
# 🐙 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](https://huggingface.co/Mathoctopus/Cross_xRFT_13B/tree/main)|
| 33B-LLaMA 1 	| 🐙 [MathOctopus-Parallel-33B](https://huggingface.co/Mathoctopus/Parallel_33B)    | 🐙 [MathOctopus-Cross-33B](https://huggingface.co/Mathoctopus/Cross_33B/tree/main)  	|
| 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}
}
```
{"language": ["en", "es", "zh", "de", "ru", "th", "sw", "ja", "fr", "bn"], "license": "apache-2.0", "datasets": ["Mathoctopus/GSM8KInstruct_Parallel"]}
transformers pytorch llama text-generation en es zh de ru th sw ja fr bn dataset:Mathoctopus/GSM8KInstruct_Parallel arxiv:2310.20246 license:apache-2.0 autotrain_compatible endpoints_compatible text-generation-inference region:us