Leveraging two-level deep learning classifiers for 2D shape recognition to automatically solve geometry math word problems

In mathematics, closed-domain systems for Question Answering (QA) have shown a distinct advantage over open-domain systems, primarily due to their focused use of supporting knowledge bases. This advantage is particularly salient in the era of online and hybrid tutoring, where automatic QA systems have become vital in addressing complex mathematical problems. This paper focuses on the challenge of geometric shape recognition in math word problems (MWPs) accompanied by figures that aid in the solution process. Existing systems rely on manually inputted shape information, which is less efficient. In this work, a novel customized two-layer deep learning model ‘2DGeoShapeNet’ for 2D geometric shape recognition has been developed. At the first level, it recognizes images in broad categories such as circles, quadrilaterals, or triangles. At the second level, the subtypes of quadrilaterals and triangles are detected. The proposed 2D shape detection model is trained and tested on a newly created integrated dataset, ‘GeoCQT’ (Circle, Quadrilateral, and Triangle), consisting of 6K+ images. The proposed deep learning technique achieved 93.98% accuracy on the ‘GeoCQT’ dataset. The performance of the proposed techniques is also evaluated on other geometry math word problem solver datasets such as GeoS, Geometry3K, GeoQA, PGDP5K, and PGPS9K. The proposed technique is compared with the already-published work that employed traditional image processing techniques for 2D shape detection. Findings highlight the superiority of two-level deep learning classifiers in detecting geometric shapes, marking a significant advancement in automated geometry problem-solving.