InfinityMATH：一个面向程序化数学推理的可扩展指令微调数据集
InfinityMATH: A Scalable Instruction Tuning Dataset in Programmatic Mathematical Reasoning
AI总结：
针对现有数学推理指令微调数据集构建依赖大量种子数据、计算成本高、扩展性差的问题，提出通过解耦数字与问题合成无数字程序的方式构建可扩展数据集InfinityMATH，微调后模型在多基准上提升显著且鲁棒性强。
摘要：
思维链（CoT）和思维程序（PoT）方法的最新进展极大提升了语言模型的数学推理能力，推动了这类方法与大语言模型（LLM）指令微调数据集的融合。然而，现有大规模数据集构建方法需要大量种子数据，且数据合成的计算成本极高，给可扩展性带来了严峻挑战。\n我们提出InfinityMATH，一个面向程序化数学推理的可扩展指令微调数据集。其构建流程的核心是将数字与数学问题解耦，以合成不依赖具体数字的程序，从而在最大限度降低对特定数值依赖的同时，实现高效灵活的规模扩展。\n我们使用Llama2、CodeLlama等开源语言模型与代码模型开展了微调实验，验证了InfinityMATH的实际效用。这些经过微调的模型在域内和域外基准上均取得了显著的相对提升，平均提升幅度在184.7%到514.3%之间。此外，这些模型在GSM8K+和MATH+基准上表现出高鲁棒性——这两个基准是仅对测试集做数字变化得到的增强版本。InfinityMATH能让模型在更广泛的数学问题上具备更强的通用性与有效性。该数据集可通过https://huggingface.co/datasets/flagopen/InfinityMATH 获取。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
