Abstract

Automatic math problem solving has recently attracted increasing attention as a longstanding AI benchmark. In this paper, we focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams, and theorem knowledge. However, the existing methods were highly dependent on handcraft rules and were merely evaluated on small-scale datasets. Therefore, we propose a Geometric Question Answering dataset GeoQA, containing 4,998 geometric problems with corresponding annotated programs, which illustrate the solving process of the given problems. Compared with another publicly available dataset GeoS, GeoQA is 25 times larger, in which the program annotations can provide a practical testbed for future research on explicit and explainable numerical reasoning. Moreover, we introduce a Neural Geometric Solver (NGS) to address geometric problems by comprehensively parsing multimodal information and generating interpretable programs. We further add multiple self-supervised auxiliary tasks on NGS to enhance cross-modal semantic representation. Extensive experiments on GeoQA validate the effectiveness of our proposed NGS and auxiliary tasks. However, the results are still significantly lower than human performance, which leaves large room for future research.

Framework

Experiment

Conclusion

In this work, we focus on the geometric problem and propose the first large-scale geometric question answering dataset “GeoQA”, containing 4,998 problems with program annotation. Besides, we propose a deep neural baseline, named as Neural Geometric Solver (NGS), to solve a geometric problem by jointly reasoning over multimodal data and generating interpretable programs. We further propose multiple novel auxiliary tasks to enhance the semantic representation of text and diagram. Extensive experimental results and analyses show that our GeoQA is challenging, and our NGS-Auxiliary outperforms other methods on GeoQA.