Challenge: Graph2Tree model encodes graph-structured input and decodes tree-structures output.
Approach: They propose a novel Graph-to-Tree Neural Network consisting of a graph encoder and a hierarchical tree decoder that encodes an augmented graph-structured input and decodes a tree-structure-output.
Outcome: The proposed model outperforms or matches the performance of other state-of-the-art models on two problems, neural semantic parsing and math word problem.

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Challenge: Existing work on adding syntactic information to NMT systems is limited to linguistically-inspired tree structures.
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Top-down Tree Structured Decoding with Syntactic Connections for Neural Machine Translation and Parsing (D18-1)

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Challenge: Neural machine translation (NMT) models are based on sequential decoding or serialisation of structured data into sequence.
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Challenge: Semantic parsing to SQL has largely ignored the structure of the database schema . a recent study used a simple DB that was observed at both training and test time.
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Compositional Semantic Parsing across Graphbanks (P19-1)

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Challenge: Existing semantic parsers that map sentences to graph-based meaning representations are hand-designed for specific graphbanks.
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A Graph-Based Neural Model for End-to-End Frame Semantic Parsing (2021.emnlp-main)

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Challenge: Existing studies focus on frame semantic parsing as a graph construction problem.
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Graph-to-Tree Learning for Solving Math Word Problems (2020.acl-main)

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Graph-to-Sequence Learning using Gated Graph Neural Networks (P18-1)

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Challenge: Existing approaches to graph-to-sequence learning ignore the full graph structure, discarding key information.
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An Edge-Enhanced Hierarchical Graph-to-Tree Network for Math Word Problem Solving (2021.findings-emnlp)

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Challenge: Existing work on graph neural networks to capture word relationships neglects the rest of the problem.
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Graph-based Dependency Parsing with Graph Neural Networks (P19-1)

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On Tree-Based Neural Sentence Modeling (D18-1)

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Challenge: Existing tree-based sentence modeling approaches adopt syntactic parsing trees as the explicit structure prior.
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