MathFusion: Enhancing Mathematic Problem-solving of LLM through
  Instruction Fusion
Authors: name: Qizhi Pei, name: Lijun Wu, name: Zhuoshi Pan, name: Yu Li, name: Honglin Lin, name: Chenlin Ming, name: Xin Gao, name: Conghui He, name: Rui Yan

Large Language Models (LLMs) have shown impressive progress in mathematical
reasoning. While data augmentation is promising to enhance mathematical
problem-solving ability, current approaches are predominantly limited to
instance-level modifications-such as rephrasing or generating syntactic
variations-which fail to capture and leverage the intrinsic relational
structures inherent in mathematical knowledge. Inspired by human learning
processes, where mathematical proficiency develops through systematic exposure
to interconnected concepts, we introduce MathFusion, a novel framework that
enhances mathematical reasoning through cross-problem instruction synthesis.
MathFusion implements this through three fusion strategies: (1) sequential
fusion, which chains related problems to model solution dependencies; (2)
parallel fusion, which combines analogous problems to reinforce conceptual
understanding; and (3) conditional fusion, which creates context-aware
selective problems to enhance reasoning flexibility. By applying these
strategies, we generate a new dataset, MathFusionQA, followed by
fine-tuning models (DeepSeekMath-7B, Mistral-7B, Llama3-8B) on it. Experimental
results demonstrate that MathFusion achieves substantial improvements in
mathematical reasoning while maintaining high data efficiency, boosting
performance by 18.0 points in accuracy across diverse benchmarks while
requiring only 45K additional synthetic instructions, representing a
substantial improvement over traditional single-instruction approaches. Our
datasets, models, and code are publicly available at
https://github.com/QizhiPei/mathfusion.