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+# MACHINE COMPREHENSION USING MATCH-LSTM AND ANSWER POINTER
+
+# Jing Jiang
+
+Shuohang Wang School of Information Systems Singapore Management University shwang.2014@phdis.smu.edu.sg
+
+School of Information Systems Singapore Management University jingjiang@smu.edu.sg
+
+# ABSTRACT
+
+Machine comprehension of text is an important problem in natural language processing. A recently released dataset, the Stanford Question Answering Dataset (SQuAD), offers a large number of real questions and their answers created by humans through crowdsourcing. SQuAD provides a challenging testbed for evaluating machine comprehension algorithms, partly because compared with previous datasets, in SQuAD the answers do not come from a small set of candidate answers and they have variable lengths. We propose an end-to-end neural architecture for the task. The architecture is based on match-LSTM, a model we proposed previously for textual entailment, and Pointer Net, a sequence-to-sequence model proposed by Vinyals et al. (2015) to constrain the output tokens to be from the input sequences. We propose two ways of using Pointer Net for our tasks. Our experiments show that both of our two models substantially outperform the best results obtained by Rajpurkar et al. (2016) using logistic regression and manually crafted features. Besides, our boundary model also achieves the best performance on the MSMARCO dataset (Nguyen et al., 2016).
+
+# 1 INTRODUCTION
+
+Machine comprehension of text is one of the ultimate goals of natural language processing. While the ability of a machine to understand text can be assessed in many different ways, in recent years, several benchmark datasets have been created to focus on answering questions as a way to evaluate machine comprehension (Richardson et al., 2013; Hermann et al., 2015; Hill et al., 2016; Weston et al., 2016; Rajpurkar et al., 2016; Nguyen et al., 2016). In this setup, typically the machine is first presented with a piece of text such as a news article or a story. The machine is then expected to answer one or multiple questions related to the text.
+
+In most of the benchmark datasets, a question can be treated as a multiple choice question, whose correct answer is to be chosen from a set of provided candidate answers (Richardson et al., 2013; Hill et al., 2016). Presumably, questions with more given candidate answers are more challenging. The Stanford Question Answering Dataset (SQuAD) introduced recently by Rajpurkar et al. (2016) contains such more challenging questions whose correct answers can be any sequence of tokens from the given text. Moreover, unlike some other datasets whose questions and answers were created automatically in Cloze style (Hermann et al., 2015; Hill et al., 2016), the questions and answers in SQuAD were created by humans through crowdsourcing, which makes the dataset more realistic. Another real dataset, the Human-Generated MAchine Reading COmprehension dataset (MSMARCO) (Nguyen et al., 2016), provided a query together with several related documents collected from Bing Index. The answer to the query is generated by human and the answer words can not only come from the given text.
+
+Given these advantages of the SQuAD and MSMARCO datasets, in this paper, we focus on these new datasets to study machine comprehension of text. A sample piece of text and three of its associated questions from SQuAD are shown in Table 1. Traditional solutions to this kind of question answering tasks rely on NLP pipelines that involve multiple steps of linguistic analyses and feature engineering, including syntactic parsing, named entity recognition, question classification, semantic parsing, etc. Recently, with the advances of applying neural network models in NLP, there has been much interest in building end-to-end neural architectures for various NLP tasks, including several pieces of work on machine comprehension (Hermann et al., 2015; Hill et al., 2016; Yin et al., 2016; Kadlec et al., 2016; Cui et al., 2016). However, given the properties of previous machine comprehension datasets, existing end-to-end neural architectures for the task either rely on the candidate answers (Hill et al., 2016; Yin et al., 2016) or assume that the answer is a single token (Hermann et al., 2015; Kadlec et al., 2016; Cui et al., 2016), which make these methods unsuitable for the SQuAD/MSMARCO dataset. In this paper, we propose a new end-to-end neural architecture to address the machine comprehension problem as defined in the SQuAD/MSMARCO dataset. And for the MSMARCO dataset, we will only make use of the words in the given text to generate the answer.
+
+Table 1: A paragraph from Wikipedia and three associated questions together with their answers, taken from the $\mathrm { S Q u A D }$ dataset. The tokens in bold in the paragraph are our predicted answers while the texts next to the questions are the ground truth answers.   
+
+<table><tr><td colspan="2">In 1870,Tesla moved to Karlovac,to attend school at the Higher Real Gymnasium,where he was profoundly influenced by a math teacher Martin Sekulic. The classes were held in German,as it was a school within the Austro-Hungarian Military Frontier.Tesla was able to perform integral calculus in his head,which prompted his teachers to believe that he was cheating.He finished a four-year term in three</td></tr><tr><td>years,graduating in 1873. 1.In what language were the classes given? 2.Who was Tesla&#x27;s main influence in Karlovac? 3.Why did Tesla go to Karlovac?</td><td>German Martin Sekulic attend school at the Higher Real Gymnasium</td></tr></table>
+
+Specifically, observing that in the SQuAD/MSMARCO dataset many questions could be entailed from some sentences in the original text, we adopt a match-LSTM model that we developed earlier for textual entailment (Wang & Jiang, 2016) as one layer of our model. We build a bi-directional match-LSTM on the given passage with attentions on the question for each word so that each position in the paragraph will have a hidden representation reflecting its relation to the question. Then we further adopt the Pointer Net (Ptr-Net) model developed by Vinyals et al. (2015) to select the words in these positions based on the hidden representations built by match-LSTM as an answer. We propose two ways to apply the Ptr-Net model for our task: a sequence model which selects the answer word by word, and a boundary model which only selects the start and end points of the answer span. Experiments on the SQuAD dataset show that our two models both outperform the best performance reported by Rajpurkar et al. (2016). Moreover, using an ensemble of several of our models, we can achieve very competitive performance on SQuAD. For the MSMARCO dataset, a real query based problem, our boundary model outperforms our sequence model with a big margin. It also outperforms the golden passage baseline.
+
+Our contributions can be summarized as follows: (1) We propose two new end-to-end neural network models for machine comprehension, which combine match-LSTM and $\mathrm { P t r }$ -Net to handle the special properties of the SQuAD dataset. To the best of our knowledge, we are the first to propose the boundary model which is more suitable to the SQuAD/MSMARCO tasks. And we are the first to integrate the attention-based word pair matching into machine comprehension tasks. (2) We have achieved the performance of an exact match score of $7 1 . 3 \%$ and an F1 score of $8 0 . 8 \%$ on the unseen SQuAD test dataset, which is much better than the feature-engineered solution (Rajpurkar et al., 2016). Our performance is also close to the state of the art on SQuAD, which is $7 4 . 8 \%$ in terms of exact match and $8 2 . 2 \%$ in terms of F1 collected from the SQuAD Leaderboard 1. Besides, our boundary model achieves the state-of-art performance on the MSMARCO dataset with BLUE$1 / 2 / 3 / 4 4 0 . 7 / 3 3 . 9 / 3 0 . 6 / 2 8 . 7$ and Rouge-L $3 7 . { \bar { 3 } } ^ { 2 }$ . (3) Our further visualization of the models reveals some useful insights of the attention mechanism for reasoning the questions. And we also show that the boundary model can overcome the early stop prediction problem in the sequence model. Besides, we also made our code available online 3.
+
+![](images/f0257a3f1eb62a4fe298cadd284177e42c85bb65ae55acc03d90347e8c89aee8.jpg)  
+Figure 1: An overview of our two models. Both models consist of an LSTM preprocessing layer, a match-LSTM layer and an Answer Pointer layer. For each match-LSTM in a particular direction, $\bar { h } _ { i } ^ { \mathrm { q } }$ , which is defined as $\mathbf { H } ^ { \mathrm { q } } \alpha _ { i } ^ { \mathsf { T } }$ , is computed using the $\alpha$ in the corresponding direction, as described in Eqn. (2)
+
+# 2 METHOD
+
+In this section, we first briefly review match-LSTM and Pointer Net. These two pieces of existing work lay the foundation of our method. We then present our end-to-end neural architecture for machine comprehension.
+
+# 2.1 MATCH-LSTM
+
+In a recent work on learning natural language inference, we proposed a match-LSTM model for predicting textual entailment (Wang & Jiang, 2016). In textual entailment, two sentences are given where one is a premise and the other is a hypothesis. To predict whether the premise entails the hypothesis, the match-LSTM model goes through the tokens of the hypothesis sequentially. At each position of the hypothesis, attention mechanism is used to obtain a weighted vector representation of the premise. This weighted premise is then to be combined with a vector representation of the current token of the hypothesis and fed into an LSTM, which we call the match-LSTM. The matchLSTM essentially sequentially aggregates the matching of the attention-weighted premise to each token of the hypothesis and uses the aggregated matching result to make a final prediction.
+
+# 2.2 POINTER NET
+
+Vinyals et al. (2015) proposed a Pointer Network (Ptr-Net) model to solve a special kind of problems where we want to generate an output sequence whose tokens must come from the input sequence. Instead of picking an output token from a fixed vocabulary, Ptr-Net uses attention mechanism as a pointer to select a position from the input sequence as an output symbol. The pointer mechanism has inspired some recent work on language processing (Gu et al., 2016; Kadlec et al., 2016). Here we adopt Ptr-Net in order to construct answers using tokens from the input text.
+
+# 2.3 OUR METHOD
+
+Formally, the problem we are trying to solve can be formulated as follows. We are given a piece of text, which we refer to as a passage, and a question related to the passage. The passage is represented by matrix $\mathbf { P } \in \mathbb { R } ^ { d \times P }$ , where $P$ is the length (number of tokens) of the passage and $d$ is the dimensionality of word embeddings. Similarly, the question is represented by matrix $\breve { \mathbf { Q } } \in \mathbb { R } ^ { d \times Q }$ where $Q$ is the length of the question. Our goal is to identify a subsequence from the passage as the answer to the question.
+
+As pointed out earlier, since the output tokens are from the input, we would like to adopt the Pointer Net for this problem. A straightforward way of applying Ptr-Net here is to treat an answer as a sequence of tokens from the input passage but ignore the fact that these tokens are consecutive in the original passage, because Ptr-Net does not make the consecutivity assumption. Specifically, we represent the answer as a sequence of integers $\mathbf { a } = ( a _ { 1 } , a _ { 2 } , . . . )$ , where each $a _ { i }$ is an integer between 1 and $P$ , indicating a certain position in the passage.
+
+Alternatively, if we want to ensure consecutivity, that is, if we want to ensure that we indeed select a subsequence from the passage as an answer, we can use the Ptr-Net to predict only the start and the end of an answer. In this case, the Ptr-Net only needs to select two tokens from the input passage, and all the tokens between these two tokens in the passage are treated as the answer. Specifically, we can represent the answer to be predicted as two integers $\mathbf { a } = ( a _ { \mathrm { s } } , a _ { \mathrm { e } } )$ , where $a _ { s }$ an $a _ { \mathrm { e } }$ are integers between 1 and $P$ .
+
+We refer to the first setting above as a sequence model and the second setting above as a boundary model. For either model, we assume that a set of training examples in the form of triplets $\{ ( \mathbf { P } _ { n } , \mathbf { Q } _ { n } , \mathbf { a } _ { n } ) \} _ { n = 1 } ^ { N }$ are given.
+
+An overview of the two neural network models are shown in Figure 1. Both models consist of three layers: (1) An LSTM preprocessing layer that preprocesses the passage and the question using LSTMs. (2) A match-LSTM layer that tries to match the passage against the question. (3) An Answer Pointer (Ans-Ptr) layer that uses Ptr-Net to select a set of tokens from the passage as the answer. The difference between the two models only lies in the third layer.
