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This paper proposes a novel framework, TATA (Teaching LLMs According to Their Aptitude), to improve the mathematical reasoning ability of large-scale language models (LLMs). While existing chain-of-thought (CoT) and tool-integrated inference (TIR) approaches have focused on generalization performance or accurate computational ability, how LLMs can autonomously adapt their inference strategies according to their abilities has been an unresolved issue. TATA provides training data tailored to the unique abilities of the model by considering the abilities of the underlying LLMs during the supervised learning fine-tuning (SFT) process. This allows LLMs to autonomously select and apply appropriate inference strategies at test time. Experimental results on various mathematical inference benchmarks show that TATA effectively combines the advantages of CoT and TIR to achieve better or similar performance than TIR alone, with improved inference efficiency. Further analysis highlights that ability-based data selection plays an important role in LLMs’ effective and adaptive inference decisions and in constructing inference strategies that match model abilities.
Takeaways, Limitations
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Takeaways:
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Presenting a novel approach to improving LLMs' mathematical reasoning ability: allowing LLMs to autonomously choose and apply reasoning strategies according to their abilities.
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Effectively combine the strengths of CoT and TIR to improve performance and efficiency: achieve performance superior to or similar to that of TIR alone.
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Emphasize the importance of data selection appropriate to the capabilities of the LLM: Capability-based data selection plays a critical role in making effective inference decisions and building inference strategies that match model capabilities.
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Limitations:
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In this paper, further research is needed on the generalization performance of the proposed TATA framework.
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Further validation of the applicability and limitations of TATA to various types of mathematical problems is needed.
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There is a lack of analysis on the computational cost and complexity of the TATA framework.
