Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems
Ting-Rui Chiang Yun-Nung Chen National Taiwan University, Taipei, Taiwan
Abstract
Solving math word problems is a challenging task that requires accurate natural language understanding to bridge natural language texts and math expressions. Motivated by the intuition about how human generates the equations given the problem texts, this paper presents a neural approach to automatically solve math word problems by operating symbols according to their semantic meanings in texts. This paper views the process of generating equations as a bridge between the semantic world and the symbolic world, where the proposed neural math solver is based on an encoder-decoder framework. In the proposed model, the encoder is designed to understand the semantics of problems, and the decoder focuses on tracking semantic meanings of the generated symbols and then deciding which symbol to generate next. The preliminary experiments are conducted in a benchmark dataset Math23K, and our model significantly outperforms both the state-of-the-art single model and the best non-retrieval-based model over about 10% accuracy, demonstrating the effectiveness of bridging the symbolic and semantic worlds from math word problems.111The source code is available at https://github.com/MiuLab/E2EMathSolv
中文速览
让机器自动解答数学应用题一直是道难题，核心挑战在于如何真正理解文字描述并将其转化为正确的数学表达式。这篇文章借鉴人类解题时"边理解语义、边写算式"的直觉，提出了一个端到端的编码器-解码器（encoder-decoder）神经网络模型：编码器负责为题目中每个数字抽取语义表示，解码器则借助一个栈（stack）结构，以后缀表达式的方式逐步生成算式，每次选择运算符时都参考栈中操作数的语义，从而模拟人类"知道两个数代表什么、才决定做什么运算"的推理过程。在大型中文数学题基准数据集 Math23K 上的实验表明，该模型比当时最优的单模型和最佳非检索模型分别高出约10个百分点的准确率。这项工作的意义在于，它不仅大幅提升了解题准确率，还让模型的推理过程具有可解释性，无需任何人工特征或额外标注，为理解机器真正"懂"数学应用题提供了新思路。
原文 arXiv:1811.00720;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1811.00720v2