让小模型学会多策略解题，自选最优路径提升数学推理能力

Large Language Models (LLMs) can transfer their reasoning skills to smaller models by teaching them to generate the intermediate reasoning process required to solve multistep reasoning tasks. While LLMs can accurately solve reasoning tasks through a variety of strategies, even without fine-tuning, smaller models are not expressive enough to fit the LLMs distribution on all strategies when distilled and tend to prioritize one strategy over the others. This reliance on one strategy poses a challenge for smaller models when attempting to solve reasoning tasks that may be difficult with their preferred strategy. To address this, we propose a distillation method SIKeD (Self-guided Iterative Knowledge Distillation for mathematical reasoning), where the LLM teaches the smaller model to approach a task using different strategies and the smaller model uses its self-generated on-policy outputs to choose the most suitable strategy for the given task. The training continues in a self-guided iterative manner, where for each training iteration, a decision is made on how to combine the LLM data with the self-generated outputs. Unlike traditional distillation methods, SIKeD allows the smaller model to learn which strategy is suitable for a given task while continuously learning to solve a task using different strategies. Our experiments on various mathematical reasoning datasets show that SIKeD significantly outperforms traditional distillation techniques across smaller models of different sizes. Our code is available at: https://github.com/kumar-shridhar/SIKeD