Mathematical Reasoning via Multi-step Self Questioning and Answering for Small Language Models

Kaiyuan Chen, Jin Wang, Xuejie Zhang

Abstract: Mathematical reasoning is challenging for large language models (LLMs), while the scaling relationship concerning LLM capacity is under-explored. Existing works have tried to leverage the rationales of LLMs to train small language models (SLMs) for enhanced reasoning abilities, referred to as distillation. However, most existing distillation methods have not considered guiding the small models to solve problems progressively from simple to complex, which can be a more effective way. This study proposes a multi-step self questioning and answering (M-SQA) method that guides SLMs to solve complex problems by starting from simple ones. Initially, multi-step self-questioning and answering rationales are extracted from LLMs based on complexity-based prompting. Subsequently, these rationales are employed for distilling SLMs in a multi-task learning framework, during which the model learns to multi-step reason in a self questioning and answering way and answer each sub-question in a single step iteratively. Experiments on current mathematical reasoning tasks demonstrate the effectiveness of the proposed approach.