构建逆向思维：开发大语言模型的逆向推理能力

Computer Science > Artificial Intelligence arXiv:2609.24760 (cs) [Submitted on 21 Sep 2026] Title:Construting Reverse Thinking: Developing Large Language Models' Reverse Thingking Ability Authors:Xin Liu, Yunhai Li, Chunfu Jia, Ziliang Chen, Jisen Song View a PDF of the paper titled Construting Reverse Thinking: Developing Large Language Models' Reverse Thingking Ability, by Xin Liu and 4 other authors View PDF HTML (experimental) Abstract: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. Furthermore, a fine-grained reward mechanism is developed, employing smoothed reward signals to strengthen the model's ability to autonomously select thinking modes during the reasoning process, thereby avoiding reward hacking. A linear-decay balanced sampling strategy is designed to maintain a balance between forward and backward reasoning path samples during training, enabling the model to converge quickly and stably. Experimental results show that our method significantly improves reasoning efficiency and accuracy in tasks such as mathematical proofs, offering a flexible and efficient reasoning paradigm for solving complex problems. Comments: Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2609.24760 [cs.AI] (or arXiv:2609.24760v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2609.24760 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Chunfu Jia [view email] [v1] Mon, 21 Sep 2026 15:29:46 UTC (197 KB) Full-text links: Access Paper: View a PDF of the paper titled Construting Reverse Thinking: Developing Large Language Models' Reverse Thingking Ability, by Xin Liu and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.AI new | recent | 2026-09 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)