@inproceedings{linger-etal-2025-theorem,
    title = "Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning",
    author = "Linger, Deng  and
      Zhu, Linghao  and
      Liu, Yuliang  and
      Wang, Yu  and
      Xie, Qunyi  and
      Wu, Jingjing  and
      Zhang, Gang  and
      Zhu, Yingying  and
      Bai, Xiang",
    editor = "Christodoulopoulos, Christos  and
      Chakraborty, Tanmoy  and
      Rose, Carolyn  and
      Peng, Violet",
    booktitle = "Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing",
    month = nov,
    year = "2025",
    address = "Suzhou, China",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-emnlp/2025.emnlp-main.38/",
    pages = "718--735",
    ISBN = "979-8-89176-332-6",
    abstract = "Large Multimodal Models (LMMs) face limitations in geometric reasoning due to insufficient Chain of Thought (CoT) image-text training data. While existing approaches leverage template-based or LLM-assisted methods for geometric CoT data creation, they often face challenges in achieving both diversity and precision. To bridge this gap, we introduce a two-stage Theorem-Validated Reverse Chain-of-Thought Reasoning Synthesis (TR-CoT) framework. The first stage, TR-Engine, synthesizes theorem-grounded geometric diagrams with structured descriptions and properties. The second stage, TR-Reasoner, employs reverse reasoning to iteratively refine question-answer pairs by cross-validating geometric properties and description fragments. Our approach expands theorem-type coverage, corrects long-standing misunderstandings, and enhances geometric reasoning. Fine-grained CoT improves theorem understanding and increases logical consistency by 24.5{\%}. Our best models surpass the baselines in MathVista and GeoQA by 10.1{\%} and 4.7{\%}, outperforming advanced closed-source models like GPT-4o."
}