The celebrated Seq2Seq technique and its numerous variants achieve excellent
performance on many tasks such as neural machine translation, semantic parsing,
and math word problem solving. However, these models either only consider input
objects as sequences while ignoring the important structural information for
encoding, or they simply treat output objects as sequence outputs instead of
structural objects for decoding. In this paper, we present a novel
Graph-to-Tree Neural Networks, namely Graph2Tree consisting of a graph encoder
and a hierarchical tree decoder, that encodes an augmented graph-structured
input and decodes a tree-structured output. In particular, we investigated our
model for solving two problems, neural semantic parsing and math word problem.
Our extensive experiments demonstrate that our Graph2Tree model outperforms or
matches the performance of other state-of-the-art models on these tasks.

本文提出一种新的图到树神经网络模型 (Graph2Tree)，该模型包含一个图编码器和一个分层树解码器，能够对图结构的输入进行编码和树结构的输出进行解码，用于解决神经语义解析和数学问题求解，实验证明该模型在这些任务上表现优异。

应用于语义解析和数学问题的图到树神经网络学习结构化输入输出翻译

Graph-to-Tree Neural Networks for Learning Structured Input-Output  Translation with Applications to Semantic Parsing and Math Word Problem

Sequence-to-sequence (SEQ2SEQ) models have been successfully applied to
automatic math word problem solving. Despite its simplicity, a drawback still
remains: a math word problem can be correctly solved by more than one
equations. This non-deterministic transduction harms the performance of maximum
likelihood estimation. In this paper, by considering the uniqueness of
expression tree, we propose an equation normalization method to normalize the
duplicated equations. Moreover, we analyze the performance of three popular
SEQ2SEQ models on the math word problem solving. We find that each model has
its own specialty in solving problems, consequently an ensemble model is then
proposed to combine their advantages. Experiments on dataset Math23K show that
the ensemble model with equation normalization significantly outperforms the
previous state-of-the-art methods.

该研究旨在解决数学问题中的非确定性问题。通过将表达树的唯一性考虑在内，我们提出了一种方程规范化方法来规范重复的方程式。我们分析了三种流行的序列到序列模型在数学问题求解中的性能，并提出了一个集成模型来结合它们各自的优点，实验结果表明，采用方程规范化的集成模型明显优于之前的最先进方法。