prompt_front: You are given a scientific article and a question. Answer the question as concisely as you can, using a single phrase or sentence if possible. If the question cannot be answered based on the information in the article, write "unanswerable". If the question is a yes/no question, answer "yes", "no", or "unanswerable". Do not provide any explanation.

Please answer the questions based on the text provided below. Which component is the least impactful?
Context 1: Introduction
The concept of message passing over graphs has been around for many years BIBREF0, BIBREF1, as well as that of graph neural networks (GNNs) BIBREF2, BIBREF3  However, GNNs have only recently started to be closely investigated, following the advent of deep learning  Some notable examples include BIBREF4, BIBREF5, BIBREF6, BIBREF7, BIBREF8, BIBREF9, BIBREF10, BIBREF11, BIBREF12  These approaches are known as spectral  Their similarity with message passing (MP) was observed by BIBREF9 and formalized by BIBREF13 and BIBREF14 
The MP framework is based on the core idea of recursive neighborhood aggregation  That is, at every iteration, the representation of each vertex is updated based on messages received from its neighbors  All spectral GNNs can be described in terms of the MP framework 
GNNs have been applied with great success to bioinformatics and social network data, for node classification, link prediction, and graph classification  However, a few studies only have focused on the application of the MP framework to representation learning on text  This paper proposes one such application  More precisely, we represent documents as word co-occurrence networks, and develop an expressive MP GNN tailored to document understanding, the Message Passing Attention network for Document understanding (MPAD)  We also propose several hierarchical variants of MPAD  Evaluation on 10 document classification datasets show that our architectures learn representations that are competitive with the state-of-the-art  Furthermore, ablation experiments shed light on the impact of various architectural choices 
In what follows, we first provide some background about the MP framework (in sec  SECREF2), thoroughly describe and explain MPAD (sec  SECREF3), present our experimental framework (sec  SECREF4), report and interpret our results (sec  SECREF5), and provide a review of the relevant literature (sec  SECREF6) 
Message Passing Neural Networks
BIBREF13 proposed a MP framework under which many of the recently introduced GNNs can be reformulated  MP consists in an aggregation phase followed by a combination phase BIBREF14  More precisely, let $G(V,E)$ be a graph, and let us consider $v \in V$  At time $t+1$, a message vector $\mathbf {m}_v^{t+1}$ is computed from the representations of the neighbors $\mathcal {N}(v)$ of $v$:
The new representation $\mathbf {h}^{t+1}_v$ of $v$ is then computed by combining its current feature vector $\mathbf {h}^{t}_v$ with the message vector $\mathbf {m}_v^{t+1}$:
Messages are passed for $T$ time steps  Each step is implemented by a different layer of the MP network  Hence, iterations correspond to network depth  The final feature vector $\mathbf {h}_v^T$ of $v$ is based on messages propagated from all the nodes in the subtree of height $T$ rooted at $v$  It captures both the topology of the neighborhood of $v$ and the distribution of the vertex representations in it 
If a graph-level feature vector is needed, e g , for classification or regression, a READOUT pooling function, that must be invariant to permutations, is applied:
Next, we present the MP network we developed for document understanding 
Message Passing Attention network for Document understanding (MPAD) ::: Word co-occurrence networks
We represent a document as a statistical word co-occurrence network BIBREF18, BIBREF19 with a sliding window of size 2 overspanning sentences  Let us denote that graph $G(V,E)$  Each unique word in the preprocessed document is represented by a node in $G$, and an edge is added between two nodes if they are found together in at least one instantiation of the window  $G$ is directed and weighted: edge directions and weights respectively capture text flow and co-occurrence counts 
$G$ is a compact representation of its document  In $G$, immediate neighbors are consecutive words in the same sentence  That is, paths of length 2 correspond to bigrams  Paths of length more than 2 can correspond either to traditional $n$-grams or to relaxed $n$-grams, that is, words that never appear in the same sentence but co-occur with the same word(s)  Such nodes are linked through common neighbors 
Master node  Inspired by BIBREF3, our $G$ also includes a special document node, linked to all other nodes via unit weight bi-directional edges  In what follows, let us denote by $n$ the number of nodes in $G$, including the master node 
Message Passing Attention network for Document understanding (MPAD) ::: Message passing
We formulate our AGGREGATE function as:
where $\mathbf {H}^t \in \mathbb {R}^{n \times d}$ contains node features ($d$ is a hyperparameter), and $\mathbf {A} \in \mathbb {R}^{n \times n}$ is the adjacency matrix of $G$  Since $G$ is directed, $\mathbf {A}$ is asymmetric  Also, $\mathbf {A}$ has zero diagonal as we choose not to consider the feature of the node itself, only that of its incoming neighbors, when updating its representation  Since $G$ is weighted, the $i^{th}$ row of $A$ contains the weights of the edges incoming on node $v_i$  $\mathbf {D} \in \mathbb {R}^{n \times n}$ is the diagonal in-degree matrix of $G$  MLP denotes a multi-layer perceptron, and $\mathbf {M}^{t+1} \in \mathbb {R}^{n \times d}$ is the message matrix 
The use of a MLP was motivated by the observation that for graph classification, MP neural nets with 1-layer perceptrons are inferior to their MLP counterparts BIBREF14  Indeed, 1-layer perceptrons are not universal approximators of multiset functions  Note that like in BIBREF14, we use a different MLP at each layer 
Renormalization  The rows of $\mathbf {D}^{-1}\mathbf {A}$ sum to 1  This is equivalent to the renormalization trick of BIBREF9, but using only the in-degrees  That is, instead of computing a weighted sum of the incoming neighbors' feature vectors, we compute a weighted average of them  The coefficients are proportional to the strength of co-occurrence between words  One should note that by averaging, we lose the ability to distinguish between different neighborhood structures in some special cases, that is, we lose injectivity  Such cases include neighborhoods in which all nodes have the same representations, and neighborhoods of different sizes containing various representations in equal proportions BIBREF14  As suggested by the results of an ablation experiment, averaging is better than summing in our application (see subsection SECREF30)  Note that instead of simply summing/averaging, we also tried using GAT-like attention BIBREF11 in early experiments, without obtaining better results 
As far as our COMBINE function, we use the Gated Recurrent Unit BIBREF20, BIBREF21:
Omitting biases for readability, we have:
where the $\mathbf {W}$ and $\mathbf {U}$ matrices are trainable weight matrices not shared across time steps, $\sigma (\mathbf {x}) = 1/(1+\exp (-\mathbf {x}))$ is the sigmoid function, and $\mathbf {R}$ and $\mathbf {Z}$ are the parameters of the reset and update gates  The reset gate controls the amount of information from the previous time step (in $\mathbf {H}^t$) that should propagate to the candidate representations, $\tilde{\mathbf {H}}^{t+1}$  The new representations $\mathbf {H}^{t+1}$ are finally obtained by linearly interpolating between the previous and the candidate ones, using the coefficients returned by the update gate 
Interpretation  Updating node representations through a GRU should in principle allow nodes to encode a combination of local and global signals (low and high values of $t$, resp ), by allowing them to remember about past iterations  In addition, we also explicitly consider node representations at all iterations when reading out (see Eq  DISPLAY_FORM18) 
Message Passing Attention network for Document understanding (MPAD) ::: Readout
After passing messages and performing updates for $T$ iterations, we obtain a matrix $\mathbf {H}^T \in \mathbb {R}^{n \times d}$ containing the final vertex representations  Let $\hat{G}$ be graph $G$ without the special document node, and matrix $\mathbf {\hat{H}}^T \in \mathbb {R}^{(n-1) \times d}$ be the corresponding representation matrix (i e , $\mathbf {H}^T$ without the row of the document node) 
We use as our READOUT function the concatenation of self-attention applied to $\mathbf {\hat{H}}^T$ with the final document node representation  More precisely, we apply a global self-attention mechanism BIBREF22 to the rows of $\mathbf {\hat{H}}^T$  As shown in Eq  DISPLAY_FORM17, $\mathbf {\hat{H}}^T$ is first passed to a dense layer parameterized by matrix $\mathbf {W}_A^T \in \mathbb {R}^{d \times d}$  An alignment vector $\mathbf {a}$ is then derived by comparing, via dot products, the rows of the output of the dense layer $\mathbf {Y}^T \in \mathbb {R}^{(n-1) \times d}$ with a trainable vector $\mathbf {v}^T \in \mathbb {R}^d$ (initialized randomly) and normalizing with a softmax  The normalized alignment coefficients are finally used to compute the attentional vector $\mathbf {u}^T \in \mathbb {R}^d$ as a weighted sum of the final representations $\mathbf {\hat{H}}^T$ 