+
+# LSTM Preprocessing Layer
+
+The purpose for the LSTM preprocessing layer is to incorporate contextual information into the representation of each token in the passage and the question. We use a standard one-directional LSTM (Hochreiter & Schmidhuber, 1997) to process the passage 4 and the question separately, as shown below:
+
+$$
+{ \bf H } ^ { \mathrm { p } } = \overrightarrow { L S T M } ( { \bf P } ) , ~ { \bf H } ^ { \mathrm { q } } = \overrightarrow { L S T M } ( { \bf Q } ) .
+$$
+
+The resulting matrices $\mathbf { H } ^ { \mathrm { p } } \in \mathbb { R } ^ { l \times P }$ and $\mathbf { H } ^ { \mathrm { q } } \in \mathbb { R } ^ { l \times Q }$ are hidden representations of the passage and the question, where $l$ is the dimensionality of the hidden vectors. In other words, the $i ^ { \mathrm { { t h } } }$ column vector $\mathbf { h } _ { i } ^ { \mathrm { p } }$ (or $\mathbf { h } _ { i . } ^ { \mathrm { q } . }$ ) in $\mathbf { H } ^ { \mathrm { p } }$ (or $\mathbf { H } ^ { \mathrm { q } }$ ) represents the $i ^ { \mathrm { { t h } } }$ token in the passage (or the question) together with some contextual information from the left.
+
+# Match-LSTM Layer
+
+We apply the match-LSTM model (Wang & Jiang, 2016) proposed for textual entailment to our machine comprehension problem by treating the question as a premise and the passage as a hypothesis. The match-LSTM sequentially goes through the passage. At position $i$ of the passage, it first uses the standard word-by-word attention mechanism to obtain attention weight vector $\vec { \alpha } _ { i } \in \mathbb { R } ^ { 1 \times Q }$ as follows:
+
+$$
+\begin{array} { r c l } { \overrightarrow { \mathbf { G } } _ { i } } & { = } & { \mathrm { t a n h } ( \mathbf { W } ^ { \ P } \mathbf { H } ^ { \ P } + ( \mathbf { W } ^ { \ P } \mathbf { h } _ { i } ^ { \ P } + \mathbf { W } ^ { \Gamma } \overrightarrow { \mathbf { h } } _ { i - 1 } ^ { \top } + \mathbf { b } ^ { \ P } ) \otimes \mathbf { e } _ { Q } ) , } \\ { \overrightarrow { \alpha } _ { i } } & { = } & { \mathrm { s o f t m a x } ( \mathbf { w } ^ { \top } \overrightarrow { \mathbf { G } } _ { i } + b \otimes \mathbf { e } _ { Q } ) , } \end{array}
+$$
+
+where $\mathbf { W } ^ { \mathrm { q } } , \mathbf { W } ^ { \mathrm { p } } , \mathbf { W } ^ { \mathrm { r } } \in \mathbb { R } _ { \cdot } ^ { l \times l }$ , $\mathbf { b } ^ { \mathrm { p } }$ , $\mathbf { w } \in \mathbb { R } ^ { l \times 1 }$ and $b \in \mathbb { R }$ are parameters to be learned, $\vec { \bf G } _ { i } \in \mathbb { R } ^ { l \times Q }$ is the intermediate result, $\vec { \bf h } _ { i - 1 } ^ { \mathrm { r } } \in \mathbb { R } ^ { l \times 1 }$ is the hidden vector of the one-directional match-LSTM (to be explained below) at position $i - 1$ , and the outer product $\left( \cdot \otimes \mathbf { e } _ { Q } \right)$ produces a matrix or row vector by repeating the vector or scalar on the left for $Q$ times.
+
+Essentially, the resulting attention weight $\overrightarrow { \alpha } _ { i , j }$ above indicates the degree of matching between the $i ^ { \mathrm { { t h } } }$ token in the passage with the $j ^ { \mathrm { t h } }$ token in the question. Next, we use the attention weight vector $\vec { \alpha _ { i } }$ to obtain a weighted version of the question and combine it with the current token of the passage to form a vector $\overline { { \mathbf { z } } } _ { i }$ :
+
+$$
+\begin{array} { r } { \vec { \bf z } _ { i } = \left[ \frac { { \bf h } _ { i } ^ { \mathrm { p } } } { { \bf H } ^ { \mathrm { q } } \vec { \alpha } _ { i } ^ { \top } } \right] , } \end{array}
+$$
+
+where $\mathbf { H } ^ { \mathrm { q } } \ \in \ \mathbb { R } ^ { l \times Q } , \ \vec { \alpha } _ { i } \ \in \ \mathbb { R } ^ { 1 \times Q }$ and $\mathbf { h } _ { i } ^ { \mathsf { p } } \in \mathbb { R } ^ { l \times 1 }$ . This vector $\vec { \textbf { z } } _ { i }$ is fed into a standard onedirectional LSTM to form our so-called match-LSTM:
+
+$$
+\begin{array} { r l r } { \overrightarrow { \mathbf { h } } _ { i } ^ { \mathrm { r } } } & { = } & { \overrightarrow { L S T M } ( \overrightarrow { \mathbf { z } } _ { i } , \overrightarrow { \mathbf { h } } _ { i - 1 } ^ { \mathrm { r } } ) , } \end{array}
+$$
+
+where $\vec { \bf h } _ { i } ^ { \mathrm { r } } \in \mathbb { R } ^ { l \times 1 }$
+
+We further build a similar match-LSTM in the reverse direction. The purpose is to obtain a representation that encodes the contexts from both directions for each token in the passage.
+
+Let $\vec { \bf H ^ { r } } \in \mathbb { R } ^ { l \times P }$ represent the hidden states $[ \vec { \bf h } _ { 1 } ^ { \mathrm { r } } , \vec { \bf h } _ { 2 } ^ { \mathrm { r } } , \ldots , \vec { \bf h } _ { P } ^ { \mathrm { r } } ]$ and $\smash { \mathbf { \overleftarrow { H } ^ { r } } } \in \mathbb { R } ^ { l \times P }$ represent $[ \overleftarrow { \mathbf { h } } _ { 1 } ^ { \mathrm { r } } , \overleftarrow { \mathbf { h } } _ { 2 } ^ { \mathrm { r } } , \ldots , \overleftarrow { \mathbf { h } } _ { P } ^ { \mathrm { r } } ]$ , the hidden states of match-LSTM in the reverse direction. We define ${ \bf H } ^ { \mathrm { r } } \in  { \bf \Phi }$ $\mathbb { R } ^ { 2 l \times P }$ as the concatenation of the two:
+
+$$
+\begin{array} { r l r } { \bf { H } ^ { \mathrm { r } } } & { = } & { \left[ \begin{array} { l } { \vec { \bf { H } } ^ { \mathrm { r } } } \\ { \vec { \bf { H } } ^ { \mathrm { r } } } \end{array} \right] . } \end{array}
+$$
+
+# Answer Pointer Layer
+
+The top layer, the Answer Pointer (Ans-Ptr) layer, is motivated by the Pointer Net introduced by Vinyals et al. (2015). This layer uses the sequence $\mathbf { H } ^ { \mathrm { r } }$ as input. Recall that we have two different models: The sequence model produces a sequence of answer tokens but these tokens may not be consecutive in the original passage. The boundary model produces only the start token and the end token of the answer, and then all the tokens between these two in the original passage are considered to be the answer. We now explain the two models separately.
+
+The Sequence Model: Recall that in the sequence model, the answer is represented by a sequence of integers $\mathbf { a } = ( a _ { 1 } , a _ { 2 } , \ldots )$ indicating the positions of the selected tokens in the original passage. The Ans-Ptr layer models the generation of these integers in a sequential manner. Because the length of an answer is not fixed, in order to stop generating answer tokens at certain point, we allow each $a _ { k }$ to take up an integer value between 1 and $P + 1$ , where $P + 1$ is a special value indicating the end of the answer. Once $a _ { k }$ is set to be $P + 1$ , the generation of the answer stops.
+
+In order to generate the $k ^ { \mathrm { { t h } } }$ answer token indicated by $a _ { k }$ , first, the attention mechanism is used again to obtain an attention weight vector $\beta _ { k } \ \in \ \mathbb { R } ^ { 1 \times \bar { ( } P + 1 ) }$ , where $\beta _ { k , j }$ $( 1 \leq j \leq P + 1 )$ is the probability of selecting the $j ^ { \mathrm { t h } }$ token from the passage as the $k ^ { \mathrm { { t h } } }$ token in the answer, and $\beta _ { k , ( P + 1 ) }$ is the probability of stopping the answer generation at position $k$ . $\beta _ { k }$ is modeled as follows:
+
+$$
+\begin{array} { r c l } { \mathbf { F } _ { k } } & { = } & { \operatorname { t a n h } ( \mathbf { V } \widetilde { \mathbf { H } } ^ { \mathrm { r } } + ( \mathbf { W } ^ { \mathrm { a } } \mathbf { h } _ { k - 1 } ^ { \mathrm { a } } + \mathbf { b } ^ { a } ) \otimes \mathbf { e } _ { ( P + 1 ) } ) , } \\ { \beta _ { k } } & { = } & { \operatorname { s o f t m a x } ( \mathbf { v } ^ { \mathsf { T } } \mathbf { F } _ { k } + c \otimes \mathbf { e } _ { ( P + 1 ) } ) , } \end{array}
+$$
+
+where $\widetilde { \mathbf { H } } ^ { \mathrm { r } } \in \mathbb { R } ^ { 2 l \times ( P + 1 ) }$ is the concatenation of $\mathbf { H } ^ { \mathrm { r } }$ with a zero vector, defined as $\widetilde { \bf H } ^ { \mathrm { r } } = [ { \bf H } ^ { \mathrm { r } } ; { \bf 0 } ]$ , $\mathbf { V } \in \mathbb { R } ^ { l \times 2 l } , \mathbf { W } ^ { \mathrm { a } } \in \mathbb { R } ^ { l \times l } , \mathbf { b } ^ { a } , \mathbf { v } \in \mathbb { R } ^ { l \times 1 }$ and $c \in \mathbb { R }$ are parameters to be learned, $\mathbf { F } _ { k } \in \mathbb { R } ^ { l \times ( P + 1 ) }$ is the intermediate result, $\left( \cdot \otimes { \mathbf e } _ { \left( P + 1 \right) } \right)$ follows the same definition as before, and $\mathbf { h } _ { k - 1 } ^ { \mathrm { a } } \in \mathbb { R } ^ { l \times 1 }$ is the hidden vector at position $k - 1$ of an answer LSTM as defined below:
+
+$$
+\mathbf { h } _ { k } ^ { \mathrm { a } } = \overrightarrow { L S T M } ( \widetilde { \mathbf { H } } ^ { \mathrm { r } } \beta _ { k } ^ { \intercal } , \mathbf { h } _ { k - 1 } ^ { \mathrm { a } } ) .
+$$
+
+We can then model the probability of generating the answer sequence as
+
+$$
+\begin{array} { l l l } { p ( { \bf a } | { \bf H ^ { r } } ) } & { = } & { \displaystyle \prod _ { k } p ( a _ { k } | a _ { 1 } , a _ { 2 } , \ldots , a _ { k - 1 } , { \bf H ^ { r } } ) , } \end{array}
+$$
+
+and
+
+$$
+\begin{array} { r c l } { p ( a _ { k } = j | a _ { 1 } , a _ { 2 } , \ldots , a _ { k - 1 } , \mathbf { H } ^ { \mathrm { r } } ) } & { = } & { \beta _ { k , j } . } \end{array}
+$$
+
+To train the model, we minimize the following loss function based on the training examples:
+
+$$
+- \sum _ { n = 1 } ^ { N } \log p ( \mathbf { a } _ { n } | \mathbf { P } _ { n } , \mathbf { Q } _ { n } ) .
