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Title: Graph2Seq: Graph to Sequence Learning with Attention-Based Neural Networks

Paper content:
The celebrated Sequence to Sequence learning (Seq2Seq) technique and its numerous variants achieve excellent performance on many tasks.
However, many machine learning tasks have inputs naturally represented as graphs; existing Seq2Seq models face a significant challenge in achieving accurate conversion from graph form to the appropriate sequence.
To address this challenge, we introduce a general end-to-end graph-to-sequence neural encoder-decoder architecture that maps an input graph to a sequence of vectors and uses an attention-based LSTM method to decode the target sequence from these vectors.
Our method first generates the node and graph embeddings using an improved graph-based neural network with a novel aggregation strategy to incorporate edge direction information in the node embeddings.
We further introduce an attention mechanism that aligns node embeddings and the decoding sequence to better cope with large graphs.
Experimental results on bAbI, Shortest Path, and Natural Language Generation tasks demonstrate that our model achieves state-of-the-art performance and significantly outperforms existing graph neural networks, Seq2Seq, and Tree2Seq models; using the proposed bi-directional node embedding aggregation strategy, the model can converge rapidly to the optimal performance.
The celebrated Sequence to Sequence learning (Seq2Seq) technique and its numerous variants achieve excellent performance on many tasks such as Neural Machine Translation BID13 , Natural Language Generation (NLG) BID24 and Speech Recognition BID24 .
Most of the proposed Seq2Seq models can be viewed as a family of encoder-decoders , where an encoder reads and encodes a source input in the form of sequences into a continuous vector representation of fixed dimension, and a decoder takes the encoded vectors and outputs a target sequence.
Many other enhancements including Bidirectional Recurrent Neural Networks (Bi-RNN) BID20 or Bidirectional Long Short-Term Memory Networks (Bi-LSTM) (Graves & Schmidhuber, 2005) as encoder, and attention mechanism Luong et al., 2015) , have been proposed to further improve its practical performance for general or domain-specific applications.Despite their flexibility and expressive power, a significant limitation with the Seq2Seq models is that they can only be applied to problems whose inputs are represented as sequences.
However, the sequences are probably the simplest structured data, and many important problems are best expressed with a more complex structure such as graphs that have more capacity to encode complicated pair-wise relationships in the data.
For example, one task in NLG applications is to translate a graph-structured semantic representation such as Abstract Meaning Representation to a text expressing its meaning BID2 .
In addition, path planning for a mobile robot (Hu & Yang, 2004) and path finding for question answering in bAbI task (Li et al., 2015) can also be cast as graph-to-sequence problems.On the other hand, even if the raw inputs are originally expressed in a sequence form, it can still benefit from the enhanced inputs with additional information (to formulate graph inputs).
For example, for semantic parsing tasks (text-to-AMR or text-to-SQL), they have been shown better performance by augmenting the original sentence sequences with other structural information such as dependency parsing trees (Pust et al., 2015) .
Intuitively, the ideal solution for graph-to-sequence tasks is to build a more powerful encoder which is able to learn the input representation regardless of its inherent structure.To cope with graph-to-sequence problems, a simple and straightforward approach is to directly convert more complex structured graph data into sequences (Iyer et al., 2016; BID15 Liu et al., 2017) , and apply sequence models to the resulting sequences.
However, the Seq2Seq model often fails to perform as well as hoped on these problems, in part because it inevitably suffers significant information loss due to the conversion of complex structured data into a sequence, especially when the input data is naturally represented as graphs.
Recently, a line of research efforts have been devoted to incorporate additional information by extracting syntactic information such as the phrase structure of a source sentence (Tree2seq) BID12 , by utilizing attention mechanisms for input sets (Set2seq) BID32 , and by encoding sentences recursively as trees (Socher et al., 2010; BID29 .
Although these methods achieve promising results on certain classes of problems, most of the presented techniques largely depend on the underlying application and may not be able to generalize to a broad class of problems in a general way.To address this issue, we propose Graph2Seq, a novel attention-based neural network architecture for graph-to-sequence learning.
The Graph2Seq model follows the conventional encoder-decoder approach with two main components, a graph encoder and a sequence decoder.
The proposed graph encoder aims to learn expressive node embeddings and then to reassemble them into the corresponding graph embeddings.
To this end, inspired by a recent graph representation learning method (Hamilton et al., 2017a) , we propose an inductive graph-based neural network to learn node embeddings from node attributes through aggregation of neighborhood information for directed and undirected graphs, which explores two distinct aggregators on each node to yield two representations that are concatenated to form the final node embedding.
In addition, we further design an attention-based RNN sequence decoder that takes the graph embedding as its initial hidden state and outputs a target prediction by learning to align and translate jointly based on the context vectors associated with the corresponding nodes and all previous predictions.
Our code and data are available at https://github.com/anonymous/Graph2Seq.Graph2Seq is simple yet general and is highly extensible where its two building blocks, graph encoder and sequence decoder, can be replaced by other models such as Graph Convolutional (Attention) Networks (Kipf & Welling, 2016; BID31 or their extensions BID19 , and LSTM (Hochreiter & Schmidhuber, 1997) .
We highlight three main contributions of this paper as follows:• We propose a new attention-based neural networks paradigm to elegantly address graphto-sequence learning problems that learns a mapping between graph-structured inputs to sequence outputs, which current Seq2Seq and Tree2Seq may be inadequate to handle.•
We propose a novel graph encoder to learn a bi-directional node embeddings for directed and undirected graphs with node attributes by employing various aggregation strategies, and to learn graph-level embedding by exploiting two different graph embedding techniques. Equally
importantly, we present an attention mechanism to learn the alignments between nodes and sequence elements to better cope with large graphs.• Experimental
results show that our model achieves state-of-the-art performance on three recently introduced graph-to-sequence tasks and significantly outperforms existing graph neural networks, Seq2Seq, and Tree2Seq models.
In this paper, we study the graph-to-sequence problem, introducing a new general and flexible Graph2Seq model that follows the encoder-decoder architecture.
We showed that, using our proposed bi-directional node embedding aggregation strategy, the graph encoder could successfully learn representations for three representative classes of directed graph, i.e., directed acyclic graphs, directed cyclic graphs and sequence-styled graphs.
Experimental results on three tasks demonstrate that our model significantly outperforms existing graph neural networks, Seq2Seq, and Tree2Seq baselines on both synthetic and real application datasets.
We also showed that introducing an attention mechanism over node representation into the decoding substantially enhances the ability of our model to produce correct target sequences from large graphs.
Since much symbolic data is represented as graphs and many tasks express their desired outputs as sequences, we expect Graph2Seq to be broadly applicable to unify symbolic AI and beyond.
A PSEUDO-CODE OF THE GRAPH-TO-SEQUENCE ALGORITHM

assistant: text: Graph to Sequence Learning with Attention-Based Neural Networks