Note that we tried with multiple context vectors, i e , with a matrix $\mathbf {V}^T$ instead of a vector $\mathbf {v}^T$, like in BIBREF22, but results were not convincing, even when adding a regularization term to the loss to favor diversity among the rows of $\mathbf {V}^T$ 
Master node skip connection  $\mathbf {h}_G^T \in \mathbb {R}^{2d}$ is obtained by concatenating $\mathbf {u}^T$ and the final master node representation  That is, the master node vector bypasses the attention mechanism  This is equivalent to a skip or shortcut connection BIBREF23  The reason behind this choice is that we expect the special document node to learn a high-level summary about the document, such as its size, vocabulary, etc  (more details are given in subsection SECREF30)  Therefore, by making the master node bypass the attention layer, we directly inject global information about the document into its final representation 
Multi-readout  BIBREF14, inspired by Jumping Knowledge Networks BIBREF12, recommend to not only use the final representations when performing readout, but also that of the earlier steps  Indeed, as one iterates, node features capture more and more global information  However, retaining more local, intermediary information might be useful too  Thus, instead of applying the readout function only to $t=T$, we apply it to all time steps and concatenate the results, finally obtaining $\mathbf {h}_G \in \mathbb {R}^{T \times 2d}$ :
In effect, with this modification, we take into account features based on information aggregated from subtrees of different heights (from 1 to $T$), corresponding to local and global features 
Message Passing Attention network for Document understanding (MPAD) ::: Hierarchical variants of MPAD
Through the successive MP iterations, it could be argued that MPAD implicitly captures some soft notion of the hierarchical structure of documents (words $\rightarrow $ bigrams $\rightarrow $ compositions of bigrams, etc )  However, it might be beneficial to explicitly capture document hierarchy  Hierarchical architectures have brought significant improvements to many NLP tasks, such as language modeling and generation BIBREF24, BIBREF25, sentiment and topic classification BIBREF26, BIBREF27, and spoken language understanding BIBREF28, BIBREF29  Inspired by this line of research, we propose several hierarchical variants of MPAD, detailed in what follows  In all of them, we represent each sentence in the document as a word co-occurrence network, and obtain an embedding for it by applying MPAD as previously described 
MPAD-sentence-att  Here, the sentence embeddings are simply combined through self-attention 
MPAD-clique  In this variant, we build a complete graph where each node represents a sentence  We then feed that graph to MPAD, where the feature vectors of the nodes are initialized with the sentence embeddings previously obtained 
MPAD-path  This variant is similar to the clique one, except that instead of a complete graph, we build a path according to the natural flow of the text  That is, two nodes are linked by a directed edge if the two sentences they represent follow each other in the document 
Experiments ::: Datasets
We evaluate the quality of the document embeddings learned by MPAD on 10 document classification datasets, covering the topic identification, coarse and fine sentiment analysis and opinion mining, and subjectivity detection tasks  We briefly introduce the datasets next  Their statistics are reported in Table TABREF21 
(1) Reuters  This dataset contains stories collected from the Reuters news agency in 1987  Following common practice, we used the ModApte split and considered only the 10 classes with the highest number of positive training examples  We also removed documents belonging to more than one class and then classes left with no document (2 classes) 
(2) BBCSport BIBREF30 contains documents from the BBC Sport website corresponding to 2004-2005 sports news articles 
(3) Polarity BIBREF31 features positive and negative labeled snippets from Rotten Tomatoes 
(4) Subjectivity BIBREF32 contains movie review snippets from Rotten Tomatoes (subjective sentences), and Internet Movie Database plot summaries (objective sentences) 
(5) MPQA BIBREF33 is made of positive and negative phrases, annotated as part of the summer 2002 NRRC Workshop on Multi-Perspective Question Answering 
(6) IMDB BIBREF34 is a collection of highly polarized movie reviews from IMDB (positive and negative)  There are at most 30 reviews for each movie 
(7) TREC BIBREF35 consists of questions that are classified into 6 different categories 
(8) SST-1 BIBREF36 contains the same snippets as Polarity  The authors used the Stanford Parser to parse the snippets and split them into multiple sentences  They then used Amazon Mechanical Turk to annotate the resulting phrases according to their polarity (very negative, negative, neutral, positive, very positive) 
(9) SST-2 BIBREF36 is the same as SST-1 but with neutral reviews removed and snippets classified as positive or negative 
(10) Yelp2013 BIBREF26 features reviews obtained from the 2013 Yelp Dataset Challenge 
Experiments ::: Baselines
We evaluate MPAD against multiple state-of-the-art baseline models, including hierarchical ones, to enable fair comparison with the hierarchical MPAD variants 
doc2vec BIBREF37  Doc2vec (or paragraph vector) is an extension of word2vec that learns vectors for documents in a fully unsupervised manner  Document embeddings are then fed to a logistic regression classifier 
CNN BIBREF38  The convolutional neural network architecture, well-known in computer vision, is applied to text  There is one spatial dimension and the word embeddings are used as channels (depth dimensions) 
DAN BIBREF39  The Deep Averaging Network passes the unweighted average of the embeddings of the input words through multiple dense layers and a final softmax 
Tree-LSTM BIBREF40 is a generalization of the standard LSTM architecture to constituency and dependency parse trees 
DRNN BIBREF41  Recursive neural networks are stacked and applied to parse trees 
LSTMN BIBREF42 is an extension of the LSTM model where the memory cell is replaced by a memory network which stores word representations 
C-LSTM BIBREF43 combines convolutional and recurrent neural networks  The region embeddings provided by a CNN are fed to a LSTM 
SPGK BIBREF44 also models documents as word co-occurrence networks  It computes a graph kernel that compares shortest paths extracted from the word co-occurrence networks and then uses a SVM to categorize documents 
WMD BIBREF45 is an application of the well-known Earth Mover's Distance to text  A k-nearest neighbor classifier is used 
S-WMD BIBREF46 is a supervised extension of the Word Mover's Distance 
Semantic-CNN BIBREF47  Here, a CNN is applied to semantic units obtained by clustering words in the embedding space 
LSTM-GRNN BIBREF26 is a hierarchical model where sentence embeddings are obtained with a CNN and a GRU-RNN is fed the sentence representations to obtain a document vector 
HN-ATT BIBREF27 is another hierarchical model, where the same encoder architecture (a bidirectional GRU-RNN) is used for both sentences and documents, with different parameters  A self-attention mechanism is applied to the RNN annotations at each level 
Experiments ::: Model configuration and training
We preprocess all datasets using the code of BIBREF38  On Yelp2013, we also replace all tokens appearing strictly less than 6 times with a special UNK token, like in BIBREF27  We then build a directed word co-occurrence network from each document, with a window of size 2 
We use two MP iterations ($T$=2) for the basic MPAD, and two MP iterations at each level, for the hierarchical variants  We set $d$ to 64, except on IMDB and Yelp on which $d=128$, and use a two-layer MLP  The final graph representations are passed through a softmax for classification  We train MPAD in an end-to-end fashion by minimizing the cross-entropy loss function with the Adam optimizer BIBREF48 and an initial learning rate of 0 001 
To regulate potential differences in magnitude, we apply batch normalization after concatenating the feature vector of the master node with the self-attentional vector, that is, after the skip connection (see subsection SECREF16)  To prevent overfitting, we use dropout BIBREF49 with a rate of 0 5  We select the best epoch, capped at 200, based on the validation accuracy  When cross-validation is used (see 3rd column of Table TABREF21), we construct a validation set by randomly sampling 10% of the training set of each fold 
On all datasets except Yelp2013, we use the publicly available 300-dimensional pre-trained Google News vectors ($D$=300) BIBREF50 to initialize the node representations $\mathbf {H}^0$  On Yelp2013, we follow BIBREF27 and learn our own word vectors from the training and validation sets with the gensim implementation of word2vec BIBREF51 
MPAD was implemented in Python 3 6 using the PyTorch library BIBREF52  All experiments were run on a single machine consisting of a 3 4 GHz Intel Core i7 CPU with 16 GB of RAM and an NVidia GeForce Titan Xp GPU 
Results and ablations ::: Results
