GPT Can Solve Mathematical Problems Without a Calculator
_{Official Pytorch Implementation}

Previous studies have typically assumed that large language models are unable to accurately perform arithmetic operations, particularly multiplication of >8 digits, and operations involving decimals and fractions, without the use of calculator tools. This paper aims to challenge this misconception. With sufficient training data, a 2 billion-parameter language model can accurately perform multi-digit arithmetic operations with almost 100% accuracy without data leakage, significantly surpassing GPT-4 (whose multi-digit multiplication accuracy is only 4.3%). We also demonstrate that our MathGLM, finetuned from GLM-10B on a dataset with additional multi-step arithmetic operations and math problems described in text, achieves similar performance to GPT-4 on a 5,000-samples Chinese math problem test set.

If you want to find the detailed introduction, Read our paper: GPT Can Solve Mathematical Problems Without a Calculator.

Demo

Arithmetic Tasks

Math Word Problem

You can access the MathGLM-10B demo by visiting the ModelScope

Model Download

Arithmetic Tasks

For arithmetic tasks, we provide various model sizes for our MathGLM. If you wish to use our MathGLM for inference, you can download it from the following links.

Model	Download
MathGLM-10M	THU-Cloud
MathGLM-100M	THU-Cloud
MathGLM-500M	THU-Cloud
MathGLM-2B	THU-Cloud

Math Word Problem

For math word problem tasks, we leverage different backbone models to tune our MathGLM on the reconstructed Ape210K dataset. Here, we provide various model sizes for our MathGLM. If you wish to use our MathGLM for inference, you can download it from the following links.

Model	Backbone Model	Model Size	Download
MathGLM-Large	GLM-Large	335M	THU-Cloud
MathGLM-10B	GLM-zh-10b	10B	THU-Cloud ModelScope
MathGLM-ChatGLM-6B	ChatGLM-6B	6B	THU-Cloud
MathGLM-ChatGLM2-6B	ChatGLM2-6B	6B	THU-Cloud

Setup

Environment

Our MathGLM relies on sat(SwissArmyTransformer), please pip install SwissArmyTransformer.

Download the repo and setup the environment with:

git clone https://github.com/THUDM/MathGLM.git
cd MathGLM
conda env create -f env.yml
conda activate mathglm

Note

For arithmetic tasks and MathGLM-10B: deepspeed==0.6.0; For math word problems on MathGLM-6B: deepspeed==0.9.5

Dataset

For arithmetic tasks, please download pre-training dataset from MathGLM-dataset. For amth word problem, the reconstructed Ape210K dataset is provided in MathGLM_MWP/dataset/data.jsonl

Inference

For arithmetic tashs, you can directly execute the following command to evaluate our MathGLM on the provided test dataset that contains 9,592 test cases:

cd MathGLM_Arithmetic
./inference.sh

For math word problem, you can evaluate our MathGLM on the Ape210K test dataset that contains 5,000 test Chinese math word problems. You can run the following command:

cd MathGLM_MWP
./inference.sh

Performance Reproduction

MathGLM achieves competitive results in comparison with the most powerful large language model GPT-4 and ChatGPT.

Model	ACC	RE
GPT-4	18.84%	-
ChatGPT	10.00%	-
MathGLM-10M	61.21%	97.83%
MathGLM-100M	70.28%	99.28%
MathGLM-500M	89.57%	99.41%
MathGLM-2B	93.03%	99.71%

MathGLM-10B achieves similar performance to GPT-4 on a 5,000-samples Chinese math problem test set.

Model	Arithmetic_ACC	Answer_ACC
GPT-4	-	59.57%
ChatGPT	-	39.78%
MathGLM-Large	62.00%	50.80%
MathGLM-GLM-6B	64.60%	48.06%
MathGLM-10B	69.08%	58.68%
MathGLM-GLM2-6B	52.24%	45.48%
MathGLM-ChatGLM-6B	58.52%	42.28%
MathGLM-ChatGLM2-6B	50.38%	43.14%

Pre-training

For arithmetic tashs, run command:

cd MathGLM_Arithmetic
./pretrain.sh

For math word problem, run command:

cd MathGLM_MWP
./continue.sh

Citation

@article{yang2023gpt,
  title={GPT Can Solve Mathematical Problems Without a Calculator},
  author={Yang, Zhen and Ding, Ming and Lv, Qingsong and Jiang, Zhihuan and He, Zehai and Guo, Yuyi and Bai, Jinfeng and Tang, Jie},
  journal={arXiv preprint arXiv:2309.03241},
  year={2023}
}