InfinityMATH: A Scalable Instruction Tuning Dataset in Programmatic Mathematical Reasoning

TL;DR

InfinityMATH is a scalable, number-independent instruction dataset for mathematical reasoning, significantly improving language models' performance and robustness across diverse math benchmarks.

Contribution

The paper introduces InfinityMATH, a novel scalable dataset construction method that decouples numbers from problems, enabling efficient synthesis and fine-tuning of models for mathematical reasoning.

Findings

Models fine-tuned on InfinityMATH show 184.7% to 514.3% improvement on benchmarks.

Enhanced models demonstrate high robustness on number-variant test sets.

InfinityMATH enables scalable and flexible dataset creation for mathematical reasoning.

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.