Dual Decoder Mathematical Word Problem Solving Model Based on Lie Group Intrinsic Mean Feature Matrix

Abstract Math Word Problems (MWP) solving involves language comprehension and mathematical reasoning. Most of the existing models are primarily based on deep learning methods. However, deep learning models often exhibit large model scales (e.g., large number of parameters), high feature dimensions, and an imbalance between accuracy and computational efficiency. To address these issues, We propose a novel dual-decoder model for solving Mathematical Word Problems (MWP), which is constructed using a Lie Group intrinsic mean feature matrix and named the Dual-Decoder Neural Symbolic Machine (DDNSM). This model projects data samples onto a Lie Group manifold to effectively reduce the output feature dimensions of the encoder through a feature matrix built around the Lie Group intrinsic mean, thereby reducing the computational load in the decoding stage and improving model inference efficiency. Additionally, we designed a dual-decoder system, comprising a decoder based on global and local attention mechanisms and another structured around a tree built from the Lie Group intrinsic mean. Extensive experiments on multiple challenging public datasets demonstrate that our model achieves competitive results in MWP tasks, achieving competitive results in MWP tasks with improved accuracy and computational efficiency.