Construting Reverse Thinking: Developing Large Language Models' Reverse Thingking Ability

Xin Liu, Yunhai Li, Chunfu Jia, Ziliang Chen, Jisen Song

When facing complex problems, humans tend to try various ideas for different issues. Human thinking patterns exhibit remarkable flexibility in adapting to diverse scenarios. GPT-o1, GPT-o3, and DeepSeek-R1 adopt long chain-of-thought models to address complex problems by increasing reasoning depth, which default to a forward reasoning mode. We conducted statistical analysis on the accuracy of different mathematical problem datasets on models of different scales, and found five reasons for errors: Insufficient solution-space coverage, Computational mistakes, Unverified assumptions, Ignoring constraint conditions, Maximum response length limitation. To address the above issues, we proposed a backward reasoning pattern construction method aimed at enhancing the model's reverse thinking ability and dynamic adaptability. First, we constructed an easy-hard two-stage Math dataset for training large models and gradually improving their inference ability at different difficulty levels. The dataset contains forward reasoning paths as well as backward reasoning paths. And a two-stage supervised fine-tuning process is applied to progressively train the model's backward reasoning capability.…