+$$
+
+The Boundary Model: The boundary model works in a way very similar to the sequence model above, except that instead of predicting a sequence of indices $a _ { 1 } , a _ { 2 } , \dotsc$ , we only need to predict two indices $a _ { s }$ and $a _ { \mathrm { e } }$ . So the main difference from the sequence model above is that in the boundary model we do not need to add the zero padding to $\mathbf { H } ^ { \mathrm { r } }$ , and the probability of generating an answer is simply modeled as
+
+$$
+\begin{array} { r l r } { p ( { \bf a } | { \bf H ^ { r } } ) } & { = } & { p ( a _ { \mathrm { s } } | { \bf H ^ { r } } ) p ( a _ { \mathrm { e } } | a _ { \mathrm { s } } , { \bf H ^ { r } } ) . } \end{array}
+$$
+
+As this boundary model could point to a span covering too many tokens without any restriction, we try to manually limit the length of the predicted span and then search the span with the highest probability computed by $p ( \mathbf { a } _ { s } ) \times p ( \mathbf { a } _ { e } | \mathbf { a } _ { s } )$ as the answer.
+
+# 3 EXPERIMENTS
+
+In this section, we present our experiment results and perform some analyses to better understand how our models works.
+
+# 3.1 DATA
+
+We use the Stanford Question Answering Dataset (SQuAD) v1.1 and the human-generated Microsoft MAchine Reading COmprehension (MSMARCO) dataset v1.1 to conduct our experiments.
+
+Passages in SQuAD come from 536 articles in Wikipedia covering a wide range of topics. Each passage is a single paragraph from a Wikipedia article, and each passage has around 5 questions associated with it. In total, there are 23,215 passages and 107,785 questions. The data has been split into a training set (with 87,599 question-answer pairs), a development set (with 10,570 questionanswer pairs) and a hidden test set.
+
+For the MSMARCO dataset, the questions are user queries issued to the Bing search engine, the context passages are real Web documents and the answers are human-generated. We select the span that has the highest F1 score with the gold standard answer for training and only predict the span in the passages during evaluation. The data has been split into a training set (82326 pairs), a development set (10047 pairs) and a test set (9650 pairs).
+
+# 3.2 EXPERIMENT SETTINGS
+
+We first tokenize all the passages, questions and answers. We use word embeddings from GloVe (Pennington et al., 2014) to initialize the model. Words not found in GloVe are initialized as zero vectors. The word embeddings are not updated during the training of the model.
+
+The dimensionality $l$ of the hidden layers is set to be 150. We use ADAMAX (Kingma & Ba, 2015) with the coefficients $\beta _ { 1 } = 0 . 9$ and $\beta _ { 2 } = 0 . 9 9 9$ to optimize the model. Each update is computed through a minibatch of 30 instances. We do not use L2-regularization.
+
+For the SQuAD dataset, the performance is measured by two metrics: percentage of exact match with the ground truth answers and word-level F1 score when comparing the tokens in the predicted answers with the tokens in the ground truth answers. Note that in the development set and the test set each question has around three ground truth answers. F1 scores with the best matching answers are used to compute the average F1 score. For the MSMARCO dataset, the metrics in the official tool of MSMARCO evaluation are BLEU-1/2/3/4 and Rouge-L, which are widely used in many domains.
+
+# 3.3 RESULTS
+
+The SQuAD and MSMARCO results of our models as well as the results of the baselines (Rajpurkar et al., 2016; Yu et al., 2016) are shown in Table 2. For the “LSTM with Ans-Ptr” models, they are the experiments with the ablation of attention mechanism in match-LSTM. Specifically, we use the final representation of the question to replace the weighted sum of the question representations. For the MSMARCO dataset, as the context for each question is consisted of around 10 documents, the “Golden Passage” is to directly use the human labeled document which could answer the question as the prediction.
+
+Table 2: Experiment Results on SQuAD and MSMARCO datasets. Here “LSTM with Ans-Ptr” removes the attention mechanism in match-LSTM (mLSTM) by using the final state of the LSTM for the question to replace the weighted sum of all the states. Our best boundary model is the further tuned model and its ablation study is shown in Table 4. “en” refers to ensemble method.   
+
+<table><tr><td></td><td colspan="4">SQuAD</td><td>MSMARCO</td></tr><tr><td></td><td colspan="2">Exact Match</td><td colspan="2">F1</td><td>BLEU1/2/3/4 /Rouge-L</td></tr><tr><td></td><td>Dev</td><td>Test</td><td>Dev</td><td>Test</td><td>Dev&amp;Test</td></tr><tr><td>Human</td><td>80.3</td><td>77.0</td><td>90.5</td><td>86.8</td><td>-&amp; 46/-l-l- /47</td></tr><tr><td>Golden Passage</td><td>-</td><td>-</td><td>-</td><td>1</td><td>19.6/18.8/18.1/17.5/32.3&amp;-</td></tr><tr><td>LR (Rajpurkar et al., 2016)</td><td>40.0</td><td>40.4</td><td>51.0</td><td>51.0</td><td></td></tr><tr><td>DCR (Yu et al., 2016)</td><td>62.5</td><td>62.5</td><td>71.2</td><td>71.0</td><td></td></tr><tr><td>LSTM with Ans-Ptr (Sequence)</td><td>37.7</td><td>-</td><td>48.5</td><td>-</td><td>10.3/7.2 /5.6 /4.6 /21.6&amp;-</td></tr><tr><td>LSTM with Ans-Ptr (Boundary)</td><td>45.2</td><td></td><td>55.3</td><td></td><td>32.0 /25.3/22.2/20.4/32.3&amp;-</td></tr><tr><td>mLSTM with Ans-Ptr (Sequence)</td><td>54.4</td><td>=</td><td>68.2</td><td>1</td><td>12.5 /9.2 /7.5 /6.5 /22.5 &amp; -</td></tr><tr><td>mLSTM with Ans-Ptr (Boundary)</td><td>63.0</td><td></td><td>72.7</td><td>=</td><td>32.9 /26.4/23.2/21.6/33.8&amp;-</td></tr><tr><td>Our best boundary model</td><td>67.0</td><td>66.9</td><td>77.2</td><td>77.1</td><td>40.1/33.3/30.1/28.2/37.2 &amp; 40.7 / 33.9 / 30.6 /28.7 / 37.3</td></tr><tr><td>mLSTM with Ans-Ptr (Boundary+en)</td><td>67.6</td><td>67.9</td><td></td><td></td><td></td></tr><tr><td>Our best boundary model (en)</td><td>71.3</td><td>72.6</td><td>76.8 80.0</td><td>77.0 80.8</td><td></td></tr></table>
+
+Table 3: Statistical analysis on the development datasets. #w: number of words on average; P: passage; Q: question; A: answer; raw: raw data from the development dataset; seq/bou: the answers generated by the sequence/boundary models with match-LSTM.   
+
+<table><tr><td>SQuAD #w in A/Q/P</td><td></td><td>MSMARCO #w in A/Q/P</td></tr><tr><td>raw</td><td>3.1/11/141</td><td>16.3/6/667</td></tr><tr><td>seq</td><td>2.4/-/-</td><td>6.7 /-/-</td></tr><tr><td>bou</td><td>3.0/-/-</td><td>15.7/ -/ -</td></tr></table>
+
+Table 4: Ablation study for our best boundary model on the development datasets. Our best model is a further tuned boundary model by considering “bi-Ans-Ptr” which adds bidirectional answer pointer, “deep” which adds another twolayer bi-directional LSTMs between the match-LSTM and the Answer Pointer layers, and “elem” which adds elementwise comparison , $( \mathbf { h } _ { i } ^ { \mathrm { p } } - \mathbf { H } ^ { \mathrm { q } } \alpha _ { i } ^ { \mathsf { T } } )$ and $( \mathbf { h } _ { i } ^ { \mathrm { p } } \odot \mathbf { H } ^ { \mathrm { q } } \alpha _ { i } ^ { \mathsf { T } } )$ , into Eqn 3. “-pre-LSTM” refers to removing the pre-processing layer.   
+
+<table><tr><td></td><td>SQuAD EM&amp;F1</td><td>MSMARCO BLEU1/2/3/4&amp;Rouge-L</td></tr><tr><td>Best model</td><td>67.0 &amp; 77.2</td><td>40.1/33.3/30.1/28.2 &amp; 37.2</td></tr><tr><td>-bi-Ans-Ptr</td><td>66.5 &amp; 76.8</td><td>39.9/32.8/29.6/27.9 &amp; 36.7</td></tr><tr><td>-deep</td><td>65.9 &amp; 75.8</td><td>39.6/32.6/29.4/27.4&amp; 35.9</td></tr><tr><td>-elem</td><td>65.2 &amp; 75.4</td><td>38.1/31.4/28.3/26.5 &amp; 35.5</td></tr><tr><td>-pre-LSTM</td><td>64.0 &amp; 72.9</td><td>39.6/32.8/29.8/27.7&amp; 36.3</td></tr></table>
+
+From the results in Table 2, we can see that the boundary model could clearly outperform the sequence model in a big margin on both datasets. We hypothesis that the sequence model is more likely to stop word generation earlier, and the boundary model can somehow overcome this problem. We have a statistical analysis on the answers generated by our sequence and boundary models shown in Table 3. We can see that the length of the answers generated by the sequence model is much shorter than the ground truth. Especially for the MSMARCO task where the answers are usually much longer, the sequence model could only generate 7 words on average, while the ground truth answers are 16 on average and the boundary model could generate nearly the same number of words with the ground truth. Several answers generated by our models are shown in Appendix A. From Table 2, we can also see that the performance gets poorer by removing the attention mechanism in match-LSTM, while for the MSMARCO dataset, the attention mechanism effects less, with no more than 2 percent reduction in BLEU and Rouge-L scores by attention mechanism ablation.
+
+Based on the effectiveness of boundary pointer and match-LSTM, we conduct further exploration of the boundary model by adding element-wise comparison $( \mathbf { h } _ { i } ^ { \mathrm { p } } { - } \mathbf { H } ^ { \mathrm { q } } \alpha _ { i } ^ { \mathsf { T } } )$ and $( \mathbf { h } _ { i } ^ { \mathrm { p } } \odot \mathbf { H } ^ { \mathrm { q } } \alpha _ { i } ^ { \mathsf { T } } )$ into Eqn 3 in match-LSTM layer, adding 2 more bi-directional LSTM layers between match-LSTM and Ans-Ptr layers, and adding bi-directional Ans-Ptr. We show the ablation study of this further tuned model in Table 4. We can see that adding element-wise matching could make the biggest improvement for our boundary model. We also try to remove the phrase-level representation by removing the pre-process LSTM and using the word-level representations as the inputs of match-LSTM. Interestingly, we find the phrase-level representation effects little on the MSMARCO task.
+
+Overall, we can see that both of our match-LSTM models have clearly outperformed the logistic regression model by Rajpurkar et al. (2016), which relies on carefully designed features. The improvement of our models over the logistic regression model shows that our end-to-end neural network models without much feature engineering are very effective on these tasks and datasets. Our boundary model also outperformed the DCR model (Yu et al., 2016), which maximizes the probability of the gold standard span from all the candidate spans through a neural network structure.
