A Symbolic Character-Aware Model for Solving Geometry Problems

TL;DR

This paper introduces a symbolic character-aware model that enhances geometry problem solving by explicitly modeling symbolic characters in text and diagrams, leading to improved accuracy and efficiency on benchmark datasets.

Contribution

The paper proposes a novel multi-modal framework that explicitly models symbolic characters in geometry problems, integrating semantic and geometric information for better understanding.

Findings

Achieved state-of-the-art accuracy on GeoQA with 64.1%

Reduced average solving steps on Geometry3K from 6.9 to 6.0

Enhanced diagram understanding through self-supervised learning

Abstract

AI has made significant progress in solving math problems, but geometry problems remain challenging due to their reliance on both text and diagrams. In the text description, symbolic characters such as "$\triangle$ABC" often serve as a bridge to connect the corresponding diagram. However, by simply tokenizing symbolic characters into individual letters (e.g., 'A', 'B' and 'C'), existing works fail to study them explicitly and thus lose the semantic relationship with the diagram. In this paper, we develop a symbolic character-aware model to fully explore the role of these characters in both text and diagram understanding and optimize the model under a multi-modal reasoning framework. In the text encoder, we propose merging individual symbolic characters to form one semantic unit along with geometric information from the corresponding diagram. For the diagram encoder, we pre-train it under a multi-label classification framework with the symbolic characters as labels. In addition, we enhance the geometry diagram understanding ability via a self-supervised learning method under the masked image modeling auxiliary task. By integrating the proposed model into a general encoder-decoder pipeline for solving geometry problems, we demonstrate its superiority on two benchmark datasets, including GeoQA and Geometry3K, with extensive experiments. Specifically, on GeoQA, the question-solving accuracy is increased from 60.0\% to 64.1\%, achieving a new state-of-the-art accuracy; on Geometry3K, we reduce the question average solving steps from 6.9 down to 6.0 with marginally higher solving accuracy.