File size: 10,552 Bytes
b6e8c8b b2e954f 2c6ee84 b6e8c8b d2ded02 b6e8c8b b2e954f b6e8c8b b2e954f b6e8c8b b2e954f b6e8c8b b2e954f b6e8c8b b2e954f b6e8c8b b2e954f b6e8c8b b2e954f b6e8c8b b2e954f b6e8c8b 2c6ee84 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 |
---
license: apache-2.0
datasets:
- Mathoctopus/GSM8KInstruct_Parallel
language:
- en
- es
- zh
- de
- ru
- th
- sw
- ja
- fr
- bn
---
# 🐙 Breaking Language Barriers in Multilingual Mathematical Reasoning: Insights and Observations
Project Page: [https://mathoctopus.github.io/](https://mathoctopus.github.io/)
Paper: [https://arxiv.org/abs/2310.20246.pdf](https://arxiv.org/abs/2310.20246.pdf)
Code: [https://github.com/microsoft/MathOctopus](https://github.com/microsoft/MathOctopus)
### Introduction
We introduce 🐙 MathOctopus, a series of open-source large language models (LLMs) specifically tailored for multilingual math problem-solving. The MathOctopus models are trained on 🤗 MGSM8KInstruct Dataset, encompassing ten distinct languages.
MathOctopus notably outperforms conventional open-source LLMs and exhibits superiority over ChatGPT in few-shot scenarios.
### Datasets
#### **MGSM8KInstruct**
| Training Dataset | En | Sw | Zh | Bn | De | Es | Fr | Ja | Ru | Th | Overall |
|:----------------------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|
| MGSM8KInstruct | 7473 | 7472 | 7466 | 6539 | 7466 | 7470 | 7469 | 7471 | 7361 | 7473 | **73.6K** |
#### **MSVAMP**
| Test Dataset | En | Sw | Zh | Bn | De | Es | Fr | Ja | Ru | Th | Overall |
|:----------------------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|
| MSVAMP | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | **10K** |
#### Usage
Our dataset and models are all available at Huggingface.
🤗 [MGSM8KInstruct_Parallel Dataset](https://huggingface.co/datasets/Mathoctopus/GSM8KInstruct_Parallel)
🤗 [MGSM8KInstruct_Cross Dataset](https://huggingface.co/datasets/Mathoctopus/MGSM8KInstruct_Cross)
🤗 [MSVAMP Dataset](https://huggingface.co/datasets/Mathoctopus/MSVAMP)
## Models
| Base Model: LLama | Parallel-Training | Cross-Training |
|----|---------------------------------------------------------------|---------------------------------------------------------------------------|
| 7B-LLaMA 2 | 🐙 [MathOctopus-Parallel-7B](https://huggingface.co/Mathoctopus/Parallel_7B) | 🐙 [MathOctopus-Cross-7B](https://huggingface.co/Mathoctopus/Cross_7B) |
|| 🐙[MathOctopus-Parallel-xRFT-7B](https://huggingface.co/Mathoctopus/Parallel_xRFT_7B)|🐙[MathOctopus-Cross-xRFT-7B](https://huggingface.co/Mathoctopus/Cross_xRFT_7B)|
| 13B-LLaMA 2 | 🐙 [MathOctopus-Parallel-13B](https://huggingface.co/Mathoctopus/Parallel_13B) | 🐙 [MathOctopus-Cross-13B](https://huggingface.co/Mathoctopus/Cross_13B) |
|| 🐙[MathOctopus-Parallel-xRFT-13B](https://huggingface.co/Mathoctopus/Parallel_xRFT_13B)|🐙[MathOctopus-Cross-xRFT-13B]|
| 33B-LLaMA 1 | 🐙 [MathOctopus-Parallel-33B](https://huggingface.co/Mathoctopus/Parallel_33B) | 🐙 [MathOctopus-Cross-33B] |
| 70B-LLaMA 2 | Coming soon! | Coming Soon! |
*-Parallel refers to our model trained with the parallel-training strategy.
*-Cross refers to our model trained with cross-training strategy.
*-xRFT means we train the model with multilingual rejection sampling.