+
+# 3.4 FURTHER ANALYSES
+
+![](images/864acbb39a507e6729b31bfe92a1fcef705d8bb019c02b3fba961e7dcf7aa7e5.jpg)  
+Figure 2: Performance breakdown by answer lengths and question types on SQuAD development dataset. Top: Plot (1) shows the performance of our two models (where $s$ refers to the sequence model , $^ b$ refers to the boundary model, and $e$ refers to the ensemble boundary model) over answers with different lengths. Plot (2) shows the numbers of answers with different lengths. Bottom: Plot (3) shows the performance our the two models on different types of questions. Plot (4) shows the numbers of different types of questions.
+
+To better understand the strengths and weaknesses of our models, we perform some further analyses of the results below.
+
+First, we suspect that longer answers are harder to predict. To verify this hypothesis, we analysed the performance in terms of both exact match and F1 score with respect to the answer length on the development set, as shown in Figure 2. For example, for questions whose answers contain more than 9 tokens, the F1 score of the boundary model drops to around $55 \%$ and the exact match score drops to only around $30 \%$ , compared to the F1 score and exact match score of close to $72 \%$ and $67 \%$ , respectively, for questions with single-token answers. And that supports our hypothesis.
+
+![](images/eb921479c5383e25d5c35305dd8dad9a57ee199afeccc9f323e1c272c7d45db1.jpg)
+
+![](images/cea1279cd9a9594b6feb7c27a9741a652cf6131a826623c46358ea527f2b9fd8.jpg)  
+Answer: European Parliament and the Council of the European Union   
+Figure 3: Visualization of the attention weights $\alpha$ for four questions. The first three questions share the same paragraph. The title is the answer predicted by our model.
+
+Next, we analyze the performance of our models on different groups of questions, as shown in Figure 2. We use a crude way to split the questions into different groups based on a set of question words we have defined, including “what,” “how,” “who,” “when,” “which,” “where,” and “why.” These different question words roughly refer to questions with different types of answers. For example, “when” questions look for temporal expressions as answers, whereas “where” questions look for locations as answers. According to the performance on the development dataset, our models work the best for “when” questions. This may be because in this dataset temporal expressions are relatively easier to recognize. Other groups of questions whose answers are noun phrases, such as “what” questions, “which” questions and “where” questions, also get relatively better results. On the other hand, “why” questions are the hardest to answer. This is not surprising because the answers to “why” questions can be very diverse, and they are not restricted to any certain type of phrases.
+
+Finally, we would like to check whether the attention mechanism used in the match-LSTM layer is effective in helping the model locate the answer. We show the attention weights $\alpha$ in Figure 3. In the figure the darker the color is the higher the weight is. We can see that some words have been well aligned based on the attention weights. For example, the word “German” in the passage is aligned well to the word “language” in the first question, and the model successfully predicts “German” as the answer to the question. For the question word “who” in the second question, the word “teacher” actually receives relatively higher attention weight, and the model has predicted the phrase “Martin Sekulic” after that as the answer, which is correct. For the third question that starts with “why”, the attention weights are more evenly distributed and it is not clear which words have been aligned to “why”. For the last question, we can see that the word knowledge needed for generating the answer can also be detected by match-LSTM. For example, the words “European”, “Parliament”, “Council”, “European” and “Union” have higher attention weights on “governing” in the question. Even though our models can solve this type of questions, they are still not able to solve the questions that need multi-sentences reasoning. More answers generated by our models for the questions related to different kinds of reasoning are shown in Appendix B.
+
+# 4 RELATED WORK
+
+Machine comprehension of text has gained much attention in recent years, and increasingly researchers are building data-drive, end-to-end neural network models for the task. We will first review the recently released datasets and then some end-to-end models on this task.
+
+# 4.1 DATASETS
+
+A number of datasets for studying machine comprehension were created in Cloze style by removing a single token from a sentence in the original corpus, and the task is to predict the missing word. For example, Hermann et al. (2015) created questions in Cloze style from CNN and Daily Mail highlights. Hill et al. (2016) created the Children’s Book Test dataset, which is based on children’s stories. Cui et al. (2016) released two similar datasets in Chinese, the People Daily dataset and the Children’s Fairy Tale dataset.
+
+Instead of creating questions in Cloze style, a number of other datasets rely on human annotators to create real questions. Richardson et al. (2013) created the well-known MCTest dataset and Tapaswi et al. (2016) created the MovieQA dataset. In these datasets, candidate answers are provided for each question. Similar to these two datasets, the SQuAD dataset (Rajpurkar et al., 2016) was also created by human annotators. Different from the previous two, however, the SQuAD dataset does not provide candidate answers, and thus all possible subsequences from the given passage have to be considered as candidate answers.
+
+Besides the datasets above, there are also a few other datasets created for machine comprehension, such as WikiReading dataset (Hewlett et al., 2016) and bAbI dataset (Weston et al., 2016), but they are quite different from the datasets above in nature.
+
+# 4.2 END-TO-END NEURAL NETWORK MODELS FOR MACHINE COMPREHENSION
+
+There have been a number of studies proposing end-to-end neural network models for machine comprehension. A common approach is to use recurrent neural networks (RNNs) to process the given text and the question in order to predict or generate the answers (Hermann et al., 2015). Attention mechanism is also widely used on top of RNNs in order to match the question with the given passage (Hermann et al., 2015; Chen et al., 2016). Given that answers often come from the given passage, Pointer Network has been adopted in a few studies in order to copy tokens from the given passage as answers (Kadlec et al., 2016; Trischler et al., 2016). Compared with existing work, we use match-LSTM to match a question and a given passage, and we use Pointer Network in a different way such that we can generate answers that contain multiple tokens from the given passage.
+
+Memory Networks (Weston et al., 2015) have also been applied to machine comprehension (Sukhbaatar et al., 2015; Kumar et al., 2016; Hill et al., 2016), but its scalability when applied to a large dataset is still an issue. In this work, we did not consider memory networks for the SQuAD/MSMARCO datasets.
+
+The setting of visual question answering (Antol et al., 2015) is quite similar to machine comprehension, while their answers are usually very short. So the sequence order of the word-level attention representation used to align the figure and the question(Xu & Saenko, 2016; Fukui et al., 2016; Lu et al., 2016), are not used in VQA. While our model focus on the word-by-word attention and use
+
+LSTM to concatenate the aligned pairs and that would be helpful to generate a longer sequence as answer.
+
+# 5 CONCLUSIONS
+
+In this paper, We developed two models for the machine comprehension problem defined in the Stanford Question Answering (SQuAD) and A Human-Generated MAchine Reading COmprehension (MSMARCO) datasets, both making use of match-LSTM and Pointer Network. Experiments on the SQuAD and MSMARCO datasets showed that our second model, the boundary model, could achieve a performance close to the state-of-the-art performance on the SQuAD dataset and achieved the state-of-the-art on the MSMARCO dataset. We also show the boundary model could overcome the early stop prediction problem of the sequence model.
+
+In the future, we plan to look further into the different types of questions and focus on those questions which currently have low performance, such as the “why’ questions and multi-sentences related questions. We also plan to test how our models could be applied to other machine comprehension datasets.
+
+# 6 ACKNOWLEDGMENTS
+
+This research is supported by the National Research Foundation, Prime Ministers Office, Singapore under its International Research Centres in Singapore Funding Initiative.
+
+We thank Pranav Rajpurkar for testing our model on the hidden test dataset and Percy Liang for helping us with the Dockerfile for Codalab.
+
+# REFERENCES
+
+Stanislaw Antol, Aishwarya Agrawal, Jiasen Lu, Margaret Mitchell, Dhruv Batra, C Lawrence Zitnick, and Devi Parikh. Vqa: Visual question answering. In Proceedings of the IEEE International Conference on Computer Vision, pp. 2425–2433, 2015.
+
+Danqi Chen, Jason Bolton, and Christopher D. Manning. A thorough examination of the CNN/Daily Mail reading comprehension task. In Proceedings of the Conference on Association for Computational Linguistics, 2016.
+
+Yiming Cui, Ting Liu, Zhipeng Chen, Shijin Wang, and Guoping Hu. Consensus attention-based neural networks for chinese reading comprehension. In arXiv preprint arXiv:1607.02250, 2016.
+
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+
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+
+Jeffrey Pennington, Richard Socher, and Christopher D Manning. GloVe: Global vectors for word representation. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, 2014.
+
+Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. SQuAD: $1 0 0 { , } 0 0 0 { + }$ questions for machine comprehension of text. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, 2016.
+
+Matthew Richardson, Christopher JC Burges, and Erin Renshaw. MCTest: A challenge dataset for the open-domain machine comprehension of text. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, 2013.
+
+Sainbayar Sukhbaatar, Jason Weston, Rob Fergus, et al. End-to-end memory networks. In Proceedings of the Conference on Advances in neural information processing systems, 2015.
+
+Makarand Tapaswi, Yukun Zhu, Rainer Stiefelhagen, Antonio Torralba, Raquel Urtasun, and Sanja Fidler. MovieQA: Understanding stories in movies through question-answering. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2016.
+
+Adam Trischler, Zheng Ye, Xingdi Yuan, and Kaheer Suleman. Natural language comprehension with the EpiReader. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, 2016.
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+Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks. In Proceedings of the Conference on Advances in Neural Information Processing Systems, 2015.
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+
+Jason Weston, Sumit Chopra, and Antoine Bordes. Memory networks. In Proceedings of the International Conference on Learning Representations, 2015.
+
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+
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+
+# A APPENDIX
+
+We show the predictions our boundary and sequence models on two cases from two datasets in Table 5. It can be seen that the sequence model is more likely to predict a shorter sequence which is the problem of early stop prediction.
+
+<table><tr><td>(1) Context</td><td>Asopposed to broadcasts of primetime series,CBS broadcast special episodes of its late night talk shows as its lead-out programs for Super Bowl 5O, beginning with a special episode of The Late Show with Stephen Colbert following the game.</td></tr><tr><td>Question (Syntactic) Golden Anwser match-LSTM (Sequence)</td><td>What CBS show followed the Super Bowl? The Late Show with Stephen Colbert The Late Show The Late Show with Stephen Colbert</td></tr><tr><td>match-LSTM (Boundary) (2) Context</td><td>Urinalysis is a test that evaluates a sample of your urine.Urinalysis is used to detect and assess a wide range of disorders,such as uri- nary tract infection, kidney disease and diabetes. Urinalysis involves examining the appearance,concentration and content of urine.Abnor- mal urinalysis results may point to a disease or illness.For example,</td></tr><tr><td>Query</td><td>a urinary tract infection can make urine look cloudy instead of clear. Increased levels of protein in urine can be a sign of kidney disease. what can urinalysis detect?</td></tr><tr><td>Golden Anwser</td><td>Detect and assess a wide range of disorders,such as urinary tract infec- tion, kidney disease and diabetes.</td></tr><tr><td>match-LSTM (Sequence) match-LSTM (Boundary)</td><td>Urinalysis Urinalysis is used to detect and assess a wide range of disorders,such as urinary tract infection,kidney disease and diabetes</td></tr></table>
+
+Table 5: Prediction samples for sequence and boundary models. The first case is sampled from SQuAD dataset and the second is sampled from MSMARCO dataset.
+
+# B APPENDIX
+
+We show how four different models work on different type of questions in SQuAD dataset through Table 6. After the analysis of a hundred cases, we see that our models are not able to solve the questions that need multi-sentences reasoning. And the model without attention mechanism has less power to identify the important key word like the third case shown in Table 6.
