Abstract Meaning Representation (AMR) Banarescu et al. (2013) is a semantic formalism that encodes the meaning of a sentence as a rooted, directed graph. Figure 1 shows an AMR graph in which the nodes (such as “describe-01” and “person”) represent the concepts, and edges (such as “:ARG0” and “:name”) represent the relations between concepts they connect. AMR has been proven helpful on other NLP tasks, such as machine translation Jones et al. (2012); Tamchyna et al. (2015), question answering Mitra and Baral (2015), summarization Takase et al. (2016) and event detection Li et al. (2015).
The task of AMR-to-text generation is to produce a text with the same meaning as a given input AMR graph. The task is challenging as word tenses and function words are abstracted away when constructing AMR graphs from texts. The translation from AMR nodes to text phrases can be far from literal. For example, shown in Figure 1, “Ryan” is represented as “(p / person :name (n / name :op1 “Ryan”))”, and “description of” is represented as “(d / describe-01 :ARG1 )”.
, recent research has demonstrated the success of deep learning, and in particular the sequence-to-sequence modelSutskever et al. (2014), which has achieved the state-of-the-art results on AMR-to-text generation Konstas et al. (2017)
. One limitation of sequence-to-sequence models, however, is that they require serialization of input AMR graphs, which adds to the challenge of representing graph structure information, especially when the graph is large. In particular, closely-related nodes, such as parents, children and siblings can be far away after serialization. It can be difficult for a linear recurrent neural network to automatically induce their original connections from bracketed string forms.
To address this issue, we introduce a novel graph-to-sequence model, where a graph-state LSTM is used to encode AMR structures directly. To capture non-local information, the encoder performs graph state transition by information exchange between connected nodes, with a graph state consisting of all node states. Multiple recurrent transition steps are taken so that information can propagate non-locally, and LSTM Hochreiter and Schmidhuber (1997) is used to avoid gradient diminishing and bursting in the recurrent process. The decoder is an attention-based LSTM model with a copy mechanism Gu et al. (2016); Gulcehre et al. (2016), which helps copy sparse tokens (such as numbers and named entities) from the input.
Trained on a standard dataset (LDC2015E86), our model surpasses a strong sequence-to-sequence baseline by 2.3 BLEU points, demonstrating the advantage of graph-to-sequence models for AMR-to-text generation compared to sequence-to-sequence models. Our final model achieves a BLEU score of 23.3 on the test set, which is 1.3 points higher than the existing state of the art Konstas et al. (2017) trained on the same dataset. When using gigaword sentences as additional training data, our model is consistently better than konstas-EtAl:2017:Long using the same amount of gigaword data, showing the effectiveness of our model on large-scale training set.
We release our code and models at https://github.com/freesunshine0316/neural-graph-to-seq-mp.
2 Baseline: a seq-to-seq model
Our baseline is a sequence-to-sequence model, which follows the encoder-decoder framework of konstas-EtAl:2017:Long.
2.1 Input representation
Given an AMR graph , where and denote the sets of nodes and edges, respectively, we use the depth-first traversal of konstas-EtAl:2017:Long to linearize it to obtain a sequence of tokens , where is the number of tokens. For example, the AMR graph in Figure 1 is serialized as “describe :arg0 ( person :name ( name :op1 ryan ) ) :arg1 person :arg2 genius”. We can see that the distance between “describe” and “genius”, which are directly connected in the original AMR, becomes 14 in the serialization result.
A simple way to calculate the representation for each token is using its word embedding :
are model parameters for compressing the input vector size.
To alleviate the data sparsity problem and obtain better word representation as the input, we also adopt a forward LSTM over the characters of the token, and concatenate the last hidden state with the word embedding:
The encoder is a bi-directional LSTM applied on the linearized graph by depth-first traversal, as in konstas-EtAl:2017:Long. At each step , the current states and are generated given the previous states and and the current input :
We use an attention-based LSTM decoder Bahdanau et al. (2015), where the attention memory () is the concatenation of the attention vectors among all input words. Each attention vector is the concatenation of the encoder states of an input token in both directions ( and ) and its input vector ():
where is the number of input tokens.
