MathScale: Scaling Instruction Tuning for Mathematical Reasoning

Zhengyang Tang, Xingxing Zhang, Benyou Wang, Furu Wei
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:47885-47900, 2024.

Abstract

Large language models (LLMs) have demonstrated remarkable capabilities in problem-solving. However, their proficiency in solving mathematical problems remains inadequate. We propose MathScale, a simple and scalable method to create high-quality mathematical reasoning data using frontier LLMs (e.g., GPT-3.5). Inspired by the cognitive mechanism in human mathematical learning, it first extracts topics and knowledge points from seed math questions and then build a concept graph, which is subsequently used to generate new math questions. MathScale exhibits effective scalability along the size axis of the math dataset that we generate. As a result, we create a mathematical reasoning dataset (MathScaleQA) containing two million math question-answer pairs. To evaluate mathematical reasoning abilities of LLMs comprehensively, we construct MWPBench, a benchmark of Math Word Problems, which is a collection of 9 datasets (including GSM8K and MATH) covering K-12, college, and competition level math problems. We apply MathScaleQA to fine-tune open-source LLMs (e.g., LLaMA-2 and Mistral), resulting in significantly improved capabilities in mathematical reasoning. Evaluated on MWPBench, MathScale-7B achieves state-of-the-art performance across all datasets, surpassing its best peers of equivalent size by 42.8% in micro average accuracy and 43.6% in macro average accuracy, respectively.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-tang24k, title = {{M}ath{S}cale: Scaling Instruction Tuning for Mathematical Reasoning}, author = {Tang, Zhengyang and Zhang, Xingxing and Wang, Benyou and Wei, Furu}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {47885--47900}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/tang24k/tang24k.pdf}, url = {https://proceedings.mlr.press/v235/tang24k.html}, abstract = {Large language models (LLMs) have demonstrated remarkable capabilities in problem-solving. However, their proficiency in solving mathematical problems remains inadequate. We propose MathScale, a simple and scalable method to create high-quality mathematical reasoning data using frontier LLMs (e.g., GPT-3.5). Inspired by the cognitive mechanism in human mathematical learning, it first extracts topics and knowledge points from seed math questions and then build a concept graph, which is subsequently used to generate new math questions. MathScale exhibits effective scalability along the size axis of the math dataset that we generate. As a result, we create a mathematical reasoning dataset (MathScaleQA) containing two million math question-answer pairs. To evaluate mathematical reasoning abilities of LLMs comprehensively, we construct MWPBench, a benchmark of Math Word Problems, which is a collection of 9 datasets (including GSM8K and MATH) covering K-12, college, and competition level math problems. We apply MathScaleQA to fine-tune open-source LLMs (e.g., LLaMA-2 and Mistral), resulting in significantly improved capabilities in mathematical reasoning. Evaluated on MWPBench, MathScale-7B achieves state-of-the-art performance across all datasets, surpassing its best peers of equivalent size by 42.8% in micro average accuracy and 43.6% in macro average accuracy, respectively.} }
Endnote
%0 Conference Paper %T MathScale: Scaling Instruction Tuning for Mathematical Reasoning %A Zhengyang Tang %A Xingxing Zhang %A Benyou Wang %A Furu Wei %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-tang24k %I PMLR %P 47885--47900 %U https://proceedings.mlr.press/v235/tang24k.html %V 235 %X Large language models (LLMs) have demonstrated remarkable capabilities in problem-solving. However, their proficiency in solving mathematical problems remains inadequate. We propose MathScale, a simple and scalable method to create high-quality mathematical reasoning data using frontier LLMs (e.g., GPT-3.5). Inspired by the cognitive mechanism in human mathematical learning, it first extracts topics and knowledge points from seed math questions and then build a concept graph, which is subsequently used to generate new math questions. MathScale exhibits effective scalability along the size axis of the math dataset that we generate. As a result, we create a mathematical reasoning dataset (MathScaleQA) containing two million math question-answer pairs. To evaluate mathematical reasoning abilities of LLMs comprehensively, we construct MWPBench, a benchmark of Math Word Problems, which is a collection of 9 datasets (including GSM8K and MATH) covering K-12, college, and competition level math problems. We apply MathScaleQA to fine-tune open-source LLMs (e.g., LLaMA-2 and Mistral), resulting in significantly improved capabilities in mathematical reasoning. Evaluated on MWPBench, MathScale-7B achieves state-of-the-art performance across all datasets, surpassing its best peers of equivalent size by 42.8% in micro average accuracy and 43.6% in macro average accuracy, respectively.
APA
Tang, Z., Zhang, X., Wang, B. & Wei, F.. (2024). MathScale: Scaling Instruction Tuning for Mathematical Reasoning. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:47885-47900 Available from https://proceedings.mlr.press/v235/tang24k.html.

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