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The researchers proposed the INSPIRE method, aimed at enhancing the example-driven mathematical reasoning capabilities of large language models. This method adopts a “internalize first, then improve” strategy, combining Reference Guidance for Internalization (RGSI) with phased scoring preference training, dividing the learning process into two stages: method-oriented and correctness-oriented. Experiments verified the consistent improvement effect of this method across various model sizes and families; its performance surpassed some larger open-source models, and it was confirmed in out-of-distribution benchmarks that it did not impair general mathematical reasoning abilities.
提出 INSPIRE 方法，采用“先内化后改进”策略提升大语言模型的示例驱动数学推理能力。该方法结合参考引导学生内化（RGSI）与分阶段评分偏好训练，将学习分解为方法导向和正确性导向两个阶段。实验在多个模型规模和家族中验证了该方法的一致性改进效果，其表现超越部分较大开源模型；且在分布外基准测试中确认未损害通用数学推理能力。