Experimental results are shown in Table TABREF28  For the baselines, the best scores reported in each original paper are shown  MPAD reaches best performance on 7 out of 10 datasets, and is close second elsewhere  Moreover, the 7 datasets on which MPAD ranks first widely differ in training set size, number of categories, and prediction task (topic, sentiment, subjectivity), which indicates that MPAD can perform well in different settings 
MPAD vs  hierarchical variants  On 9 datasets out of 10, one or more of the hierarchical variants outperform the vanilla MPAD architecture, highlighting the benefit of explicitly modeling the hierarchical nature of documents 
However, on Subjectivity, standard MPAD outperforms all hierarchical variants  On TREC, it reaches the same accuracy  We hypothesize that in some cases, using a different graph to separately encode each sentence might be worse than using one single graph to directly encode the document  Indeed, in the single document graph, some words that never appear in the same sentence can be connected through common neighbors, as was explained in subsection SECREF7  So, this way, some notion of cross-sentence context is captured while learning representations of words, bigrams, etc  at each MP iteration  This creates better informed representations, resulting in a better document embedding  With the hierarchical variants, on the other hand, each sentence vector is produced in isolation, without any contextual information about the other sentences in the document  Therefore, the final sentence embeddings might be of lower quality, and as a group might also contain redundant/repeated information  When the sentence vectors are finally combined into a document representation, it is too late to take context into account 
Results and ablations ::: Ablation studies
To understand the impact of some hyperparameters on performance, we conducted additional experiments on the Reuters, Polarity, and IMDB datasets, with the non-hierarchical version of MPAD  Results are shown in Table TABREF29 
Number of MP iterations  First, we varied the number of message passing iterations from 1 to 4  We can clearly see in Table TABREF29 that having more iterations improves performance  We attribute this to the fact that we are reading out at each iteration from 1 to $T$ (see Eq  DISPLAY_FORM18), which enables the final graph representation to encode a mixture of low-level and high-level features  Indeed, in initial experiments involving readout at $t$=$T$ only, setting $T\ge 2$ was always decreasing performance, despite the GRU-based updates (Eq  DISPLAY_FORM14)  These results were consistent with that of BIBREF53 and BIBREF9, who both are reading out only at $t$=$T$ too  We hypothesize that node features at $T\ge 2$ are too diffuse to be entirely relied upon during readout  More precisely, initially at $t$=0, node representations capture information about words, at $t$=1, about their 1-hop neighborhood (bigrams), at $t$=2, about compositions of bigrams, etc  Thus, pretty quickly, node features become general and diffuse  In such cases, considering also the lower-level, more precise features of the earlier iterations when reading out may be necessary 
Undirected edges  On Reuters, using an undirected graph leads to better performance, while on Polarity and IMDB, it is the opposite  This can be explained by the fact that Reuters is a topic classification task, for which the presence or absence of some patterns is important, but not necessarily the order in which they appear, while Polarity and IMDB are sentiment analysis tasks  To capture sentiment, modeling word order is crucial, e g , in detecting negation 
No master node  Removing the master node deteriorates performance across all datasets, clearly showing the value of having such a node  We hypothesize that since the special document node is connected to all other nodes, it is able to encode during message passing a summary of the document 
No renormalization  Here, we do not use the renormalization trick of BIBREF9 during MP (see subsection SECREF10)  That is, Eq  DISPLAY_FORM11 becomes $\mathbf {M}^{t+1} = \textsc {MLP}^{t+1}\big (\mathbf {A}\mathbf {H}^{t}\big )$  In other words, instead of computing a weighted average of the incoming neighbors' feature vectors, we compute a weighted sum of them  Unlike the mean, which captures distributions, the sum captures structural information BIBREF14  As shown in Table TABREF29, using sum instead of mean decreases performance everywhere, suggesting that in our application, capturing the distribution of neighbor representations is more important that capturing their structure  We hypothesize that this is the case because statistical word co-occurrence networks tend to have similar structural properties, regardless of the topic, polarity, sentiment, etc  of the corresponding documents 
Neighbors-only  In this experiment, we replaced the GRU combine function (see Eq  DISPLAY_FORM14) with the identity function  That is, we simply have $\mathbf {H}^{t+1}$=$\mathbf {M}^{t+1}$  Since $\mathbf {A}$ has zero diagonal, by doing so, we completely ignore the previous feature of the node itself when updating its representation  That is, the update is based entirely on its neighbors  Except on Reuters (almost no change), performance always suffers, stressing the need to take into account the root node during updates, not only its neighborhood 
Related work
In what follows, we offer a brief review of relevant studies, ranked by increasing order of similarity with our work 
BIBREF9, BIBREF54, BIBREF11, BIBREF10 conduct some node classification experiments on citation networks, where nodes are scientific papers, i e , textual data  However, text is only used to derive node feature vectors  The external graph structure, which plays a central role in determining node labels, is completely unrelated to text 
On the other hand, BIBREF55, BIBREF7 experiment on traditional document classification tasks  They both build $k$-nearest neighbor similarity graphs based on the Gaussian diffusion kernel  More precisely, BIBREF55 build one single graph where nodes are documents and distance is computed in the BoW space  Node features are then used for classification  Closer to our work, BIBREF7 represent each document as a graph  All document graphs are derived from the same underlying structure  Only node features, corresponding to the entries of the documents' BoW vectors, vary  The underlying, shared structure is that of a $k$-NN graph where nodes are vocabulary terms and similarity is the cosine of the word embedding vectors  BIBREF7 then perform graph classification  However they found performance to be lower than that of a naive Bayes classifier 
BIBREF56 use a GNN for hierarchical classification into a large taxonomy of topics  This task differs from traditional document classification  The authors represent documents as unweighted, undirected word co-occurrence networks with word embeddings as node features  They then use the spatial GNN of BIBREF15 to perform graph classification 
The work closest to ours is probably that of BIBREF53  The authors adopt the semi-supervised node classification approach of BIBREF9  They build one single undirected graph from the entire dataset, with both word and document nodes  Document-word edges are weighted by TF-IDF and word-word edges are weighted by pointwise mutual information derived from co-occurrence within a sliding window  There are no document-document edges  The GNN is trained based on the cross-entropy loss computed only for the labeled nodes, that is, the documents in the training set  When the final node representations are obtained, one can use that of the test documents to classify them and evaluate prediction performance 
There are significant differences between BIBREF53 and our work  First, our approach is inductive, not transductive  Indeed, while the node classification approach of BIBREF53 requires all test documents at training time, our graph classification model is able to perform inference on new, never-seen documents  The downside of representing documents as separate graphs, however, is that we lose the ability to capture corpus-level dependencies  Also, our directed graphs capture word ordering, which is ignored by BIBREF53  Finally, the approach of BIBREF53 requires computing the PMI for every word pair in the vocabulary, which may be prohibitive on datasets with very large vocabularies  On the other hand, the complexity of MPAD does not depend on vocabulary size 
Conclusion
We have proposed an application of the message passing framework to NLP, the Message Passing Attention network for Document understanding (MPAD)  Experiments conducted on 10 standard text classification datasets show that our architecture is competitive with the state-of-the-art  By processing weighted, directed word co-occurrence networks, MPAD is sensitive to word order and word-word relationship strength  To explicitly capture the hierarchical structure of documents, we also propose three hierarchical variants of MPAD, that we show bring improvements over the vanilla architecture 
Acknowledgments
We thank the NVidia corporation for the donation of a GPU as part of their GPU grant program 

ground_truth: Based on table results provided changing directed to undirected edges had least impact - max abs difference of 0.33 points on all three datasets.

