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Solving Geometry Problems via Feature Learning and Contrastive Learning of Multimodal Data

Pengpeng Jian1, Fucheng Guo1,*, Yanli Wang2, Yang Li1

1 North China University of Water Resources and Electric Power, Zhengzhou, 450046, China
2 Henan University of Economics and Law, Zhengzhou, 450046, China

* Corresponding Author: Fucheng Guo. Email:

(This article belongs to this Special Issue: Humanized Computing and Reasoning in Teaching and Learning)

Computer Modeling in Engineering & Sciences 2023, 136(2), 1707-1728.


This paper presents an end-to-end deep learning method to solve geometry problems via feature learning and contrastive learning of multimodal data. A key challenge in solving geometry problems using deep learning is to automatically adapt to the task of understanding single-modal and multimodal problems. Existing methods either focus on single-modal or multimodal problems, and they cannot fit each other. A general geometry problem solver should obviously be able to process various modal problems at the same time. In this paper, a shared feature-learning model of multimodal data is adopted to learn the unified feature representation of text and image, which can solve the heterogeneity issue between multimodal geometry problems. A contrastive learning model of multimodal data enhances the semantic relevance between multimodal features and maps them into a unified semantic space, which can effectively adapt to both single-modal and multimodal downstream tasks. Based on the feature extraction and fusion of multimodal data, a proposed geometry problem solver uses relation extraction, theorem reasoning, and problem solving to present solutions in a readable way. Experimental results show the effectiveness of the method.


Cite This Article

Jian, P., Guo, F., Wang, Y., Li, Y. (2023). Solving Geometry Problems via Feature Learning and Contrastive Learning of Multimodal Data. CMES-Computer Modeling in Engineering & Sciences, 136(2), 1707–1728.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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