{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/mathscale-scaling-instruction-tuning-for","title":"MathScale: Scaling Instruction Tuning for Mathematical Reasoning","arxiv_id":"2403.02884","date":"2024-03-05","proceeding":null,"authors":["Zhengyang Tang","Xingxing Zhang","Benyou Wan","Furu Wei"],"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., {\\tt 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 {\\sc MwpBench}, a benchmark of Math Word Problems, which is a collection of ten 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 {\\sc MwpBench}, MathScale-7B achieves state-of-the-art performance across all datasets, surpassing its best peers of equivalent size by 42.9\\% in micro average accuracy and 43.7\\% in macro average accuracy, respectively.","url_abs":"https://arxiv.org/abs/2403.02884v1","url_pdf":"https://arxiv.org/pdf/2403.02884v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"mathscale-scaling-instruction-tuning-for","repo_url":"https://github.com/microsoft/unilm/tree/master/mathscale","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"gsm8k","task_name":"GSM8K"},{"task_slug":"math","task_name":"Math"},{"task_slug":"mathematical-reasoning","task_name":"Mathematical Reasoning"}],"methods":[{"method_slug":"adam","method_name":"Adam"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"attention-dropout","method_name":"Attention Dropout"},{"method_slug":"bpe","method_name":"BPE"},{"method_slug":"cosine-annealing","method_name":"Cosine Annealing"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"gpt-3","method_name":"GPT-3"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"linear-warmup-with-cosine-annealing","method_name":"Linear Warmup With Cosine Annealing"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"weight-decay","method_name":"Weight Decay"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2403.02884","atlas_url":"https://app.syntology.ai/?focus=2403.02884","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}