  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.