+
+Table 6: Different types of reasoning samples in SQuAD dataset. “match-LSTM” refers to the “match-LSTM with Ans-Ptr” and “LSTM” refers to the “LSTM with Ans-Ptr” which is the ablation of attention mechanism in match-LSTM.   
+
+<table><tr><td>(1) Context</td><td>The Rankine cycle is sometimes referred to as a practical Carnot cycle be- cause,when an efficient turbine is used, the TS diagram begins to resemble the</td></tr><tr><td>Question (Synonymy) Golden Anwser</td><td>Carnot cycle. What is the Rankine cycle sometimes called? practical Carnot cycle</td></tr><tr><td>LSTM (Sequence) match-LSTM (Sequence)</td><td>Carnot cycle</td></tr><tr><td>LSTM (Boundary) match-LSTM (Boundary)</td><td>Carnot cycle practical Carnot cycle</td></tr><tr><td>(2) Context</td><td>Carnot cycle</td></tr><tr><td></td><td>While the Commission has a monopoly on initiating legislation,the European Parliament and the Council of the European Union have powers of amend-</td></tr><tr><td></td><td>ment and veto during the legislative process.</td></tr><tr><td>Question (Knowledge) Golden Anwser</td><td>Which two governing bodies have legislative veto power? the European Parliament and the Council of the European Union</td></tr><tr><td>LSTM (Sequence)</td><td>European Parliament and the Council of the European Union</td></tr><tr><td>match-LSTM (Sequence) LSTM (Boundary)</td><td>European Parliament and the Council of the European Union</td></tr><tr><td>match-LSTM (Boundary)</td><td>European Parliament and the Council of the European Union</td></tr><tr><td>(3) Context</td><td>European Parliament and the Council of the European Union</td></tr><tr><td></td><td>Current faculty include the anthropologist Marshall Sahlins, historian Dipesh Chakrabarty,... Shakespeare scholar David Bevington, and renowned political</td></tr><tr><td>Question (Syntactic) Golden Anwser</td><td>scientists John Mearsheimer and Robert Pape. What Shakespeare scholar is currently on the university&#x27;s faculty?</td></tr><tr><td>LSTM (Sequence)</td><td>David Bevington Marshall Sahlins</td></tr><tr><td>match-LSTM (Sequence) LSTM(Boundary)</td><td>David Bevington Marshall Sahlins</td></tr><tr><td>match-LSTM (Boundary) (4) Context</td><td>David Bevington</td></tr><tr><td></td><td>The V&amp;A Theatre &amp; Performance galleries,formerly the Theatre Museum, opened in March 2Oo9.The collections are stored by the V&amp;A,and are available for research,exhibitions and other shows.They hold the UK&#x27;s biggest national</td></tr><tr><td></td><td>collection of material about live performance in the UK since Shakespeare&#x27;s day,covering drama, dance,musical theatre, circus,music hall,rock and pop, and most other forms of live entertainment.</td></tr><tr><td>Question (Reasoning) Golden Anwser</td><td>What collection does the V&amp;A Theatre &amp; Performance galleries hold? material about live performance</td></tr><tr><td>LSTM (Sequence) match-LSTM (Sequence) LSTM (Boundary)</td><td>Theatre the Theatre Museum</td></tr><tr><td>match-LSTM (Boundary)</td><td>research,exhibitions and other shows</td></tr><tr><td></td><td>Theatre Museum</td></tr><tr><td></td><td></td></tr><tr><td>(5) Context</td><td>Along with giving the offender his &quot;just deserts&quot;,achieving crime control via</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td>Question (Ambiguous)</td><td>incapacitation and deterrence is a major goal of criminal punishment.</td></tr><tr><td></td><td></td></tr><tr><td>Golden Anwser</td><td>What is the main goal of criminal punishment of civil disobedients ?</td></tr><tr><td></td><td></td></tr><tr><td></td><td>achieving crime control via incapacitation and deterrence</td></tr><tr><td>LSTM (Sequence)</td><td></td></tr><tr><td></td><td>deterrence</td></tr><tr><td>match-LSTM (Sequence) LSTM (Boundary)</td><td>just deserts incapacitation and deterrence</td></tr></table>

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+        "text": "ABSTRACT ",
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+        "text": "Machine comprehension of text is an important problem in natural language processing. A recently released dataset, the Stanford Question Answering Dataset (SQuAD), offers a large number of real questions and their answers created by humans through crowdsourcing. SQuAD provides a challenging testbed for evaluating machine comprehension algorithms, partly because compared with previous datasets, in SQuAD the answers do not come from a small set of candidate answers and they have variable lengths. We propose an end-to-end neural architecture for the task. The architecture is based on match-LSTM, a model we proposed previously for textual entailment, and Pointer Net, a sequence-to-sequence model proposed by Vinyals et al. (2015) to constrain the output tokens to be from the input sequences. We propose two ways of using Pointer Net for our tasks. Our experiments show that both of our two models substantially outperform the best results obtained by Rajpurkar et al. (2016) using logistic regression and manually crafted features. Besides, our boundary model also achieves the best performance on the MSMARCO dataset (Nguyen et al., 2016). ",
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+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+        "text": "Machine comprehension of text is one of the ultimate goals of natural language processing. While the ability of a machine to understand text can be assessed in many different ways, in recent years, several benchmark datasets have been created to focus on answering questions as a way to evaluate machine comprehension (Richardson et al., 2013; Hermann et al., 2015; Hill et al., 2016; Weston et al., 2016; Rajpurkar et al., 2016; Nguyen et al., 2016). In this setup, typically the machine is first presented with a piece of text such as a news article or a story. The machine is then expected to answer one or multiple questions related to the text. ",
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+        "type": "text",
+        "text": "In most of the benchmark datasets, a question can be treated as a multiple choice question, whose correct answer is to be chosen from a set of provided candidate answers (Richardson et al., 2013; Hill et al., 2016). Presumably, questions with more given candidate answers are more challenging. The Stanford Question Answering Dataset (SQuAD) introduced recently by Rajpurkar et al. (2016) contains such more challenging questions whose correct answers can be any sequence of tokens from the given text. Moreover, unlike some other datasets whose questions and answers were created automatically in Cloze style (Hermann et al., 2015; Hill et al., 2016), the questions and answers in SQuAD were created by humans through crowdsourcing, which makes the dataset more realistic. Another real dataset, the Human-Generated MAchine Reading COmprehension dataset (MSMARCO) (Nguyen et al., 2016), provided a query together with several related documents collected from Bing Index. The answer to the query is generated by human and the answer words can not only come from the given text. ",
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+        "text": "Given these advantages of the SQuAD and MSMARCO datasets, in this paper, we focus on these new datasets to study machine comprehension of text. A sample piece of text and three of its associated questions from SQuAD are shown in Table 1. Traditional solutions to this kind of question answering tasks rely on NLP pipelines that involve multiple steps of linguistic analyses and feature engineering, including syntactic parsing, named entity recognition, question classification, semantic parsing, etc. Recently, with the advances of applying neural network models in NLP, there has been much interest in building end-to-end neural architectures for various NLP tasks, including several pieces of work on machine comprehension (Hermann et al., 2015; Hill et al., 2016; Yin et al., 2016; Kadlec et al., 2016; Cui et al., 2016). However, given the properties of previous machine comprehension datasets, existing end-to-end neural architectures for the task either rely on the candidate answers (Hill et al., 2016; Yin et al., 2016) or assume that the answer is a single token (Hermann et al., 2015; Kadlec et al., 2016; Cui et al., 2016), which make these methods unsuitable for the SQuAD/MSMARCO dataset. In this paper, we propose a new end-to-end neural architecture to address the machine comprehension problem as defined in the SQuAD/MSMARCO dataset. And for the MSMARCO dataset, we will only make use of the words in the given text to generate the answer. ",
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+        "type": "table",
+        "img_path": "images/a180153f0d140ba3c4ea05e734b5a44317d614c0823277b09cd38cb3c7fe9be3.jpg",
+        "table_caption": [
+            "Table 1: A paragraph from Wikipedia and three associated questions together with their answers, taken from the $\\mathrm { S Q u A D }$ dataset. The tokens in bold in the paragraph are our predicted answers while the texts next to the questions are the ground truth answers. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">In 1870,Tesla moved to Karlovac,to attend school at the Higher Real Gymnasium,where he was profoundly influenced by a math teacher Martin Sekulic. The classes were held in German,as it was a school within the Austro-Hungarian Military Frontier.Tesla was able to perform integral calculus in his head,which prompted his teachers to believe that he was cheating.He finished a four-year term in three</td></tr><tr><td>years,graduating in 1873. 1.In what language were the classes given? 2.Who was Tesla&#x27;s main influence in Karlovac? 3.Why did Tesla go to Karlovac?</td><td>German Martin Sekulic attend school at the Higher Real Gymnasium</td></tr></table>",
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+        "text": "Specifically, observing that in the SQuAD/MSMARCO dataset many questions could be entailed from some sentences in the original text, we adopt a match-LSTM model that we developed earlier for textual entailment (Wang & Jiang, 2016) as one layer of our model. We build a bi-directional match-LSTM on the given passage with attentions on the question for each word so that each position in the paragraph will have a hidden representation reflecting its relation to the question. Then we further adopt the Pointer Net (Ptr-Net) model developed by Vinyals et al. (2015) to select the words in these positions based on the hidden representations built by match-LSTM as an answer. We propose two ways to apply the Ptr-Net model for our task: a sequence model which selects the answer word by word, and a boundary model which only selects the start and end points of the answer span. Experiments on the SQuAD dataset show that our two models both outperform the best performance reported by Rajpurkar et al. (2016). Moreover, using an ensemble of several of our models, we can achieve very competitive performance on SQuAD. For the MSMARCO dataset, a real query based problem, our boundary model outperforms our sequence model with a big margin. It also outperforms the golden passage baseline. ",
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+        "type": "text",
+        "text": "Our contributions can be summarized as follows: (1) We propose two new end-to-end neural network models for machine comprehension, which combine match-LSTM and $\\mathrm { P t r }$ -Net to handle the special properties of the SQuAD dataset. To the best of our knowledge, we are the first to propose the boundary model which is more suitable to the SQuAD/MSMARCO tasks. And we are the first to integrate the attention-based word pair matching into machine comprehension tasks. (2) We have achieved the performance of an exact match score of $7 1 . 3 \\%$ and an F1 score of $8 0 . 8 \\%$ on the unseen SQuAD test dataset, which is much better than the feature-engineered solution (Rajpurkar et al., 2016). Our performance is also close to the state of the art on SQuAD, which is $7 4 . 8 \\%$ in terms of exact match and $8 2 . 2 \\%$ in terms of F1 collected from the SQuAD Leaderboard 1. Besides, our boundary model achieves the state-of-art performance on the MSMARCO dataset with BLUE$1 / 2 / 3 / 4 4 0 . 7 / 3 3 . 9 / 3 0 . 6 / 2 8 . 7$ and Rouge-L $3 7 . { \\bar { 3 } } ^ { 2 }$ . (3) Our further visualization of the models reveals some useful insights of the attention mechanism for reasoning the questions. And we also show that the boundary model can overcome the early stop prediction problem in the sequence model. Besides, we also made our code available online 3. ",