### **Overall Results on MGSM**
| 7B Model | En | Sw | Zh | Bn | De | Es | Fr | Ja | Ru | Th | Overall |
|:--------------------------------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|
| MathOctopus<sup>C</sup> | 52.0 | 23.6 | 31.6 | 18.8 | 38.0 | 39.2 | 36.4 | 27.2 | 33.6 | 21.6 | 32.2 |
| **xRFT**-MathOctopus<sup>C</sup>| 51.2 | 24.0 | 33.2 | 18.8 | 36.0 | 41.2 | 37.6 | 29.6 | 36.4 | 25.2 | 33.3 |
| MathOctopus<sup>P</sup>-LoRA | 30.4 | 15.2 | 23.6 | 10.4 | 22.8 | 24.8 | 26.4 | 18.0 | 22.0 | 14.8 | 20.8 |
| MathOctopus<sup>P</sup> | 52.4 | 39.2 | 38.4 | 28.8 | 44.8 | 42.4 | 43.6 | 36.0 | 39.6 | 34.4 | 40.0 |
| **xRFT**-MathOctopus<sup>P</sup>| 54.8 | 38.4 | 45.2 | 33.2 | 43.6 | 45.2 | 38.0 | 35.6 | 48.4 | 36.4 | 41.9 |
<p></p >
| 13B Model | En | Sw | Zh | Bn | De | Es | Fr | Ja | Ru | Th | Overall |
|:--------------------------------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|
| MathOctopus<sup>C</sup> | 56.4 | 27.2 | 39.2 | 24.0 | 47.6 | 49.6 | 47.6 | 40.4 | 42.0 | 24.8 | 39.9 |
| **xRFT**-MathOctopus<sup>C</sup>| 53.6 | 28.0 | 45.2 | 21.2 | 48.0 | 46.4 | 46.0 | 35.2 | 45.6 | 28.8 | 39.8 |
| MathOctopus<sup>P</sup> | 53.2 | 42.8 | 48.8 | 35.2 | 44.4 | 48.0 | 48.4 | 43.2 | 47.6 | 46.8 | 45.8 |
| **xRFT**-MathOctopus<sup>P</sup>| 51.6 | 46.0 | 51.2 | 42.0 | 49.2 | 53.2 | 49.6 | 39.6 | 47.6 | 46.0 | 47.6 |
<p></p >
| 30-34B Model | En | Sw | Zh | Bn | De | Es | Fr | Ja | Ru | Th | Overall |
|:--------------------------------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|
| MathOctopus<sup>C</sup> | 55.6 | 24.4 | 36.0 | 19.2 | 40.4 | 51.2 | 44.4 | 27.2 | 37.2 | 21.6 | 35.7 |
| **xRFT**-MathOctopus<sup>C</sup>| 53.6 | 27.6 | 34.4 | 19.2 | 47.2 | 47.6 | 44.8 | 30.8 | 38.8 | 22.8 | 36.7 |
| MathOctopus<sup>P</sup> | 56.4 | 46.8 | 52.0 | 35.2 | 47.2 | 53.2 | 48.0 | 39.2 | 45.6 | 41.2 | 46.5 |
| **xRFT**-MathOctopus<sup>P</sup>| 51.6 | 47.2 | 52.4 | 37.6 | 51.2 | 52.8 | 44.4 | 41.6 | 50.0 | 47.6 | 47.6 |
### **Overall Results on MSVAMP**
| 7B Model | En | Sw | Zh | Bn | De | Es | Fr | Ja | Ru | Th | Overall |
|:--------------------------------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|
| MathOctopus<sup>C</sup> | 49.2 | 36.6 | 43.6 | 30.2 | 48.6 | 46.8 | 46.4 | 42.5 | 46.7 | 34.0 | 42.5 |
| **xRFT**-MathOctopus<sup>C</sup>| 49.9 | 37.7 | 43.3 | 32.9 | 46.5 | 47.6 | 47.3 | 42.7 | 46.6 | 36.2 | 43.1 |
| MathOctopus<sup>P</sup>-LoRA | 30.4 | 15.2 | 23.6 | 10.4 | 22.8 | 24.8 | 26.4 | 18.0 | 22.0 | 14.8 | 20.8 |
| MathOctopus<sup>P</sup> | 46.5 | 40.1 | 42.5 | 29.1 | 43.5 | 45.4 | 46.0 | 42.5 | 45.4 | 35.7 | 41.7 |
