 \
--learning_rate 2e-5 \
--weight_decay 0. \
--warmup_ratio 0.03 \
--lr_scheduler_type "cosine" \
--logging_steps 1 \
--fsdp "full_shard auto_wrap" \
--fsdp_transformer_layer_cls_to_wrap 'LlamaDecoderLayer' \
--tf32 True
```
### Supervised fine-tuning
We supervised fine-tune MetaMath-7B with the following hyperparameters:
| Hyperparameter | LLaMA 2 7B |
|----------------|-------------|
| Batch size | 128 |
| Learning rate | 2e-5 |
| Epochs | 3 |
| Max length | 512 |
| LR scheduler | cosine |
<h2 id="evaluation">Evaluation</h2>
we use the vllm to help the fast generation:
```
python eval_gsm8k.py --model "path/to/save" --data_file ./data/test/GSM8K_test.jsonl
python eval_math.py --model "path/to/save" --data_file ./data/test/MATH_test.jsonl
```
where the "path/to/save" should be replaced by the finetuned model, you can also download our series of MetaMath models in huggingface:
🤗 <a href="https://huggingface.co/meta-math/MetaMath-7B-V1.0" target="_blank">MetaMath 7B</a> 🤗 <a href="https://huggingface.co/meta-math/MetaMath-13B-V1.0" target="_blank">MetaMath 13B</a> 🤗 <a href="https://huggingface.co/meta-math/MetaMath-70B-V1.0" target="_blank">MetaMath 70B</a>
The inference prompt for our MetaMath is:
```
"Below is an instruction that describes a task. Write a response that appropriately completes the request.\n\n### Instruction:\n{instruction}\n\n### Response: Let's think step by step."
```
Thanks for the open source code of [WizardMath](https://github.com/nlpxucan/WizardLM/tree/main/WizardMath) and [RFT](https://github.com/OFA-Sys/gsm8k-ScRel/tree/main). Some of our codes are based on them.
<h2 id="citation">Citation</h2>
Please cite the paper if you refer to our model, code, data or paper from MetaMath.
```
@article{yu2023metamath,
title={MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models},
author={Yu, Longhui and Jiang, Weisen and Shi, Han and Yu, Jincheng and Liu, Zhengying and Zhang, Yu and Kwok, James T and Li, Zhenguo and Weller, Adrian and Liu, Weiyang},
journal={arXiv preprint arXiv:2309.12284},
year={2023}
}
```
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