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+        "img_path": "images/f0257a3f1eb62a4fe298cadd284177e42c85bb65ae55acc03d90347e8c89aee8.jpg",
+        "image_caption": [
+            "Figure 1: An overview of our two models. Both models consist of an LSTM preprocessing layer, a match-LSTM layer and an Answer Pointer layer. For each match-LSTM in a particular direction, $\\bar { h } _ { i } ^ { \\mathrm { q } }$ , which is defined as $\\mathbf { H } ^ { \\mathrm { q } } \\alpha _ { i } ^ { \\mathsf { T } }$ , is computed using the $\\alpha$ in the corresponding direction, as described in Eqn. (2) "
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+        "text": "2 METHOD ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section, we first briefly review match-LSTM and Pointer Net. These two pieces of existing work lay the foundation of our method. We then present our end-to-end neural architecture for machine comprehension. ",
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+        "text": "2.1 MATCH-LSTM ",
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+        "text": "In a recent work on learning natural language inference, we proposed a match-LSTM model for predicting textual entailment (Wang & Jiang, 2016). In textual entailment, two sentences are given where one is a premise and the other is a hypothesis. To predict whether the premise entails the hypothesis, the match-LSTM model goes through the tokens of the hypothesis sequentially. At each position of the hypothesis, attention mechanism is used to obtain a weighted vector representation of the premise. This weighted premise is then to be combined with a vector representation of the current token of the hypothesis and fed into an LSTM, which we call the match-LSTM. The matchLSTM essentially sequentially aggregates the matching of the attention-weighted premise to each token of the hypothesis and uses the aggregated matching result to make a final prediction. ",
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+        "text": "2.2 POINTER NET ",
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+        "text": "Vinyals et al. (2015) proposed a Pointer Network (Ptr-Net) model to solve a special kind of problems where we want to generate an output sequence whose tokens must come from the input sequence. Instead of picking an output token from a fixed vocabulary, Ptr-Net uses attention mechanism as a pointer to select a position from the input sequence as an output symbol. The pointer mechanism has inspired some recent work on language processing (Gu et al., 2016; Kadlec et al., 2016). Here we adopt Ptr-Net in order to construct answers using tokens from the input text. ",
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+        "text": "2.3 OUR METHOD ",
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+        "text": "Formally, the problem we are trying to solve can be formulated as follows. We are given a piece of text, which we refer to as a passage, and a question related to the passage. The passage is represented by matrix $\\mathbf { P } \\in \\mathbb { R } ^ { d \\times P }$ , where $P$ is the length (number of tokens) of the passage and $d$ is the dimensionality of word embeddings. Similarly, the question is represented by matrix $\\breve { \\mathbf { Q } } \\in \\mathbb { R } ^ { d \\times Q }$ where $Q$ is the length of the question. Our goal is to identify a subsequence from the passage as the answer to the question. ",
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+        "type": "text",
+        "text": "As pointed out earlier, since the output tokens are from the input, we would like to adopt the Pointer Net for this problem. A straightforward way of applying Ptr-Net here is to treat an answer as a sequence of tokens from the input passage but ignore the fact that these tokens are consecutive in the original passage, because Ptr-Net does not make the consecutivity assumption. Specifically, we represent the answer as a sequence of integers $\\mathbf { a } = ( a _ { 1 } , a _ { 2 } , . . . )$ , where each $a _ { i }$ is an integer between 1 and $P$ , indicating a certain position in the passage. ",
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+        "type": "text",
+        "text": "Alternatively, if we want to ensure consecutivity, that is, if we want to ensure that we indeed select a subsequence from the passage as an answer, we can use the Ptr-Net to predict only the start and the end of an answer. In this case, the Ptr-Net only needs to select two tokens from the input passage, and all the tokens between these two tokens in the passage are treated as the answer. Specifically, we can represent the answer to be predicted as two integers $\\mathbf { a } = ( a _ { \\mathrm { s } } , a _ { \\mathrm { e } } )$ , where $a _ { s }$ an $a _ { \\mathrm { e } }$ are integers between 1 and $P$ . ",
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+        "type": "text",
+        "text": "We refer to the first setting above as a sequence model and the second setting above as a boundary model. For either model, we assume that a set of training examples in the form of triplets $\\{ ( \\mathbf { P } _ { n } , \\mathbf { Q } _ { n } , \\mathbf { a } _ { n } ) \\} _ { n = 1 } ^ { N }$ are given. ",
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+        "type": "text",
+        "text": "An overview of the two neural network models are shown in Figure 1. Both models consist of three layers: (1) An LSTM preprocessing layer that preprocesses the passage and the question using LSTMs. (2) A match-LSTM layer that tries to match the passage against the question. (3) An Answer Pointer (Ans-Ptr) layer that uses Ptr-Net to select a set of tokens from the passage as the answer. The difference between the two models only lies in the third layer. ",
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+        "text": "LSTM Preprocessing Layer ",
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+        "text": "The purpose for the LSTM preprocessing layer is to incorporate contextual information into the representation of each token in the passage and the question. We use a standard one-directional LSTM (Hochreiter & Schmidhuber, 1997) to process the passage 4 and the question separately, as shown below: ",
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+        "img_path": "images/3f9cd4df82b63f2ffd05b19720a358baf36abb54931dce857110d2c0f3d68670.jpg",
+        "text": "$$\n{ \\bf H } ^ { \\mathrm { p } } = \\overrightarrow { L S T M } ( { \\bf P } ) , ~ { \\bf H } ^ { \\mathrm { q } } = \\overrightarrow { L S T M } ( { \\bf Q } ) .\n$$",
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+        "type": "text",
+        "text": "The resulting matrices $\\mathbf { H } ^ { \\mathrm { p } } \\in \\mathbb { R } ^ { l \\times P }$ and $\\mathbf { H } ^ { \\mathrm { q } } \\in \\mathbb { R } ^ { l \\times Q }$ are hidden representations of the passage and the question, where $l$ is the dimensionality of the hidden vectors. In other words, the $i ^ { \\mathrm { { t h } } }$ column vector $\\mathbf { h } _ { i } ^ { \\mathrm { p } }$ (or $\\mathbf { h } _ { i . } ^ { \\mathrm { q } . }$ ) in $\\mathbf { H } ^ { \\mathrm { p } }$ (or $\\mathbf { H } ^ { \\mathrm { q } }$ ) represents the $i ^ { \\mathrm { { t h } } }$ token in the passage (or the question) together with some contextual information from the left. ",
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+        "type": "text",
+        "text": "Match-LSTM Layer ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We apply the match-LSTM model (Wang & Jiang, 2016) proposed for textual entailment to our machine comprehension problem by treating the question as a premise and the passage as a hypothesis. The match-LSTM sequentially goes through the passage. At position $i$ of the passage, it first uses the standard word-by-word attention mechanism to obtain attention weight vector $\\vec { \\alpha } _ { i } \\in \\mathbb { R } ^ { 1 \\times Q }$ as follows: ",
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+        "text": "$$\n\\begin{array} { r c l } { \\overrightarrow { \\mathbf { G } } _ { i } } & { = } & { \\mathrm { t a n h } ( \\mathbf { W } ^ { \\ P } \\mathbf { H } ^ { \\ P } + ( \\mathbf { W } ^ { \\ P } \\mathbf { h } _ { i } ^ { \\ P } + \\mathbf { W } ^ { \\Gamma } \\overrightarrow { \\mathbf { h } } _ { i - 1 } ^ { \\top } + \\mathbf { b } ^ { \\ P } ) \\otimes \\mathbf { e } _ { Q } ) , } \\\\ { \\overrightarrow { \\alpha } _ { i } } & { = } & { \\mathrm { s o f t m a x } ( \\mathbf { w } ^ { \\top } \\overrightarrow { \\mathbf { G } } _ { i } + b \\otimes \\mathbf { e } _ { Q } ) , } \\end{array}\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "where $\\mathbf { W } ^ { \\mathrm { q } } , \\mathbf { W } ^ { \\mathrm { p } } , \\mathbf { W } ^ { \\mathrm { r } } \\in \\mathbb { R } _ { \\cdot } ^ { l \\times l }$ , $\\mathbf { b } ^ { \\mathrm { p } }$ , $\\mathbf { w } \\in \\mathbb { R } ^ { l \\times 1 }$ and $b \\in \\mathbb { R }$ are parameters to be learned, $\\vec { \\bf G } _ { i } \\in \\mathbb { R } ^ { l \\times Q }$ is the intermediate result, $\\vec { \\bf h } _ { i - 1 } ^ { \\mathrm { r } } \\in \\mathbb { R } ^ { l \\times 1 }$ is the hidden vector of the one-directional match-LSTM (to be explained below) at position $i - 1$ , and the outer product $\\left( \\cdot \\otimes \\mathbf { e } _ { Q } \\right)$ produces a matrix or row vector by repeating the vector or scalar on the left for $Q$ times. ",
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+        "type": "text",
+        "text": "Essentially, the resulting attention weight $\\overrightarrow { \\alpha } _ { i , j }$ above indicates the degree of matching between the $i ^ { \\mathrm { { t h } } }$ token in the passage with the $j ^ { \\mathrm { t h } }$ token in the question. Next, we use the attention weight vector $\\vec { \\alpha _ { i } }$ to obtain a weighted version of the question and combine it with the current token of the passage to form a vector $\\overline { { \\mathbf { z } } } _ { i }$ : ",
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+        "img_path": "images/ad4e851c43d11f470f83820054d3db8a981c4051a48d7f6eedc81045d29b882f.jpg",
+        "text": "$$\n\\begin{array} { r } { \\vec { \\bf z } _ { i } = \\left[ \\frac { { \\bf h } _ { i } ^ { \\mathrm { p } } } { { \\bf H } ^ { \\mathrm { q } } \\vec { \\alpha } _ { i } ^ { \\top } } \\right] , } \\end{array}\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "where $\\mathbf { H } ^ { \\mathrm { q } } \\ \\in \\ \\mathbb { R } ^ { l \\times Q } , \\ \\vec { \\alpha } _ { i } \\ \\in \\ \\mathbb { R } ^ { 1 \\times Q }$ and $\\mathbf { h } _ { i } ^ { \\mathsf { p } } \\in \\mathbb { R } ^ { l \\times 1 }$ . This vector $\\vec { \\textbf { z } } _ { i }$ is fed into a standard onedirectional LSTM to form our so-called match-LSTM: ",
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+    {
+        "type": "equation",
+        "img_path": "images/402b8b6826adbd8b294f810ac51cf4b6949c576ae0e1128f22e003c37310533b.jpg",
+        "text": "$$\n\\begin{array} { r l r } { \\overrightarrow { \\mathbf { h } } _ { i } ^ { \\mathrm { r } } } & { = } & { \\overrightarrow { L S T M } ( \\overrightarrow { \\mathbf { z } } _ { i } , \\overrightarrow { \\mathbf { h } } _ { i - 1 } ^ { \\mathrm { r } } ) , } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\vec { \\bf h } _ { i } ^ { \\mathrm { r } } \\in \\mathbb { R } ^ { l \\times 1 }$ ",
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+        "type": "text",
+        "text": "We further build a similar match-LSTM in the reverse direction. The purpose is to obtain a representation that encodes the contexts from both directions for each token in the passage. ",
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+        "type": "text",