prompt_front: You are given a scientific article and a question. Answer the question as concisely as you can, using a single phrase or sentence if possible. If the question cannot be answered based on the information in the article, write "unanswerable". If the question is a yes/no question, answer "yes", "no", or "unanswerable". Do not provide any explanation.

Please answer the questions based on the text provided below. Were any of the pipeline components based on deep learning models?
Context 2: Introduction
The automatic identification, extraction and representation of the information conveyed in texts is a key task nowadays  In fact, this research topic is increasing its relevance with the exponential growth of social networks and the need to have tools that are able to automatically process them BIBREF0 
Some of the domains where it is more important to be able to perform this kind of action are the juridical and legal ones  Effectively, it is crucial to have the capability to analyse open access text sources, like social nets (Twitter and Facebook, for instance), blogs, online newspapers, and to be able to extract the relevant information and represent it in a knowledge base, allowing posterior inferences and reasoning 
In the context of this work, we will present results of the R&D project Agatha, where we developed a pipeline of processes that analyses texts (in Portuguese, Spanish, or English) and is able to populate a specialized ontology BIBREF1 (related to criminal law) for the representation of events, depicted in such texts  Events are represented by objects having associated actions, agents, elements, places and time  After having populated the event ontology, we have an automatic process linking the identified entities to external referents, creating, this way, a linked data knowledge base 
It is important to point out that, having the text information represented in an ontology allows us to perform complex queries and inferences, which can detect patterns of typical criminal actions 
Another axe of innovation in this research is the development, for the Portuguese language, of a pipeline of Natural Language Processing (NLP) processes, that allows us to fully process sentences and represent their content in an ontology  Although there are several tools for the processing of the Portuguese language, the combination of all these steps in a integrated tool is a new contribution 
Moreover, we have already explored other related research path, namely author profiling BIBREF2, aggression identification BIBREF3 and hate-speech detection BIBREF4 over social media, plus statute law retrieval and entailment for Japanese BIBREF5 
The remainder of this paper is organized as follows: Section SECREF2 describes our proposed architecture together with the Portuguese modules for its computational processing  Section SECREF3 discusses different design options and Section SECREF4 provides our conclusions together with some pointers for future work 
Framework for Processing Portuguese Text
The framework for processing Portuguese texts is depicted in Fig  FIGREF2, which illustrates how relevant pieces of information are extracted from the text  Namely, input files (Portuguese texts) go through a series of modules: part-of-speech tagging, named entity recognition, dependency parsing, semantic role labeling, subject-verb-object triple extraction, and lexicon matching 
The main goal of all the modules except lexicon matching is to identify events given in the text  These events are then used to populate an ontology 
The lexicon matching, on the other hand, was created to link words that are found in the text source with the data available not only on Eurovoc BIBREF6 thesaurus but also on the EU's terminology database IATE BIBREF7 (see Section SECREF12 for details) 
Most of these modules are deeply related and are detailed in the subsequent subsections 
Framework for Processing Portuguese Text ::: Part-Of-Speech Tagging
Part-of-speech tagging happens after language detection  It labels each word with a tag that indicates its syntactic role in the sentence  For instance, a word could be a noun, verb, adjective or adverb (or other syntactic tag)  We used Freeling BIBREF8 library to provide the tags  This library resorts to a Hidden Markov Model as described by Brants BIBREF9  The end result is a tag for each word as described by the EAGLES tagset  
Framework for Processing Portuguese Text ::: Named Entity Recognition
We use the named entity recognition module after part-of-speech tagging  This module labels each part of the sentence into different categories such as "PERSON", "LOCATION", or "ORGANIZATION"  We also used Freeling to label the named entities and the details of the algorithm are shown in the paper by Carreras et al BIBREF10  Aside from the three aforementioned categories, we also extracted "DATE/TIME" and "CURRENCY" values by looking at the part-of-speech tags: date/time words have a tag of "W", while currencies have "Zm" 
Framework for Processing Portuguese Text ::: Dependency Parsing
Dependency parsing involves tagging a word based on different features to indicate if it is dependent on another word  The Freeling library also has dependency parsing models for Portuguese  Since we wanted to build a SRL (Semantic Role Labeling) module on top of the dependency parser and the current released version of Freeling does not have an SRL module for Portuguese, we trained a different Portuguese dependency parsing model that was compatible (in terms of used tags) with the available annotated 
We used the dataset from System-T BIBREF11, which has SRL tags, as well as, the other preceding tags  It was necessary to do some pre-processing and tag mapping in order to make it viable to train a Portuguese model 
We made 589 tag conversions over 14 different categories  The breakdown of tag conversions per category is given by table TABREF7  These rules can be further seen in the corresponding Github repository BIBREF12  The modified training and development datasets are also available on another Github repositorypage BIBREF13 for further research and comparison purposes 
Framework for Processing Portuguese Text ::: Semantic Role Labeling
We execute the SRL (Semantic Role Labeling) module after obtaining the word dependencies  This module aims at giving a semantic role to a syntactic constituent of a sentence  The semantic role is always in relation to a verb and these roles could either be an actor, object, time, or location, which are then tagged as A0, A1, AM-TMP, AM-LOC, respectively  We trained a model for this module on top of the dependency parser described in the previous subsection using the modified dataset from System-T  The module also needs co-reference resolution to work and, to achieve this, we adapted the Spanish co-reference modules for Portuguese, changing the words that are equivalent (in total, we changed 253 words) 
Framework for Processing Portuguese Text ::: SVO Extraction
From the yield of the SRL (Semantic Role Labeling) module, our framework can distinguish actors, actions, places, time and objects from the sentences  Utilizing this extracted data, we can distinguish subject-verb-object (SVO) triples using the SVO extraction algorithm BIBREF14  The algorithm finds, for each sentence, the verb and the tuples related to that verb using Semantic Role Labeling (subsection SECREF8)  After the extraction of SVOs from texts, they are inserted into a specific event ontology (see section SECREF12 for the creation of a knowledge base) 
Framework for Processing Portuguese Text ::: Lexicon Matching
The sole purpose of this module is to find important terms and/or concepts from the extracted text  To do this, we use Euvovoc BIBREF6, a multilingual thesaurus that was developed for and by the European Union  The Euvovoc has 21 fields and each field is further divided into a variable number of micro-thesauri  Here, due to the application of this work in the Agatha project (mentioned in Section SECREF1), we use the terms of the criminal law BIBREF15 micro-thesaurus  Further, we classified each term of the criminal law micro-thesaurus into four categories namely, actor, event, place and object  The term classification can be seen in Table TABREF11 
After the classification of these terms, we implemented two different matching algorithms between the extracted words and the criminal law micro-thesaurus terms  The first is an exact string match wherein lowercase equivalents of the words of the input sentences are matched exactly with lower case equivalents of the predefined terms  The second matching algorithm uses Levenshtein distance BIBREF16, allowing some near-matches that are close enough to the target term 
Framework for Processing Portuguese Text ::: Linked Data: Ontology, Thesaurus and Terminology
In the computer science field, an ontology can be defined has:
