@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://aclanthology.org/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."
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<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.</abstract>
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%0 Conference Proceedings
%T Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning
%A Linger, Deng
%A Zhu, Linghao
%A Liu, Yuliang
%A Wang, Yu
%A Xie, Qunyi
%A Wu, Jingjing
%A Zhang, Gang
%A Zhu, Yingying
%A Bai, Xiang
%Y Christodoulopoulos, Christos
%Y Chakraborty, Tanmoy
%Y Rose, Carolyn
%Y Peng, Violet
%S Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing
%D 2025
%8 November
%I Association for Computational Linguistics
%C Suzhou, China
%@ 979-8-89176-332-6
%F linger-etal-2025-theorem
%X 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.
%U https://aclanthology.org/2025.emnlp-main.38/
%P 718-735
Markdown (Informal)
[Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning](https://aclanthology.org/2025.emnlp-main.38/) (Linger et al., EMNLP 2025)
ACL
- Deng Linger, Linghao Zhu, Yuliang Liu, Yu Wang, Qunyi Xie, Jingjing Wu, Gang Zhang, Yingying Zhu, and Xiang Bai. 2025. Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning. In Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 718–735, Suzhou, China. Association for Computational Linguistics.