+        "text": "Let $\\vec { \\bf H ^ { r } } \\in \\mathbb { R } ^ { l \\times P }$ represent the hidden states $[ \\vec { \\bf h } _ { 1 } ^ { \\mathrm { r } } , \\vec { \\bf h } _ { 2 } ^ { \\mathrm { r } } , \\ldots , \\vec { \\bf h } _ { P } ^ { \\mathrm { r } } ]$ and $\\smash { \\mathbf { \\overleftarrow { H } ^ { r } } } \\in \\mathbb { R } ^ { l \\times P }$ represent $[ \\overleftarrow { \\mathbf { h } } _ { 1 } ^ { \\mathrm { r } } , \\overleftarrow { \\mathbf { h } } _ { 2 } ^ { \\mathrm { r } } , \\ldots , \\overleftarrow { \\mathbf { h } } _ { P } ^ { \\mathrm { r } } ]$ , the hidden states of match-LSTM in the reverse direction. We define ${ \\bf H } ^ { \\mathrm { r } } \\in  { \\bf \\Phi }$ $\\mathbb { R } ^ { 2 l \\times P }$ as the concatenation of the two: ",
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+        "type": "equation",
+        "img_path": "images/c7d08d45a72385d65f2e1ca6402ab62a222098691c3f07bf1b8dbe214a84b991.jpg",
+        "text": "$$\n\\begin{array} { r l r } { \\bf { H } ^ { \\mathrm { r } } } & { = } & { \\left[ \\begin{array} { l } { \\vec { \\bf { H } } ^ { \\mathrm { r } } } \\\\ { \\vec { \\bf { H } } ^ { \\mathrm { r } } } \\end{array} \\right] . } \\end{array}\n$$",
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+        "type": "text",
+        "text": "Answer Pointer Layer ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The top layer, the Answer Pointer (Ans-Ptr) layer, is motivated by the Pointer Net introduced by Vinyals et al. (2015). This layer uses the sequence $\\mathbf { H } ^ { \\mathrm { r } }$ as input. Recall that we have two different models: The sequence model produces a sequence of answer tokens but these tokens may not be consecutive in the original passage. The boundary model produces only the start token and the end token of the answer, and then all the tokens between these two in the original passage are considered to be the answer. We now explain the two models separately. ",
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+    {
+        "type": "text",
+        "text": "The Sequence Model: Recall that in the sequence model, the answer is represented by a sequence of integers $\\mathbf { a } = ( a _ { 1 } , a _ { 2 } , \\ldots )$ indicating the positions of the selected tokens in the original passage. The Ans-Ptr layer models the generation of these integers in a sequential manner. Because the length of an answer is not fixed, in order to stop generating answer tokens at certain point, we allow each $a _ { k }$ to take up an integer value between 1 and $P + 1$ , where $P + 1$ is a special value indicating the end of the answer. Once $a _ { k }$ is set to be $P + 1$ , the generation of the answer stops. ",
+        "bbox": [
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+        "type": "text",
+        "text": "In order to generate the $k ^ { \\mathrm { { t h } } }$ answer token indicated by $a _ { k }$ , first, the attention mechanism is used again to obtain an attention weight vector $\\beta _ { k } \\ \\in \\ \\mathbb { R } ^ { 1 \\times \\bar { ( } P + 1 ) }$ , where $\\beta _ { k , j }$ $( 1 \\leq j \\leq P + 1 )$ is the probability of selecting the $j ^ { \\mathrm { t h } }$ token from the passage as the $k ^ { \\mathrm { { t h } } }$ token in the answer, and $\\beta _ { k , ( P + 1 ) }$ is the probability of stopping the answer generation at position $k$ . $\\beta _ { k }$ is modeled as follows: ",
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+    {
+        "type": "equation",
+        "img_path": "images/0b0551b6d8c0c3e9ceace7f2beb10b0e541b2db8093eaf5e13c6657cb124a49d.jpg",
+        "text": "$$\n\\begin{array} { r c l } { \\mathbf { F } _ { k } } & { = } & { \\operatorname { t a n h } ( \\mathbf { V } \\widetilde { \\mathbf { H } } ^ { \\mathrm { r } } + ( \\mathbf { W } ^ { \\mathrm { a } } \\mathbf { h } _ { k - 1 } ^ { \\mathrm { a } } + \\mathbf { b } ^ { a } ) \\otimes \\mathbf { e } _ { ( P + 1 ) } ) , } \\\\ { \\beta _ { k } } & { = } & { \\operatorname { s o f t m a x } ( \\mathbf { v } ^ { \\mathsf { T } } \\mathbf { F } _ { k } + c \\otimes \\mathbf { e } _ { ( P + 1 ) } ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where $\\widetilde { \\mathbf { H } } ^ { \\mathrm { r } } \\in \\mathbb { R } ^ { 2 l \\times ( P + 1 ) }$ is the concatenation of $\\mathbf { H } ^ { \\mathrm { r } }$ with a zero vector, defined as $\\widetilde { \\bf H } ^ { \\mathrm { r } } = [ { \\bf H } ^ { \\mathrm { r } } ; { \\bf 0 } ]$ , $\\mathbf { V } \\in \\mathbb { R } ^ { l \\times 2 l } , \\mathbf { W } ^ { \\mathrm { a } } \\in \\mathbb { R } ^ { l \\times l } , \\mathbf { b } ^ { a } , \\mathbf { v } \\in \\mathbb { R } ^ { l \\times 1 }$ and $c \\in \\mathbb { R }$ are parameters to be learned, $\\mathbf { F } _ { k } \\in \\mathbb { R } ^ { l \\times ( P + 1 ) }$ is the intermediate result, $\\left( \\cdot \\otimes { \\mathbf e } _ { \\left( P + 1 \\right) } \\right)$ follows the same definition as before, and $\\mathbf { h } _ { k - 1 } ^ { \\mathrm { a } } \\in \\mathbb { R } ^ { l \\times 1 }$ is the hidden vector at position $k - 1$ of an answer LSTM as defined below: ",
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+    {
+        "type": "equation",
+        "img_path": "images/3d535e2f9291de4c96efecec12b43810d04842e269511473ee8552d063b5a581.jpg",
+        "text": "$$\n\\mathbf { h } _ { k } ^ { \\mathrm { a } } = \\overrightarrow { L S T M } ( \\widetilde { \\mathbf { H } } ^ { \\mathrm { r } } \\beta _ { k } ^ { \\intercal } , \\mathbf { h } _ { k - 1 } ^ { \\mathrm { a } } ) .\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "We can then model the probability of generating the answer sequence as ",
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+        "type": "equation",
+        "img_path": "images/7af02595c4cabfba2eed3ff69c83c808ef375253d0783fee8f78b1891b035f98.jpg",
+        "text": "$$\n\\begin{array} { l l l } { p ( { \\bf a } | { \\bf H ^ { r } } ) } & { = } & { \\displaystyle \\prod _ { k } p ( a _ { k } | a _ { 1 } , a _ { 2 } , \\ldots , a _ { k - 1 } , { \\bf H ^ { r } } ) , } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "and ",
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+    {
+        "type": "equation",
+        "img_path": "images/2a6d21719e8af2bb784842c098c3ea59cd124fe6e4403fd0c9f1336359ad17ee.jpg",
+        "text": "$$\n\\begin{array} { r c l } { p ( a _ { k } = j | a _ { 1 } , a _ { 2 } , \\ldots , a _ { k - 1 } , \\mathbf { H } ^ { \\mathrm { r } } ) } & { = } & { \\beta _ { k , j } . } \\end{array}\n$$",
+        "text_format": "latex",
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "To train the model, we minimize the following loss function based on the training examples: ",
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+    {
+        "type": "equation",
+        "img_path": "images/0f2e784d1470c2da81246f67876aac0bdd1271025ec52b638baf190189ad6f48.jpg",
+        "text": "$$\n- \\sum _ { n = 1 } ^ { N } \\log p ( \\mathbf { a } _ { n } | \\mathbf { P } _ { n } , \\mathbf { Q } _ { n } ) .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "The Boundary Model: The boundary model works in a way very similar to the sequence model above, except that instead of predicting a sequence of indices $a _ { 1 } , a _ { 2 } , \\dotsc$ , we only need to predict two indices $a _ { s }$ and $a _ { \\mathrm { e } }$ . So the main difference from the sequence model above is that in the boundary model we do not need to add the zero padding to $\\mathbf { H } ^ { \\mathrm { r } }$ , and the probability of generating an answer is simply modeled as ",
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+    {
+        "type": "equation",
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+        "text": "$$\n\\begin{array} { r l r } { p ( { \\bf a } | { \\bf H ^ { r } } ) } & { = } & { p ( a _ { \\mathrm { s } } | { \\bf H ^ { r } } ) p ( a _ { \\mathrm { e } } | a _ { \\mathrm { s } } , { \\bf H ^ { r } } ) . } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "As this boundary model could point to a span covering too many tokens without any restriction, we try to manually limit the length of the predicted span and then search the span with the highest probability computed by $p ( \\mathbf { a } _ { s } ) \\times p ( \\mathbf { a } _ { e } | \\mathbf { a } _ { s } )$ as the answer. ",
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+    {
+        "type": "text",
+        "text": "3 EXPERIMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section, we present our experiment results and perform some analyses to better understand how our models works. ",
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+    {
+        "type": "text",
+        "text": "3.1 DATA ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We use the Stanford Question Answering Dataset (SQuAD) v1.1 and the human-generated Microsoft MAchine Reading COmprehension (MSMARCO) dataset v1.1 to conduct our experiments. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Passages in SQuAD come from 536 articles in Wikipedia covering a wide range of topics. Each passage is a single paragraph from a Wikipedia article, and each passage has around 5 questions associated with it. In total, there are 23,215 passages and 107,785 questions. The data has been split into a training set (with 87,599 question-answer pairs), a development set (with 10,570 questionanswer pairs) and a hidden test set. ",
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+    {
+        "type": "text",
+        "text": "For the MSMARCO dataset, the questions are user queries issued to the Bing search engine, the context passages are real Web documents and the answers are human-generated. We select the span that has the highest F1 score with the gold standard answer for training and only predict the span in the passages during evaluation. The data has been split into a training set (82326 pairs), a development set (10047 pairs) and a test set (9650 pairs). ",
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+    {
+        "type": "text",
+        "text": "3.2 EXPERIMENT SETTINGS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We first tokenize all the passages, questions and answers. We use word embeddings from GloVe (Pennington et al., 2014) to initialize the model. Words not found in GloVe are initialized as zero vectors. The word embeddings are not updated during the training of the model. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The dimensionality $l$ of the hidden layers is set to be 150. We use ADAMAX (Kingma & Ba, 2015) with the coefficients $\\beta _ { 1 } = 0 . 9$ and $\\beta _ { 2 } = 0 . 9 9 9$ to optimize the model. Each update is computed through a minibatch of 30 instances. We do not use L2-regularization. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For the SQuAD dataset, the performance is measured by two metrics: percentage of exact match with the ground truth answers and word-level F1 score when comparing the tokens in the predicted answers with the tokens in the ground truth answers. Note that in the development set and the test set each question has around three ground truth answers. F1 scores with the best matching answers are used to compute the average F1 score. For the MSMARCO dataset, the metrics in the official tool of MSMARCO evaluation are BLEU-1/2/3/4 and Rouge-L, which are widely used in many domains. ",
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+    {
+        "type": "text",
+        "text": "3.3 RESULTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The SQuAD and MSMARCO results of our models as well as the results of the baselines (Rajpurkar et al., 2016; Yu et al., 2016) are shown in Table 2. For the “LSTM with Ans-Ptr” models, they are the experiments with the ablation of attention mechanism in match-LSTM. Specifically, we use the final representation of the question to replace the weighted sum of the question representations. For the MSMARCO dataset, as the context for each question is consisted of around 10 documents, the “Golden Passage” is to directly use the human labeled document which could answer the question as the prediction. ",
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+    {
+        "type": "table",
+        "img_path": "images/56f436d905695a601721ea66352f6537f9516eb9215c34fe7400d842fea8e4f8.jpg",
+        "table_caption": [