a formal specification of a conceptualization;
shared vocabulary and taxonomy which models a domain with the definition of objects and/or concepts and their properties and relations;
the representation of entities, ideas, and events, along with their properties and relations, according to a system of categories 
A knowledge base is one kind of repository typically used to store answers to questions or solutions to problems enabling rapid search, retrieval, and reuse, either by an ontology or directly by those requesting support  For a more detailed description of ontologies and knowledge bases, see for instance BIBREF17 
For designing the ontology adequate for our goals, we referred to the Simple Event Model (SEM) BIBREF18 as a baseline model  A pictorial representation of this ontology is given in Figure FIGREF16
Considering the criminal law domain case study, we made a few changes to the original SEM ontology  The entities of the model are:
Actor: person involved with event
Place: location of the event
Time: time of the event
Object: that actor act upon
Organization: organization involved with event
Currency: money involved with event
The proposed ontology was designed in such a manner that it can incorporate information extracted from multiple documents  In this context, suppose that the source of documents is aare a legal police department, where each document isare under the hood of a particular case/crime; furthermoreFurther, a single case can have documents from multiple languages  Now, considering case 1 has 100 documents and case 2 has 100 documents then there is not only a connection among the documents of a single case but rather among all the cases with all the combined 200 documents  In this way, the proposed method is able to produce a detailed and well-connected knowledge base 
Figure FIGREF23 shows the proposed ontology, which, in our evaluation procedure, was populated with 3121 events entries from 51 documents 
Protege BIBREF19 tool was used for creating the ontology and GraphDB BIBREF20 for populating & querying the data  GraphDB is an enterprise-ready Semantic Graph Database, compliant with W3C Standards  Semantic Graph Databases (also called RDF triplestores) provide the core infrastructure for solutions where modeling agility, data integration, relationship exploration, and cross-enterprise data publishing and consumption are important  GraphDB has a SPARQL (SQL-like query language) interface for RDF graph databases with the following types:
SELECT: returns tabular results
CONSTRUCT: creates a new RDF graph based on query results
ASK: returns "YES", if the query has a solution, otherwise "NO"
DESCRIBE: returns RDF data about a resource  This is useful when the RDF data structure in the data source is not known
INSERT: inserts triples into a graph
DELETE: deletes triples from a graph
Furthermore, we have extended the ontology BIBREF21 to connect the extracted terms with Eurovoc criminal law (discussed in subsection SECREF10) and IATE BIBREF7 terms  IATE (Interactive Terminology for Europe) is the EU's general terminology database and its aim is to provide a web-based infrastructure for all EU terminology resources, enhancing the availability and standardization of the information  The extended ontology has a number of sub-classes for Actor, Event, Object and Place classes detailed in Table TABREF30 
Discussion
We have defined a major design principle for our architecture: it should be modular and not rely on human made rules allowing, as much as possible, its independence from a specific language  In this way, its potential application to another language would be easier, simply by changing the modules or the models of specific modules  In fact, we have explored the use of already existing modules and adopted and integrated several of these tools into our pipeline 
It is important to point out that, as far as we know, there is no integrated architecture supporting the full processing pipeline for the Portuguese language  We evaluated several systems like Rembrandt BIBREF22 or LinguaKit: the former only has the initial steps of our proposal (until NER) and the later performed worse than our system 
This framework, developed within the context of the Agatha project (described in Section SECREF1) has the full processing pipeline for Portuguese texts: it receives sentences as input and outputs ontological information: a) first performs all NLP typical tasks until semantic role labelling; b) then, it extracts subject-verb-object triples; c) and, then, it performs ontology matching procedures  As a final result, the obtained output is inserted into a specialized ontology 
We are aware that each of the architecture modules can, and should, be improved but our main goal was the creation of a full working text processing pipeline for the Portuguese language 
Conclusions and Future Work
Besides the end–to–end NLP pipeline for the Portuguese language, the other main contributions of this work can be summarize as follows:
Development of an ontology for the criminal law domain;
Alignment of the Eurovoc thesaurus and IATE terminology with the ontology created;
Representation of the extracted events from texts in the linked knowledge base defined 
The obtained results support our claim that the proposed system can be used as a base tool for information extraction for the Portuguese language  Being composed by several modules, each of them with a high level of complexity, it is certain that our approach can be improved and an overall better performance can be achieved 
As future work we intend, not only to continue improving the individual modules, but also plan to extend this work to the:
automatic creation of event timelines;
incorporation in the knowledge base of information obtained from videos or pictures describing scenes relevant to criminal investigations 
Acknowledgments
The authors would like to thank COMPETE 2020, PORTUGAL 2020 Program, the European Union, and ALENTEJO 2020 for supporting this research as part of Agatha Project SI & IDT number 18022 (Intelligent analysis system of open of sources information for surveillance/crime control)  The authors would also like to thank LISP - Laboratory of Informatics, Systems and Parallelism 
Context 3: Introduction
Data annotation is a major bottleneck for the application of supervised learning approaches to many problems  As a result, unsupervised methods that learn directly from unlabeled data are increasingly important  For tasks related to unsupervised syntactic analysis, discrete generative models have dominated in recent years – for example, for both part-of-speech (POS) induction BIBREF0 , BIBREF1 and unsupervised dependency parsing BIBREF2 , BIBREF3 , BIBREF4   While similar models have had success on a range of unsupervised tasks, they have mostly ignored the apparent utility of continuous word representations evident from supervised NLP applications BIBREF5 , BIBREF6   In this work, we focus on leveraging and explicitly representing continuous word embeddings within unsupervised models of syntactic structure 
Pre-trained word embeddings from massive unlabeled corpora offer a compact way of injecting a prior notion of word similarity into models that would otherwise treat words as discrete, isolated categories  However, the specific properties of language captured by any particular embedding scheme can be difficult to control, and, further, may not be ideally suited to the task at hand  For example, pre-trained skip-gram embeddings BIBREF7 with small context window size are found to capture the syntactic properties of language well BIBREF8 , BIBREF9   However, if our goal is to separate syntactic categories, this embedding space is not ideal – POS categories correspond to overlapping interspersed regions in the embedding space, evident in Figure SECREF4  
In our approach, we propose to learn a new latent embedding space as a projection of pre-trained embeddings (depicted in Figure SECREF5 ), while jointly learning latent syntactic structure – for example, POS categories or syntactic dependencies  To this end, we introduce a new generative model (shown in Figure FIGREF6 ) that first generates a latent syntactic representation (e g  a dependency parse) from a discrete structured prior (which we also call the “syntax model”), then, conditioned on this representation, generates a sequence of latent embedding random variables corresponding to each word, and finally produces the observed (pre-trained) word embeddings by projecting these latent vectors through a parameterized non-linear function  The latent embeddings can be jointly learned with the structured syntax model in a completely unsupervised fashion 
