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About this paper
Jiayi Kuang, Haojing Huang, Yinghui Li, Xinnian Liang, Zhikun Xu, Yangning Li, Xiaoyu Tan, Chao Qu and 3 more
A collaborative research effort introduces the "atomic thinking" paradigm to dissect large language models' mathematical reasoning into fundamental capabilities, revealing that algebraic skills and conceptual understanding are foundational and highly transferable for improved performance across diverse mathematical domains.
Key insights
- Algebraic abilities demonstrate consistent positive transfer effects, significantly improving performance in other mathematical fields like Analysis and Geometry, highlighting their foundational and transferable nature.
- Deep conceptual understanding is crucial, as training on conceptual comprehension tasks markedly enhances both forward and backward logical reasoning abilities, underscoring its foundational role.
- LLMs, particularly smaller open-source models, show significant struggles with abstract fields like Geometry and Topology, formal mathematical language, and counterexample generation, indicating gaps in higher-level abstraction and precise conceptual representation.
Summary by alphaXiv.
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