| **xRFT**-MathOctopus<sup>P</sup>| 46.8 | 42.3 | 43.2 | 32.8 | 43.1 | 44.5 | 45.3 | 43.2 | 42.1 | 40.5 | 42.4 |
<p></p >
| 13B Model | En | Sw | Zh | Bn | De | Es | Fr | Ja | Ru | Th | Overall |
|:--------------------------------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|
| MathOctopus<sup>C</sup> | 56.6 | 40.4 | 49.0 | 30.3 | 50.9 | 54.2 | 54.7 | 46.3 | 52.4 | 35.7 | 47.1 |
| **xRFT**-MathOctopus<sup>C</sup>| 52.9 | 41.9 | 49.2 | 34.1 | 50.5 | 52.8 | 51.5 | 45.8 | 50.2 | 35.7 | 46.5 |
| MathOctopus<sup>P</sup> | 50.7 | 43.4 | 42.6 | 31.8 | 48.4 | 49.4 | 50.6 | 41.1 | 46.9 | 39.3 | 44.4 |
| **xRFT**-MathOctopus<sup>P</sup>| 44.6 | 43.4 | 46.4 | 34.2 | 47.7 | 48.2 | 49.9 | 43.1 | 48.2 | 39.5 | 44.5 |
<p></p >
| 30-34B Model | En | Sw | Zh | Bn | De | Es | Fr | Ja | Ru | Th | Overall |
|:--------------------------------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|:--------|
| MathOctopus<sup>C</sup> | 51.5 | 42.1 | 46.2 | 23.2 | 50.5 | 52.1 | 52.9 | 42.2 | 50.5 | 33.4 | 44.5 |
| **xRFT**-MathOctopus<sup>C</sup>| 48.1 | 42.8 | 43.6 | 23.3 | 48.7 | 50.0 | 48.9 | 43.4 | 44.6 | 35.5 | 42.9 |
| MathOctopus<sup>P</sup> | 56.4 | 46.8 | 52.0 | 35.2 | 47.2 | 53.2 | 48.0 | 39.2 | 45.6 | 41.2 | 46.5 |
| **xRFT**-MathOctopus<sup>P</sup>| 48.0 | 42.3 | 46.1 | 36.2 | 47.5 | 48.5 | 48.3 | 45.8 | 47.2 | 41.2 | 45.1 |
### **MathOctopus in English**
| Models | GSM8K | SVAMP |
|:--------------------------------|:--------|:--------|
| LLaMA 2-7B | 42.4 | 38.3 |
| MathOctopus<sup>P</sup>-7B | 49.3 | 46.8 |
| MathOctopus<sup>C</sup>-7B | 50.8 | 49.3 |
| LLaMA 2-13B | 51.0 | 50.9 |
| MathOctopus<sup>P</sup>-13B | 55.5 | 52.1 |
| MathOctopus<sup>C</sup>-13B | 56.6 | 56.6 |
| LLaMA 1-33B | 50.0 | 49.0 |
| MathOctopus<sup>P</sup>-33B | 56.0 | 52.5 |
| MathOctopus<sup>C</sup>-33B | 53.7 | 51.5 |
## Intended Uses
These models are trained for research purposes. They are designed to solve multilingual math problems. They can be used in educational software, tutoring systems, or any application where a solution to a math problem is needed.
## Citation
Please cite our paper if you use our data, model or code. Please also kindly cite the original dataset papers.
```
@misc{chen2023breaking,
title={Breaking Language Barriers in Multilingual Mathematical Reasoning: Insights and Observations},
author={Nuo Chen and Zinan Zheng and Ning Wu and Linjun Shou and Ming Gong and Yangqiu Song and Dongmei Zhang and Jia Li},
year={2023},
eprint={2310.20246},
archivePrefix={arXiv},
primaryClass={cs.CL}
}
``` |