By choosing an invertible neural network as our non-linear projector, and then parameterizing our model in terms of the projection's inverse, we are able to derive tractable exact inference and marginal likelihood computation procedures so long as inference is tractable in the underlying syntax model  In sec:learn-with-inv we show that this derivation corresponds to an alternate view of our approach whereby we jointly learn a mapping of observed word embeddings to a new embedding space that is more suitable for the syntax model, but include an additional Jacobian regularization term to prevent information loss 
Recent work has sought to take advantage of word embeddings in unsupervised generative models with alternate approaches BIBREF9 , BIBREF10 , BIBREF11 , BIBREF12   BIBREF9 build an HMM with Gaussian emissions on observed word embeddings, but they do not attempt to learn new embeddings  BIBREF10 , BIBREF11 , and BIBREF12 extend HMM or dependency model with valence (DMV) BIBREF2 with multinomials that use word (or tag) embeddings in their parameterization  However, they do not represent the embeddings as latent variables 
In experiments, we instantiate our approach using both a Markov-structured syntax model and a tree-structured syntax model – specifically, the DMV  We evaluate on two tasks: part-of-speech (POS) induction and unsupervised dependency parsing without gold POS tags  Experimental results on the Penn Treebank BIBREF13 demonstrate that our approach improves the basic HMM and DMV by a large margin, leading to the state-of-the-art results on POS induction, and state-of-the-art results on unsupervised dependency parsing in the difficult training scenario where neither gold POS annotation nor punctuation-based constraints are available 
Model
As an illustrative example, we first present a baseline model for Markov syntactic structure (POS induction) that treats a sequence of pre-trained word embeddings as observations  Then, we propose our novel approach, again using Markov structure, that introduces latent word embedding variables and a neural projector  Lastly, we extend our approach to more general syntactic structures 
Example: Gaussian HMM
We start by describing the Gaussian hidden Markov model introduced by BIBREF9 , which is a locally normalized model with multinomial transitions and Gaussian emissions  Given a sentence of length INLINEFORM0 , we denote the latent POS tags as INLINEFORM1 , observed (pre-trained) word embeddings as INLINEFORM2 , transition parameters as INLINEFORM3 , and Gaussian emission parameters as INLINEFORM4   The joint distribution of data and latent variables factors as:
DISPLAYFORM0
where INLINEFORM0 is the multinomial transition probability and INLINEFORM1 is the multivariate Gaussian emission probability 
While the observed word embeddings do inform this model with a notion of word similarity – lacking in the basic multinomial HMM – the Gaussian emissions may not be sufficiently flexible to separate some syntactic categories in the complex pre-trained embedding space – for example the skip-gram embedding space as visualized in Figure SECREF4 where different POS categories overlap  Next we introduce a new approach that adds flexibility to the emission distribution by incorporating new latent embedding variables 
Markov Structure with Neural Projector
To flexibly model observed embeddings and yield a new representation space that is more suitable for the syntax model, we propose to cascade a neural network as a projection function, deterministically transforming the simple space defined by the Gaussian HMM to the observed embedding space  We denote the latent embedding of the INLINEFORM0 word in a sentence as INLINEFORM1 , and the neural projection function as INLINEFORM2 , parameterized by INLINEFORM3   In the case of sequential Markov structure, our new model corresponds to the following generative process:
For each time step INLINEFORM0 ,
[noitemsep, leftmargin=*]
Draw the latent state INLINEFORM0
Draw the latent embedding INLINEFORM0
Deterministically produce embedding
INLINEFORM0
The graphical model is depicted in Figure FIGREF6   The deterministic projection can also be viewed as sampling each observation from a point mass at INLINEFORM0   The joint distribution of our model is: DISPLAYFORM0
where INLINEFORM0 is a conditional Gaussian distribution, and INLINEFORM1 is the Dirac delta function centered at INLINEFORM2 : DISPLAYFORM0
General Structure with Neural Projector
Our approach can be applied to a broad family of structured syntax models  We denote latent embedding variables as INLINEFORM0 , discrete latent variables in the syntax model as INLINEFORM1 ( INLINEFORM2 ), where INLINEFORM3 are conditioned to generate INLINEFORM4   The joint probability of our model factors as:
DISPLAYFORM0
where INLINEFORM0 represents the probability of the syntax model, and can encode any syntactic structure – though, its factorization structure will determine whether inference is tractable in our full model  As shown in Figure FIGREF6 , we focus on two syntax models for syntactic analysis in this paper  The first is Markov-structured, which we use for POS induction, and the second is DMV-structured, which we use to learn dependency parses without supervision 
The marginal data likelihood of our model is: DISPLAYFORM0
While the discrete variables INLINEFORM0 can be marginalized out with dynamic program in many cases, it is generally intractable to marginalize out the latent continuous variables, INLINEFORM1 , for an arbitrary projection INLINEFORM2 in Eq  ( EQREF17 ), which means inference and learning may be difficult  In sec:opt, we address this issue by constraining INLINEFORM3 to be invertible, and show that this constraint enables tractable exact inference and marginal likelihood computation 
Learning & Inference
In this section, we introduce an invertibility condition for our neural projector to tackle the optimization challenge  Specifically, we constrain our neural projector with two requirements: (1) INLINEFORM0 and (2) INLINEFORM1 exists  Invertible transformations have been explored before in independent components analysis BIBREF14 , gaussianization BIBREF15 , and deep density models BIBREF16 , BIBREF17 , BIBREF18 , for unstructured data  Here, we generalize this style of approach to structured learning, and augment it with discrete latent variables ( INLINEFORM2 )  Under the invertibility condition, we derive a learning algorithm and give another view of our approach revealed by the objective function  Then, we present the architecture of a neural projector we use in experiments: a volume-preserving invertible neural network proposed by BIBREF16 for independent components estimation 
Learning with Invertibility
For ease of exposition, we explain the learning algorithm in terms of Markov structure without loss of generality  As shown in Eq  ( EQREF17 ), the optimization challenge in our approach comes from the intractability of the marginalized emission factor INLINEFORM0   If we can marginalize out INLINEFORM1 and compute INLINEFORM2 , then the posterior and marginal likelihood of our Markov-structured model can be computed with the forward-backward algorithm  We can apply Eq  ( EQREF14 ) and obtain : INLINEFORM3
By using the change of variable rule to the integration, which allows the integration variable INLINEFORM0 to be replaced by INLINEFORM1 , the marginal emission factor can be computed in closed-form when the invertibility condition is satisfied: DISPLAYFORM0
where INLINEFORM0 is a conditional Gaussian distribution, INLINEFORM1 is the Jacobian matrix of function INLINEFORM2 at INLINEFORM3 , and INLINEFORM4 represents the absolute value of its determinant  This Jacobian term is nonzero and differentiable if and only if INLINEFORM5 exists 
Eq  ( EQREF19 ) shows that we can directly calculate the marginal emission distribution INLINEFORM0   Denote the marginal data likelihood of Gaussian HMM as INLINEFORM1 , then the log marginal data likelihood of our model can be directly written as: DISPLAYFORM0
where INLINEFORM0 represents the new sequence of embeddings after applying INLINEFORM1 to each INLINEFORM2   Eq  ( EQREF20 ) shows that the training objective of our model is simply the Gaussian HMM log likelihood with an additional Jacobian regularization term  From this view, our approach can be seen as equivalent to reversely projecting the data through INLINEFORM3 to another manifold INLINEFORM4 that is directly modeled by the Gaussian HMM, with a regularization term  Intuitively, we optimize the reverse projection INLINEFORM5 to modify the INLINEFORM6 space, making it more appropriate for the syntax model  The Jacobian regularization term accounts for the volume expansion or contraction behavior of the projection  Maximizing it can be thought of as preventing information loss  In the extreme case, the Jacobian determinant is equal to zero, which means the projection is non-invertible and thus information is being lost through the projection  Such “information preserving” regularization is crucial during optimization, otherwise the trivial solution of always projecting data to the same single point to maximize likelihood is viable 