The decoder yields an output sequence by calculating a sequence of hidden states recurrently. While generating the -th word, the decoder considers five factors: (1) the attention memory ; (2) the previous hidden state of the LSTM model ; (3) the embedding of the current input (previously generated word) ; (4) the previous context vector , which is calculated with attention from ; and (5) the previous coverage vector , which is the accumulation of all attention distributions so far Tu et al. (2016). When , we initialize and as zero vectors, set to the embedding of the start token “s”, and as the average of all encoder states.
For each time-step , the decoder feeds the concatenation of the embedding of the current input and the previous context vector
into the LSTM model to update its hidden state. Then the attention probabilityon the attention vector for the time-step is calculated as:
where , , , and are model parameters. The coverage vector is updated by , and the new context vector is calculated via .
The output probability distribution over a vocabulary at the current state is calculated by:
where and are learnable parameters, and the number of rows in represents the number of words in the vocabulary.
3 The graph-to-sequence model
Unlike the baseline sequence-to-sequence model, we leverage a recurrent graph encoder to represent each input AMR, which directly models the graph structure without serialization.
3.1 The graph encoder
Figure 2 shows the overall structure of our graph encoder. Formally, given a graph , we use a hidden state vector to represent each node . The state of the graph can thus be represented as:
In order to capture non-local interaction between nodes, we allow information exchange between nodes through a sequence of state transitions, leading to a sequence of states , where . The initial state consists of a set of initial node states , where
is a hyperparameter of the model.
A recurrent neural network is used to model the state transition process. In particular, the transition from to consists of a hidden state transition for each node, as shown in Figure 2. At each state transition step , we allow direct communication between a node and all nodes that are directly connected to the node. To avoid gradient diminishing or bursting, LSTM Hochreiter and Schmidhuber (1997) is adopted, where a cell is taken to record memory for . We use an input gate , an output gate and a forget gate to control information flow from the inputs and to the output .
The inputs include representations of edges that are connected to , where can be either the source or the target of the edge. We define each edge as a triple , where and are indices of the source and target nodes, respectively, and is the edge label. is the representation of edge , detailed in Section 3.3. The inputs for are distinguished by incoming and outgoing edges, before being summed up:
where and denote the sets of incoming and outgoing edges of , respectively.
In addition to edge inputs, a cell also takes the hidden states of its incoming nodes and outgoing nodes during a state transition. In particular, the states of all incoming nodes and outgoing nodes are summed up before being passed to the cell and gate nodes:
Based on the above definitions of , , and , the state transition from to , as represented by , can be defined as:
where , and are the input, output and forget gates mentioned earlier. , , , , , where , are model parameters.
3.2 Recurrent steps
Using the above state transition mechanism, information from each node propagates to all its neighboring nodes after each step. Therefore, for the worst case where the input graph is a chain of nodes, the maximum number of steps necessary for information from one arbitrary node to reach another is equal to the size of the graph. We experiment with different transition steps to study the effectiveness of global encoding.
Note that unlike the sequence LSTM encoder, our graph encoder allows parallelization in node-state updates, and thus can be highly efficient using a GPU. It is general and can be potentially applied to other tasks, including sequences, syntactic trees and cyclic structures.
3.3 Input Representation
Different from sequences, the edges of an AMR graph contain labels, which represent relations between the nodes they connect, and are thus important for modeling the graphs. Similar with Section 2, we adopt two different ways for calculating the representation for each edge :
where and are the embeddings of edge label and source node , denotes the last hidden state of the character LSTM over , and and are trainable parameters. The equations correspond to Equations 1 and 2 in Section 2.1, respectively.
We adopt the attention-based LSTM decoder as described in Section 2.3. Since our graph encoder generates a sequence of graph states, only the last graph state is adopted in the decoder. In particular, we make the following changes to the decoder. First, each attention vector becomes , where is the last state for node . Second, the decoder initial state is the average of the last states of all nodes.
