Unifying the syntax and semantics for math word problem solving

Abstract

Math word problem solving is a complex task for natural language processing systems, requiring both comprehension of problem descriptions and deduction of accurate solutions. Existing studies have shown that graph-based approaches can achieve competitive results by applying multilayer graph neural networks to syntactic structure graphs. However, challenges such as incorrect parsing of syntactic dependency trees and insensitivity to numerical information may lead to misinterpretations in the representation. In this paper, we introduce a novel synthetic graph, the Number-Centered Synthetic Semantic Graph (NC-SSG), to address these challenges by reorganizing the dependency tree layout around numerical elements. We propose a double-channel graph transformer to enhance the connections between numbers and their contextual elements, thereby improving the understanding of problem descriptions. Additionally, we present a question-driven tree decoder to generate more accurate solutions, aiming to overcome shallow heuristics. Our approach mitigates the impact of parsing errors in syntactic dependency trees, yielding more precise representations and solutions. Experimental evaluations on two benchmark datasets demonstrate that our solver outperforms previous methods and achieves competitive performance compared to large language models.