More generally, for an arbitrary syntax model the data likelihood of our approach is: DISPLAYFORM0
If the syntax model itself allows for tractable inference and marginal likelihood computation, the same dynamic program can be used to marginalize out INLINEFORM0   Therefore, our joint model inherits the tractability of the underlying syntax model 
Invertible Volume-Preserving Neural Net
For the projection we can use an arbitrary invertible function, and given the representational power of neural networks they seem a natural choice  However, calculating the inverse and Jacobian of an arbitrary neural network can be difficult, as it requires that all component functions be invertible and also requires storage of large Jacobian matrices, which is memory intensive  To address this issue, several recent papers propose specially designed invertible networks that are easily trainable yet still powerful BIBREF16 , BIBREF17 , BIBREF19   Inspired by these works, we use the invertible transformation proposed by BIBREF16 , which consists of a series of “coupling layers”  This architecture is specially designed to guarantee a unit Jacobian determinant (and thus the invertibility property) 
From Eq  ( EQREF22 ) we know that only INLINEFORM0 is required for accomplishing learning and inference; we never need to explicitly construct INLINEFORM1   Thus, we directly define the architecture of INLINEFORM2   As shown in Figure FIGREF24 , the nonlinear transformation from the observed embedding INLINEFORM3 to INLINEFORM4 represents the first coupling layer  The input in this layer is partitioned into left and right halves of dimensions, INLINEFORM5 and INLINEFORM6 , respectively  A single coupling layer is defined as: DISPLAYFORM0
where INLINEFORM0 is the coupling function and can be any nonlinear form  This transformation satisfies INLINEFORM1 , and BIBREF16 show that its Jacobian matrix is triangular with all ones on the main diagonal  Thus the Jacobian determinant is always equal to one (i e  volume-preserving) and the invertibility condition is naturally satisfied 
To be sufficiently expressive, we compose multiple coupling layers as suggested in BIBREF16   Specifically, we exchange the role of left and right half vectors at each layer as shown in Figure FIGREF24   For instance, from INLINEFORM0 to INLINEFORM1 the left subset INLINEFORM2 is unchanged, while from INLINEFORM3 to INLINEFORM4 the right subset INLINEFORM5 remains the same  Also note that composing multiple coupling layers does not change the volume-preserving and invertibility properties  Such a sequence of invertible transformations from the data space INLINEFORM6 to INLINEFORM7 is also called normalizing flow BIBREF20  
Experiments
In this section, we first describe our datasets and experimental setup  We then instantiate our approach with Markov and DMV-structured syntax models, and report results on POS tagging and dependency grammar induction respectively  Lastly, we analyze the learned latent embeddings 
Data
For both POS tagging and dependency parsing, we run experiments on the Wall Street Journal (WSJ) portion of the Penn Treebank  To create the observed data embeddings, we train skip-gram word embeddings BIBREF7 that are found to capture syntactic properties well when trained with small context window BIBREF8 , BIBREF9   Following BIBREF9 , the dimensionality INLINEFORM0 is set to 100, and the training context window size is set to 1 to encode more syntactic information  The skip-gram embeddings are trained on the one billion word language modeling benchmark dataset BIBREF21 in addition to the WSJ corpus 
General Experimental Setup
For the neural projector, we employ rectified networks as coupling function INLINEFORM0 following BIBREF16   We use a rectified network with an input layer, one hidden layer, and linear output units, the number of hidden units is set to the same as the number of input units  The number of coupling layers are varied as 4, 8, 16 for both tasks

ground_truth: No

No

prompt_front: You are given a scientific article and a question. Answer the question as concisely as you can, using a single phrase or sentence if possible. If the question cannot be answered based on the information in the article, write "unanswerable". If the question is a yes/no question, answer "yes", "no", or "unanswerable". Do not provide any explanation.

Please answer the questions based on the text provided below. What is the invertibility condition?
Context 3:  We optimize marginal data likelihood directly using Adam BIBREF22   For both tasks in the fully unsupervised setting, we do not tune the hyper-parameters using supervised data 
Unsupervised POS tagging
For unsupervised POS tagging, we use a Markov-structured syntax model in our approach, which is a popular structure for unsupervised tagging tasks BIBREF9 , BIBREF10  
Following existing literature, we train and test on the entire WSJ corpus (49208 sentences, 1M tokens)  We use 45 tag clusters, the number of POS tags that appear in WSJ corpus  We train the discrete HMM and the Gaussian HMM BIBREF9 as baselines  For the Gaussian HMM, mean vectors of Gaussian emissions are initialized with the empirical mean of all word vectors with an additive noise  We assume diagonal covariance matrix for INLINEFORM0 and initialize it with the empirical variance of the word vectors  Following BIBREF9 , the covariance matrix is fixed during training  The multinomial probabilities are initialized as INLINEFORM1 , where INLINEFORM2   For our approach, we initialize the syntax model and Gaussian parameters with the pre-trained Gaussian HMM  The weights of layers in the rectified network are initialized from a uniform distribution with mean zero and a standard deviation of INLINEFORM3 , where INLINEFORM4 is the input dimension  We evaluate the performance of POS tagging with both Many-to-One (M-1) accuracy BIBREF23 and V-Measure (VM) BIBREF24   Given a model we found that the tagging performance is well-correlated with the training data likelihood, thus we use training data likelihood as a unsupervised criterion to select the trained model over 10 random restarts after training 50 epochs  We repeat this process 5 times and report the mean and standard deviation of performance 
We compare our approach with basic HMM, Gaussian HMM, and several state-of-the-art systems, including sophisticated HMM variants and clustering techniques with hand-engineered features  The results are presented in Table TABREF32   Through the introduced latent embeddings and additional neural projection, our approach improves over the Gaussian HMM by 5 4 points in M-1 and 5 6 points in VM  Neural HMM (NHMM) BIBREF10 is a baseline that also learns word representation jointly  Both their basic model and extended Conv version does not outperform the Gaussian HMM  Their best model incorporates another LSTM to model long distance dependency and breaks the Markov assumption, yet our approach still achieves substantial improvement over it without considering more context information  Moreover, our method outperforms the best published result that benefits from hand-engineered features BIBREF27 by 2 0 points on VM 
We found that most tagging errors happen in noun subcategories  Therefore, we do the one-to-one mapping between gold POS tags and induced clusters and plot the normalized confusion matrix of noun subcategories in Figure FIGREF35   The Gaussian HMM fails to identify “NN” and “NNS” correctly for most cases, and it often recognizes “NNPS” as “NNP”  In contrast, our approach corrects these errors well 
Unsupervised Dependency Parsing without gold POS tags
For the task of unsupervised dependency parse induction, we employ the Dependency Model with Valence (DMV) BIBREF2 as the syntax model in our approach  DMV is a generative model that defines a probability distribution over dependency parse trees and syntactic categories, generating tokens and dependencies in a head-outward fashion  While, traditionally, DMV is trained using gold POS tags as observed syntactic categories, in our approach, we treat each tag as a latent variable, as described in sec:general-neural 
Most existing approaches to this task are not fully unsupervised since they rely on gold POS tags following the original experimental setup for DMV  This is partially because automatically parsing from words is difficult even when using unsupervised syntactic categories BIBREF29   However, inducing dependencies from words alone represents a more realistic experimental condition since gold POS tags are often unavailable in practice  Previous work that has trained from words alone often requires additional linguistic constraints (like sentence internal boundaries) BIBREF29 , BIBREF30 , BIBREF31 , BIBREF32 , acoustic cues BIBREF33 , additional training data BIBREF4 , or annotated data from related languages BIBREF34   Our approach is naturally designed to train on word embeddings directly, thus we attempt to induce dependencies without using gold POS tags or other extra linguistic information 