3.5 Integrating the copy mechanism
Open-class tokens, such as dates, numbers and named entities, account for a large portion in the AMR corpus. Most appear only a few times, resulting in a data sparsity problem. To address this issue, konstas-EtAl:2017:Long adopt anonymization for dealing with the data sparsity problem. In particular, they first replace the subgraphs that represent dates, numbers and named entities (such as “(q / quantity :quant 3)” and “(p / person :name (n / name :op1 “Ryan”))”) with predefined placeholders (such as “num_0” and “person_name_0”) before decoding, and then recover the corresponding surface tokens (such as “3” and “Ryan”) after decoding. This method involves hand-crafted rules, which can be costly.
to solve this problem. The mechanism works on top of an attention-based RNN decoder by integrating the attention distribution into the final vocabulary distribution. The final probability distribution is defined as the interpolation between two probability distributions:
where is a switch for controlling generating a word from the vocabulary or directly copying it from the input graph. is the probability distribution of directly generating the word, as defined in Equation 5, and is calculated based on the attention distribution by summing the probabilities of the graph nodes that contain identical concept. Intuitively, is relevant to the current decoder input and state , and the context vector . Therefore, we define it as:
where vectors , , and scalar are model parameters. The copy mechanism favors generating words that appear in the input. For AMR-to-text generation, it facilitates the generation of dates, numbers, and named entities that appear in AMR graphs.
Copying vs anonymization
Both copying and anonymization alleviate the data sparsity problem by handling the open-class tokens. However, the copy mechanism has the following advantages over anonymization: (1) anonymization requires significant manual work to define the placeholders and heuristic rules both from subgraphs to placeholders and from placeholders to the surface tokens, (2) the copy mechanism automatically learns what to copy, while anonymization relies on hard rules to cover all types of the open-class tokens, and (3) the copy mechanism is easier to adapt to new domains and languages than anonymization.
4 Training and decoding
We train our models using the cross-entropy loss over each gold-standard output sequence :
where is the input graph, and is the model parameters. Adam Kingma and Ba (2014) with a learning rate of 0.001 is used as the optimizer, and the model that yields the best devset performance is selected to evaluate on the test set. Dropout with rate 0.1 is used during training. Beam search with beam size to 5 is used for decoding. Both training and decoding use Tesla K80 GPUs.
We use a standard AMR corpus (LDC2015E86) as our experimental dataset, which contains 16,833 instances for training, 1368 for development and 1371 for test. Each instance contains a sentence and an AMR graph.
Following konstas-EtAl:2017:Long, we supplement the gold data with large-scale automatic data. We take Gigaword as the external data to sample raw sentences, and train our model on both the sampled data and LDC2015E86. We adopt konstas-EtAl:2017:Long’s strategy for sampling sentences from Gigaword, and choose JAMR Flanigan et al. (2016a)
to parse selected sentences into AMRs, as the AMR parser of konstas-EtAl:2017:Long only works on the anonymized data. For training on both sampled data and LDC2015E86, we also follow the method of konstas-EtAl:2017:Long, which is fine-tuning the model on the AMR corpus after every epoch of pretraining on the gigaword data.
We extract a vocabulary from the training set, which is shared by both the encoder and the decoder. The word embeddings are initialized from Glove pretrained word embeddings Pennington et al. (2014) on Common Crawl, and are not updated during training. Following existing work, we evaluate the results with the BLEU metric Papineni et al. (2002).
For model hyperparameters, we set the graph state transition number as 9 according to development experiments. Each node takes information from at most 10 neighbors. The hidden vector sizes for both encoder and decoder are set to 300 (They are set to 600 for experiments using large-scale automatic data). Both character embeddings and hidden layer sizes for character LSTMs are set 100, and at most 20 characters are taken for each graph node or linearized token.
5.3 Development experiments
As shown in Table 1, we compare our model with a set of baselines on the AMR devset to demonstrate how the graph encoder and the copy mechanism can be useful when training instances are not sufficient. Seq2seq is the sequence-to-sequence baseline described in Section 2. Seq2seq+copy extends Seq2seq with the copy mechanism, and Seq2seq+charLSTM+copy further extends Seq2seq+copy with character LSTM. Graph2seq is our graph-to-sequence model, Graph2seq+copy extends Graph2seq with the copy mechanism, and Graph2seq+charLSTM+copy further extends Graph2seq+copy with the character LSTM. We also try Graph2seq+Anon, which applies our graph-to-sequence model on the anonymized data from konstas-EtAl:2017:Long.
