An Augmented Benchmark Dataset for Geometric Question Answering through Dual Parallel Text Encoding

Proceedings of the 29th International Conference on Computational Linguistics, pages 1511–1520 October 12–17, 2022. 1511 An Augmented Benchmark Dataset for Geometric Question Answering through Dual Parallel Text Encoding Jie Cao School of Computer Science South China Normal University jiecao@m.scnu.edu.cn Jing Xiao∗ School of Computer Science South China Normal University xiaojing@scnu.edu.cn Abstract Automatic math problem solving has attracted much attention of NLP researchers recently. However, most of the works focus on the solv- ing of Math Word Problems (MWPs). In this paper, we study on the Geometric Problem Solving based on neural networks. Solving ge- ometric problems requires the integration of text and diagram information as well as the knowledge of the relevant theorems. The lack of high-quality datasets and efficient neural geometric solvers impedes the development of automatic geometric problems solving. Based on GeoQA, we newly annotate 2,518 geo- metric problems with richer types and greater difficulty to form an augmented benchmark dataset GeoQA+1, containing 6,027 problems in training set and 7,528 totally. We further perform data augmentation method to expand the training set to 12,054. Besides, we design a Dual Parallel text Encoder (DPE) to effi- ciently encode long and medium-length prob- lem text. The experimental results validate the effectiveness of GeoQA+ and DPE mod- ule, and the accuracy of automatic geometric problem solving is improved to 66.09%. 1 Introduction In recent years, with the continuous development of deep learning technology in NLP, more and more math problem solvers have been developed. However, most of these works focus on solving arithmetic and algebra problems (Xie and Sun, 2019; Lin et al., 2021; Wu et al., 2020). There are few systems for geometric problem solving, especially those based on the method of the neural networks. The solving of geometric problems re- quires a combination of text and diagram informa- tion, and therefore the study of it also helps to pro- mote the development of cross-modal problem- solving. ∗Corresponding Author 1The source code and benchmark of this paper are avail- able at: https://github.com/SCNU203/GeoQA-Plus Figure 1: A typical geometry problem in GeoQA+ dataset and its annotating and solving process. As shown in Figure 1, a typical geometry prob- lem mainly consists of textual descriptions and ge- ometric diagrams. There are three steps to solve this problem. First, the text and diagram infor- mation are encoded separately. Second, the solver needs to understand the semantics of the text and diagram information simultaneously. Third, in or- der to solve the problem, we may need to com- bine the information of Text-Diagram with rele- vant theorem knowledge. For example, the prob- lem in Figure 1 use the theorem of complemen- tary adjacent angles of a parallelogram. Though some previous methods attempt to solve geometric problems automatically, the performance of their solving system is far away from satisfactory (Seo et al., 2014, 2015; Sachan and Xing, 2017). They highly relied on limited handcraft rules and were only validated on small-scale datasets, making it hard to generalize to more complex and real-world cases(Chen et al., 2021). In …

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