Like previous work we use sections 02-21 of WSJ corpus as training data and evaluate on section 23, we remove punctuations and train the models on sentences of length INLINEFORM0 , “head-percolation” rules BIBREF39 are applied to obtain gold dependencies for evaluation  We train basic DMV, extended DMV (E-DMV) BIBREF35 and Gaussian DMV (which treats POS tag as unknown latent variables and generates observed word embeddings directly conditioned on them following Gaussian distribution) as baselines  Basic DMV and E-DMV are trained with Viterbi EM BIBREF40 on unsupervised POS tags induced from our Markov-structured model described in sec:pos  Multinomial parameters of the syntax model in both Gaussian DMV and our model are initialized with the pre-trained DMV baseline  Other parameters are initialized in the same way as in the POS tagging experiment  The directed dependency accuracy (DDA) is used for evaluation and we report accuracy on sentences of length INLINEFORM1 and all lengths  We train the parser until training data likelihood converges, and report the mean and standard deviation over 20 random restarts 
Our model directly observes word embeddings and does not require gold POS tags during training  Thus, results from related work trained on gold tags are not directly comparable  However, to measure how these systems might perform without gold tags, we run three recent state-of-the-art systems in our experimental setting: UR-A E-DMV BIBREF36 , Neural E-DMV BIBREF11 , and CRF Autoencoder (CRFAE) BIBREF37   We use unsupervised POS tags (induced from our Markov-structured model) in place of gold tags  We also train basic DMV on gold tags and include several state-of-the-art results on gold tags as reference points 
As shown in Table TABREF39 , our approach is able to improve over the Gaussian DMV by 4 8 points on length INLINEFORM0 and 4 8 points on all lengths, which suggests the additional latent embedding layer and neural projector are helpful  The proposed approach yields, to the best of our knowledge, state-of-the-art performance without gold POS annotation and without sentence-internal boundary information  DMV, UR-A E-DMV, Neural E-DMV, and CRFAE suffer a large decrease in performance when trained on unsupervised tags – an effect also seen in previous work BIBREF29 , BIBREF34   Since our approach induces latent POS tags jointly with dependency trees, it may be able to learn POS clusters that are more amenable to grammar induction than the unsupervised tags  We observe that CRFAE underperforms its gold-tag counterpart substantially  This may largely be a result of the model's reliance on prior linguistic rules that become unavailable when gold POS tag types are unknown  Many extensions to DMV can be considered orthogonal to our approach – they essentially focus on improving the syntax model  It is possible that incorporating these more sophisticated syntax models into our approach may lead to further improvements 
Sensitivity Analysis
In the above experiments we initialize the structured syntax components with the pre-trained Gaussian or discrete baseline, which is shown as a useful technique to help train our deep models  We further study the results with fully random initialization  In the POS tagging experiment, we report the results in Table TABREF48   While the performance with 4 layers is comparable to the pre-trained Gaussian initialization, deeper projections (8 or 16 layers) result in a dramatic drop in performance  This suggests that the structured syntax model with very deep projections is difficult to train from scratch, and a simpler projection might be a good compromise in the random initialization setting 
Different from the Markov prior in POS tagging experiments, our parsing model seems to be quite sensitive to the initialization  For example, directed accuracy of our approach on sentences of length INLINEFORM0 is below 40 0 with random initialization  This is consistent with previous work that has noted the importance of careful initialization for DMV-based models such as the commonly used harmonic initializer BIBREF2   However, it is not straightforward to apply the harmonic initializer for DMV directly in our model without using some kind of pre-training since we do not observe gold POS 
We investigate the effect of the choice of pre-trained embedding on performance while using our approach  To this end, we additionally include results using fastText embeddings BIBREF41 – which, in contrast with skip-gram embeddings, include character-level information  We set the context windows size to 1 and the dimension size to 100 as in the skip-gram training, while keeping other parameters set to their defaults  These results are summarized in Table TABREF50 and Table TABREF51   While fastText embeddings lead to reduced performance with our model, our approach still yields an improvement over the Gaussian baseline with the new observed embeddings space 
Qualitative Analysis of Embeddings
We perform qualitative analysis to understand how the latent embeddings help induce syntactic structures  First we filter out low-frequency words and punctuations in WSJ, and visualize the rest words (10k) with t-SNE BIBREF42 under different embeddings  We assign each word with its most likely gold POS tags in WSJ and color them according to the gold POS tags 
For our Markov-structured model, we have displayed the embedding space in Figure SECREF5 , where the gold POS clusters are well-formed  Further, we present five example target words and their five nearest neighbors in terms of cosine similarity  As shown in Table TABREF53 , the skip-gram embedding captures both semantic and syntactic aspects to some degree, yet our embeddings are able to focus especially on the syntactic aspects of words, in an unsupervised fashion without using any extra morphological information 
In Figure FIGREF54 we depict the learned latent embeddings with the DMV-structured syntax model  Unlike the Markov structure, the DMV structure maps a large subset of singular and plural nouns to the same overlapping region  However, two clusters of singular and plural nouns are actually separated  We inspect the two clusters and the overlapping region in Figure FIGREF54 , it turns out that the nouns in the separated clusters are words that can appear as subjects and, therefore, for which verb agreement is important to model  In contrast, the nouns in the overlapping region are typically objects  This demonstrates that the latent embeddings are focusing on aspects of language that are specifically important for modeling dependency without ever having seen examples of dependency parses  Some previous work has deliberately created embeddings to capture different notions of similarity BIBREF43 , BIBREF44 , while they use extra morphology or dependency annotations to guide the embedding learning, our approach provides a potential alternative to create new embeddings that are guided by structured syntax model, only using unlabeled text corpora 
Related Work
Our approach is related to flow-based generative models, which are first described in NICE BIBREF16 and have recently received more attention BIBREF17 , BIBREF19 , BIBREF18   This relevant work mostly adopts simple (e g  Gaussian) and fixed priors and does not attempt to learn interpretable latent structures  Another related generative model class is variational auto-encoders (VAEs) BIBREF45 that optimize a lower bound on the marginal data likelihood, and can be extended to learn latent structures BIBREF46 , BIBREF47   Against the flow-based models, VAEs remove the invertibility constraint but sacrifice the merits of exact inference and exact log likelihood computation, which potentially results in optimization challenges BIBREF48   Our approach can also be viewed in connection with generative adversarial networks (GANs) BIBREF49 that is a likelihood-free framework to learn implicit generative models  However, it is non-trivial for a gradient-based method like GANs to propagate gradients through discrete structures 
Conclusion
In this work, we define a novel generative approach to leverage continuous word representations for unsupervised learning of syntactic structure  Experiments on both POS induction and unsupervised dependency parsing tasks demonstrate the effectiveness of our proposed approach  Future work might explore more sophisticated invertible projections, or recurrent projections that jointly transform the entire input sequence 

ground_truth: The neural projector must be invertible.

we constrain our neural projector with two requirements: (1) INLINEFORM0 and (2) INLINEFORM1 exists