The graph encoder
As can be seen from Table 1, the performance of Graph2seq is 1.6 BLEU points higher than Seq2seq, which shows that our graph encoder is effective when applied alone. Adding the copy mechanism (Graph2seq+copy vs Seq2seq+copy), the gap becomes 2.3. This shows that the graph encoder learns better node representations compared to the sequence encoder, which allows attention and copying to function better.
Applying the graph encoder together with the copy mechanism gives a gain of 3.4 BLEU points over the baseline (Graph2seq+copy vs Seq2seq). The graph encoder is consistently better than the sequence encoder no matter whether character LSTMs are used.
We also list the encoding part of decoding times on the devset, as the decoders of the seq2seq and the graph2seq models are similar, so the time differences reflect efficiencies of the encoders. Our graph encoder gives consistently better efficiency compared with the sequence encoder, showing the advantage of parallelization.
The copy mechanism
Table 1 shows that the copy mechanism is effective on both the graph-to-sequence and the sequence-to-sequence models. Anonymization gives comparable overall performance gains on our graph-to-sequence model as the copy mechanism (comparing Graph2seq+Anon with Graph2seq+copy). However, the copy mechanism has several advantages over anonymization as discussed in Section 3.5.
Character LSTM helps to increase the performances of both systems by roughly 0.6 BLEU points. This is largely because it further alleviates the data sparsity problem by handling unseen words, which may share common substrings with in-vocabulary words.
5.4 Effectiveness on graph state transitions
We report a set of development experiments for understanding the graph LSTM encoder.
Number of iterations
We analyze the influence of the number of state transitions to the model performance on the devset. Figure 3 shows the BLEU scores of different state transition numbers, when both incoming and outgoing edges are taken for calculating the next state (as shown in Figure 2). The system is Graph2seq+charLSTM+copy. Executing only 1 iteration results in a poor BLEU score of 14.1. In this case the state for each node only contains information about immediately adjacent nodes. The performance goes up dramatically to 21.5 when increasing the iteration number to 5. In this case, the state for each node contains information of all nodes within a distance of 5. The performance further goes up to 22.8 when increasing the iteration number from 5 to 9, where all nodes with a distance of less than 10 are incorporated in the state for each node.
We analyze the percentage of the AMR graphs in the devset with different graph diameters and show the cumulative distribution in Figure 4. The diameter of an AMR graph is defined as the longest distance between two AMR nodes.111The diameter of single-node graphs is 0. Even though the diameters for less than 80% of the AMR graphs are less or equal than 10, our development experiments show that it is not necessary to incorporate the whole-graph information for each node. Further increasing state transition number may lead to additional improvement. We do not perform exhaustive search for finding the optimal state transition number.
Incoming and outgoing edges
As shown in Figure 3, we analyze the efficiency of state transition when only incoming or outgoing edges are used. From the results, we can see that there is a huge drop when state transition is performed only with incoming or outgoing edges. Using edges of one direction, the node states only contain information of ancestors or descendants. On the other hand, node states contain information of ancestors, descendants, and siblings if edges of both directions are used. From the results, we can conclude that not only the ancestors and descendants, but also the siblings are important for modeling the AMR graphs. This is similar to observations on syntactic parsing tasks McDonald et al. (2005), where sibling features are adopted.
