InfinityMATH: A Scalable Instruction Tuning Dataset in Programmatic Mathematical Reasoning

• URL: http://arxiv.org/abs/2408.07089v1
• Date: Fri, 9 Aug 2024 08:18:20 GMT
• Title: InfinityMATH: A Scalable Instruction Tuning Dataset in Programmatic Mathematical Reasoning
• Authors: Bo-Wen Zhang, Yan Yan, Lin Li, Guang Liu,
• Abstract summary: We introduce InfinityMATH, a scalable instruction tuning dataset for programmatic mathematical reasoning. Fine-tuning experiments with open-source language and code models, such as Llama2 and CodeLlama, demonstrate the practical benefits of InfinityMATH.
• Score: 13.728595670907136
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Recent advancements in Chain-of-Thoughts (CoT) and Program-of-Thoughts (PoT) methods have greatly enhanced language models' mathematical reasoning capabilities, facilitating their integration into instruction tuning datasets with LLMs. However, existing methods for large-scale dataset creation require substantial seed data and high computational costs for data synthesis, posing significant challenges for scalability. We introduce InfinityMATH, a scalable instruction tuning dataset for programmatic mathematical reasoning. The construction pipeline emphasizes decoupling numbers from mathematical problems to synthesize number-independent programs, enabling efficient and flexible scaling while minimizing dependency on specific numerical values. Fine-tuning experiments with open-source language and code models, such as Llama2 and CodeLlama, demonstrate the practical benefits of InfinityMATH. These fine-tuned models, showed significant relative improvements on both in-domain and out-of-domain benchmarks, ranging from 184.7% to 514.3% on average. Additionally, these models exhibited high robustness on the GSM8K+ and MATH+ benchmarks, which are enhanced version of test sets with simply the number variations. InfinityMATH ensures that models are more versatile and effective across a broader range of mathematical problems. The data is available at https://huggingface.co/datasets/flagopen/InfinityMATH.

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