| --- |
| 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) |
|
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| 🤗 [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} |
| } |
| ``` |