We perform a similar experiment for the Seq2seq+copy
baseline by only executing single-directional LSTM for the encoder. We observe BLEU scores of 11.8 and 12.7 using only forward or backward LSTM, respectively. This is consistent with our graph model in that execution using only one direction leads to a huge performance drop. The contrast is also reminiscent of using the normal input versus the reversed input in neural machine translation(Sutskever et al., 2014).
|Graph2seq+charLSTM+copy (2M)||33.6222It was 33.0 at submission, and has been improved.|
Table 2 compares our final results with existing work. MSeq2seq+Anon Konstas et al. (2017) is an attentional multi-layer sequence-to-sequence model trained with the anonymized data. PBMT Pourdamghani et al. (2016) adopts a phrase-based model for machine translation Koehn et al. (2003) on the input of linearized AMR graph, SNRG Song et al. (2017) uses synchronous node replacement grammar for parsing the AMR graph while generating the text, and Tree2Str Flanigan et al. (2016b) converts AMR graphs into trees by splitting the re-entrances before using a tree transducer to generate the results.
Graph2seq+charLSTM+copy achieves a BLEU score of 23.3, which is 1.3 points better than MSeq2seq+Anon trained on the same AMR corpus. In addition, our model without character LSTM is still 0.7 BLEU points higher than MSeq2seq+Anon. Note that MSeq2seq+Anon relies on anonymization, which requires additional manual work for defining mapping rules, thus limiting its usability on other languages and domains. The neural models tend to underperform statistical models when trained on limited (16K) gold data, but performs better with scaled silver data Konstas et al. (2017).
Following konstas-EtAl:2017:Long, we also evaluate our model using both the AMR corpus and sampled sentences from Gigaword. Using additional 200K or 2M gigaword sentences, Graph2seq+charLSTM+copy achieves BLEU scores of 28.2 and 33.0, respectively, which are 0.8 and 0.7 BLEU points better than MSeq2seq+Anon using the same amount of data, respectively. The BLEU scores are 5.3 and 10.1 points better than the result when it is only trained with the AMR corpus, respectively. This shows that our model can benefit from scaled data with automatically generated AMR graphs, and it is more effective than MSeq2seq+Anon using the same amount of data. Using 2M gigaword data, our model is better than all existing methods. konstas-EtAl:2017:Long also experimented with 20M external data, obtaining a BLEU of 33.8. We did not try this setting due to hardware limitations. The Seq2seq+charLSTM+copy baseline trained on the large-scale data is close to MSeq2seq+Anon using the same amount of training data, yet is much worse than our model.
5.6 Case study
We conduct case studies for better understanding the model performances. Table 3 shows example outputs of sequence-to-sequence (S2S), graph-to-sequence (G2S) and graph-to-sequence with copy mechanism (G2S+CP). Ref denotes the reference output sentence, and Lin shows the serialization results of input AMRs. The best hyperparameter configuration is chosen for each model.
For the first example, S2S fails to recognize the concept “a / account” as a noun and loses the concept “o / old” (both are underlined). The fact that “a / account” is a noun is implied by “a / account :mod (o / old)” in the original AMR graph. Though directly connected in the original graph, their distance in the serialization result (the input of S2S) is 26, which may be why S2S makes these mistakes. In contrast, G2S handles “a / account” and “o / old” correctly. In addition, the copy mechanism helps to copy “look-over” from the input, which rarely appears in the training set. In this case, G2S+CP is incorrect only on hyphens and literal reference to “anti-japanese war”, although the meaning is fully understandable.
For the second case, both G2S and G2S+CP correctly generate the noun “agreement” for “a / agree” in the input AMR, while S2S fails to. The fact that “a / agree” represents a noun can be determined by the original graph segment “p / provide :ARG0 (a / agree)”, which indicates that “a / agree” is the subject of “p / provide”. In the serialization output, the two nodes are close to each other. Nevertheless, S2S still failed to capture this structural relation, which reflects the fact that a sequence encoder is not designed to explicitly model hierarchical information encoded in the serialized graph. In the training instances, serialized nodes that are close to each other can originate from neighboring graph nodes, or distant graph nodes, which prevents the decoder from confidently deciding the correct relation between them. In contrast, G2S sends the node “p / provide” simultaneously with relation “ARG0” when calculating hidden states for “a / agree”, which facilitates the yielding of “the agreement provides”.
