Abstract:

Existing tree decoder is only suitable for solving single variable problems， but has no good effect of solving multivariate problems. At the same time， most mathematical solvers select truth expression wrongly， which leads to learning deviation occurred in training. Aiming at the above problems， a Graph to Equation Tree （GET） model based on expression level-by-level aggregation and dynamic selection was proposed. Firstly， text semantics was learned through the graph encoder. Then， subexpressions were obtained by aggregating quantities and unknown variables iteratively from bottom of the equation tree layer by layer. Finally， combined with the longest prefix of output expression， truth expression was selected dynamically to minimize the deviation. Experimental results show that the precision of proposed model reaches 83.10% on Math23K dataset， which is 5.70 percentage points higher than that of Graph to Tree （Graph2Tree） model. Therefore， the proposed model can be applied to solution of complex multivariate mathematical problems， and can reduce influence of learning deviation on experimental results.

Key words: layer-by-layer aggregation, dynamic selection, Graph to Equation Tree (GET), multivariate mathematical problem

摘要：

现有树解码器仅适合求解单变量问题而求解多元问题的效果欠佳，而大多数数学求解器对真值表达式的错误选择导致训练出现学习偏差。针对上述问题，提出基于表达式的逐层聚合和动态选择的图到方程树（GET）模型。首先，通过图编码器学习文本语义；其次，从方程树的底层开始逐层迭代地聚合数量和未知变量以得到子表达式；最后，结合输出表达式的最长前缀动态地选择真值表达式以实现偏差最小化。实验结果表明，所提模型在Math23K数据集上的精度达到83.10%，相较于图到树（Graph2Tree）模型提升了5.70个百分点。可见，所提模型适用于复杂多元数学问题的求解，并能降低学习偏差对实验结果的影响。

关键词: 逐层聚合, 动态选择, 图到方程树, 多元数学问题