|(p / possible-01 :polarity -|
|:ARG1 (l / look-over-06|
|:ARG0 (w / we)|
|:ARG1 (a / account-01|
|:ARG1 (w2 / war-01|
|:ARG1 (c2 / country :wiki “Japan”|
|:name (n2 / name :op1 “Japan”))|
|:time (p2 / previous)|
|:ARG1-of (c / call-01|
|:mod (s / so)))|
|:mod (o / old))))|
|Lin: possible :polarity - :arg1 ( look-over :arg0 we :arg1 ( account :arg1 ( war :arg1 ( country :wiki japan :name ( name :op1 japan ) ) :time previous :arg1-of ( call :mod so ) ) :mod old ) )|
|Ref: we can n’t look over the old accounts of the previous so-called anti-japanese war .|
|S2S: we can n’t be able to account the past drawn out of japan ’s entire war .|
|G2S: we can n’t be able to do old accounts of the previous and so called japan war.|
|G2S+CP: we can n’t look-over the old accounts of the previous so called war on japan .|
|(p / provide-01|
|:ARG0 (a / agree-01)|
|:ARG1 (a2 / and|
|:op1 (s / staff|
|:prep-for (c / center|
|:mod (r / research-01)))|
|:op2 (f / fund-01|
|Lin: provide :arg0 agree :arg1 ( and :op1 ( staff :prep-for ( center :mod research ) ) :op2 ( fund :prep-for center ) )|
|Ref: the agreement will provide staff and funding for the research center .|
|S2S: agreed to provide research and institutes in the center .|
|G2S: the agreement provides the staff of research centers and funding .|
|G2S+CP: the agreement provides the staff of the research center and the funding .|
6 Related work
Among early statistical methods for AMR-to-text generation, jeff2016amrgen convert input graphs to trees by splitting re-entrances, and then translate the trees into sentences with a tree-to-string transducer. song-EtAl:2017:Short use a synchronous node replacement grammar to parse input AMRs and generate sentences at the same time. pourdamghani-knight-hermjakob:2016:INLG linearize input graphs by breadth-first traversal, and then use a phrase-based machine translation system333http://www.statmt.org/moses/ to generate results by translating linearized sequences.
Prior work using graph neural networks for NLP include the use graph convolutional networks (GCN) Kipf and Welling (2017) for semantic role labeling Marcheggiani and Titov (2017), neural machine translation Bastings et al. (2017) and graph-to-sequence learning Xu et al. (2018)
. Both GCN and the graph LSTM update node states by exchanging information between neighboring nodes within each iteration. However, our graph state LSTM adopts gated operations for making updates, while GCN uses a linear transformation. Intuitively, the former has better learning power than the later. Another major difference is that our graph state LSTM keeps a cell vector for each node to remember all history. The contrast between our model with GCN is reminiscent of the contrast between RNN and CNN. We leave empirical comparison of their effectiveness to future work. In this work our main goal is to show that graph LSTM encoding of AMR is superior compared with sequence LSTM.
Closest to our work, TACL1028 modeled syntactic and discourse structures using DAG LSTM, which can be viewed as extensions to tree LSTMs Tai et al. (2015). The state update follows the sentence order for each node, and has sequential nature. Our state update is in parallel. In addition, TACL1028 split input graphs into separate DAGs before their method can be used. To our knowledge, we are the first to apply an LSTM structure to encode AMR graphs.
The recurrent information exchange mechanism in our state transition process is remotely related to the idea of loopy belief propagation (LBP) Murphy et al. (1999)
. However, there are two major differences. First, messages between LSTM states are gated neural node values, rather than probabilities in LBP. Second, while the goal of LBP is to estimate marginal probabilities, the goal of information exchange between graph states in our LSTM is to find neural representation features, which are directly optimized by a task objective.
We introduced a novel graph-to-sequence model for AMR-to-text generation. Compared to sequence-to-sequence models, which require linearization of AMR before decoding, a graph LSTM is leveraged to directly model full AMR structure. Allowing high parallelization, the graph encoder is more efficient than the sequence encoder. In our experiments, the graph model outperforms a strong sequence-to-sequence model, achieving the best performance.
We thank the anonymized reviewers for the insightful comments, and the Center for Integrated Research Computing (CIRC) of University of Rochester for special reservations of computation resources.
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