+            "Table 2: Experiment Results on SQuAD and MSMARCO datasets. Here “LSTM with Ans-Ptr” removes the attention mechanism in match-LSTM (mLSTM) by using the final state of the LSTM for the question to replace the weighted sum of all the states. Our best boundary model is the further tuned model and its ablation study is shown in Table 4. “en” refers to ensemble method. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"4\">SQuAD</td><td>MSMARCO</td></tr><tr><td></td><td colspan=\"2\">Exact Match</td><td colspan=\"2\">F1</td><td>BLEU1/2/3/4 /Rouge-L</td></tr><tr><td></td><td>Dev</td><td>Test</td><td>Dev</td><td>Test</td><td>Dev&amp;Test</td></tr><tr><td>Human</td><td>80.3</td><td>77.0</td><td>90.5</td><td>86.8</td><td>-&amp; 46/-l-l- /47</td></tr><tr><td>Golden Passage</td><td>-</td><td>-</td><td>-</td><td>1</td><td>19.6/18.8/18.1/17.5/32.3&amp;-</td></tr><tr><td>LR (Rajpurkar et al., 2016)</td><td>40.0</td><td>40.4</td><td>51.0</td><td>51.0</td><td></td></tr><tr><td>DCR (Yu et al., 2016)</td><td>62.5</td><td>62.5</td><td>71.2</td><td>71.0</td><td></td></tr><tr><td>LSTM with Ans-Ptr (Sequence)</td><td>37.7</td><td>-</td><td>48.5</td><td>-</td><td>10.3/7.2 /5.6 /4.6 /21.6&amp;-</td></tr><tr><td>LSTM with Ans-Ptr (Boundary)</td><td>45.2</td><td></td><td>55.3</td><td></td><td>32.0 /25.3/22.2/20.4/32.3&amp;-</td></tr><tr><td>mLSTM with Ans-Ptr (Sequence)</td><td>54.4</td><td>=</td><td>68.2</td><td>1</td><td>12.5 /9.2 /7.5 /6.5 /22.5 &amp; -</td></tr><tr><td>mLSTM with Ans-Ptr (Boundary)</td><td>63.0</td><td></td><td>72.7</td><td>=</td><td>32.9 /26.4/23.2/21.6/33.8&amp;-</td></tr><tr><td>Our best boundary model</td><td>67.0</td><td>66.9</td><td>77.2</td><td>77.1</td><td>40.1/33.3/30.1/28.2/37.2 &amp; 40.7 / 33.9 / 30.6 /28.7 / 37.3</td></tr><tr><td>mLSTM with Ans-Ptr (Boundary+en)</td><td>67.6</td><td>67.9</td><td></td><td></td><td></td></tr><tr><td>Our best boundary model (en)</td><td>71.3</td><td>72.6</td><td>76.8 80.0</td><td>77.0 80.8</td><td></td></tr></table>",
+        "bbox": [
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+    {
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+        "img_path": "images/126b7f50d861ff2b24261f0ed8a17729f946a6a75d973aa153a6a0f68b3cfd0b.jpg",
+        "table_caption": [
+            "Table 3: Statistical analysis on the development datasets. #w: number of words on average; P: passage; Q: question; A: answer; raw: raw data from the development dataset; seq/bou: the answers generated by the sequence/boundary models with match-LSTM. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>SQuAD #w in A/Q/P</td><td></td><td>MSMARCO #w in A/Q/P</td></tr><tr><td>raw</td><td>3.1/11/141</td><td>16.3/6/667</td></tr><tr><td>seq</td><td>2.4/-/-</td><td>6.7 /-/-</td></tr><tr><td>bou</td><td>3.0/-/-</td><td>15.7/ -/ -</td></tr></table>",
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 4: Ablation study for our best boundary model on the development datasets. Our best model is a further tuned boundary model by considering “bi-Ans-Ptr” which adds bidirectional answer pointer, “deep” which adds another twolayer bi-directional LSTMs between the match-LSTM and the Answer Pointer layers, and “elem” which adds elementwise comparison , $( \\mathbf { h } _ { i } ^ { \\mathrm { p } } - \\mathbf { H } ^ { \\mathrm { q } } \\alpha _ { i } ^ { \\mathsf { T } } )$ and $( \\mathbf { h } _ { i } ^ { \\mathrm { p } } \\odot \\mathbf { H } ^ { \\mathrm { q } } \\alpha _ { i } ^ { \\mathsf { T } } )$ , into Eqn 3. “-pre-LSTM” refers to removing the pre-processing layer. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>SQuAD EM&amp;F1</td><td>MSMARCO BLEU1/2/3/4&amp;Rouge-L</td></tr><tr><td>Best model</td><td>67.0 &amp; 77.2</td><td>40.1/33.3/30.1/28.2 &amp; 37.2</td></tr><tr><td>-bi-Ans-Ptr</td><td>66.5 &amp; 76.8</td><td>39.9/32.8/29.6/27.9 &amp; 36.7</td></tr><tr><td>-deep</td><td>65.9 &amp; 75.8</td><td>39.6/32.6/29.4/27.4&amp; 35.9</td></tr><tr><td>-elem</td><td>65.2 &amp; 75.4</td><td>38.1/31.4/28.3/26.5 &amp; 35.5</td></tr><tr><td>-pre-LSTM</td><td>64.0 &amp; 72.9</td><td>39.6/32.8/29.8/27.7&amp; 36.3</td></tr></table>",
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+    {
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+    {
+        "type": "text",
+        "text": "From the results in Table 2, we can see that the boundary model could clearly outperform the sequence model in a big margin on both datasets. We hypothesis that the sequence model is more likely to stop word generation earlier, and the boundary model can somehow overcome this problem. We have a statistical analysis on the answers generated by our sequence and boundary models shown in Table 3. We can see that the length of the answers generated by the sequence model is much shorter than the ground truth. Especially for the MSMARCO task where the answers are usually much longer, the sequence model could only generate 7 words on average, while the ground truth answers are 16 on average and the boundary model could generate nearly the same number of words with the ground truth. Several answers generated by our models are shown in Appendix A. From Table 2, we can also see that the performance gets poorer by removing the attention mechanism in match-LSTM, while for the MSMARCO dataset, the attention mechanism effects less, with no more than 2 percent reduction in BLEU and Rouge-L scores by attention mechanism ablation. ",
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+    {
+        "type": "text",
+        "text": "Based on the effectiveness of boundary pointer and match-LSTM, we conduct further exploration of the boundary model by adding element-wise comparison $( \\mathbf { h } _ { i } ^ { \\mathrm { p } } { - } \\mathbf { H } ^ { \\mathrm { q } } \\alpha _ { i } ^ { \\mathsf { T } } )$ and $( \\mathbf { h } _ { i } ^ { \\mathrm { p } } \\odot \\mathbf { H } ^ { \\mathrm { q } } \\alpha _ { i } ^ { \\mathsf { T } } )$ into Eqn 3 in match-LSTM layer, adding 2 more bi-directional LSTM layers between match-LSTM and Ans-Ptr layers, and adding bi-directional Ans-Ptr. We show the ablation study of this further tuned model in Table 4. We can see that adding element-wise matching could make the biggest improvement for our boundary model. We also try to remove the phrase-level representation by removing the pre-process LSTM and using the word-level representations as the inputs of match-LSTM. Interestingly, we find the phrase-level representation effects little on the MSMARCO task. ",
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+    {
+        "type": "text",
+        "text": "Overall, we can see that both of our match-LSTM models have clearly outperformed the logistic regression model by Rajpurkar et al. (2016), which relies on carefully designed features. The improvement of our models over the logistic regression model shows that our end-to-end neural network models without much feature engineering are very effective on these tasks and datasets. Our boundary model also outperformed the DCR model (Yu et al., 2016), which maximizes the probability of the gold standard span from all the candidate spans through a neural network structure. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3.4 FURTHER ANALYSES ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "image",
+        "img_path": "images/864acbb39a507e6729b31bfe92a1fcef705d8bb019c02b3fba961e7dcf7aa7e5.jpg",
+        "image_caption": [
+            "Figure 2: Performance breakdown by answer lengths and question types on SQuAD development dataset. Top: Plot (1) shows the performance of our two models (where $s$ refers to the sequence model , $^ b$ refers to the boundary model, and $e$ refers to the ensemble boundary model) over answers with different lengths. Plot (2) shows the numbers of answers with different lengths. Bottom: Plot (3) shows the performance our the two models on different types of questions. Plot (4) shows the numbers of different types of questions. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "To better understand the strengths and weaknesses of our models, we perform some further analyses of the results below. ",
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+    {
+        "type": "text",
+        "text": "First, we suspect that longer answers are harder to predict. To verify this hypothesis, we analysed the performance in terms of both exact match and F1 score with respect to the answer length on the development set, as shown in Figure 2. For example, for questions whose answers contain more than 9 tokens, the F1 score of the boundary model drops to around $55 \\%$ and the exact match score drops to only around $30 \\%$ , compared to the F1 score and exact match score of close to $72 \\%$ and $67 \\%$ , respectively, for questions with single-token answers. And that supports our hypothesis. ",
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+    {
+        "type": "image",
+        "img_path": "images/eb921479c5383e25d5c35305dd8dad9a57ee199afeccc9f323e1c272c7d45db1.jpg",
+        "image_caption": [],
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/cea1279cd9a9594b6feb7c27a9741a652cf6131a826623c46358ea527f2b9fd8.jpg",
+        "image_caption": [
+            "Answer: European Parliament and the Council of the European Union ",
+            "Figure 3: Visualization of the attention weights $\\alpha$ for four questions. The first three questions share the same paragraph. The title is the answer predicted by our model. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            458,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Next, we analyze the performance of our models on different groups of questions, as shown in Figure 2. We use a crude way to split the questions into different groups based on a set of question words we have defined, including “what,” “how,” “who,” “when,” “which,” “where,” and “why.” These different question words roughly refer to questions with different types of answers. For example, “when” questions look for temporal expressions as answers, whereas “where” questions look for locations as answers. According to the performance on the development dataset, our models work the best for “when” questions. This may be because in this dataset temporal expressions are relatively easier to recognize. Other groups of questions whose answers are noun phrases, such as “what” questions, “which” questions and “where” questions, also get relatively better results. On the other hand, “why” questions are the hardest to answer. This is not surprising because the answers to “why” questions can be very diverse, and they are not restricted to any certain type of phrases. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Finally, we would like to check whether the attention mechanism used in the match-LSTM layer is effective in helping the model locate the answer. We show the attention weights $\\alpha$ in Figure 3. In the figure the darker the color is the higher the weight is. We can see that some words have been well aligned based on the attention weights. For example, the word “German” in the passage is aligned well to the word “language” in the first question, and the model successfully predicts “German” as the answer to the question. For the question word “who” in the second question, the word “teacher” actually receives relatively higher attention weight, and the model has predicted the phrase “Martin Sekulic” after that as the answer, which is correct. For the third question that starts with “why”, the attention weights are more evenly distributed and it is not clear which words have been aligned to “why”. For the last question, we can see that the word knowledge needed for generating the answer can also be detected by match-LSTM. For example, the words “European”, “Parliament”, “Council”, “European” and “Union” have higher attention weights on “governing” in the question. Even though our models can solve this type of questions, they are still not able to solve the questions that need multi-sentences reasoning. More answers generated by our models for the questions related to different kinds of reasoning are shown in Appendix B. ",
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+    },
+    {
+        "type": "text",
+        "text": "",
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+    },
+    {
+        "type": "text",
+        "text": "4 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Machine comprehension of text has gained much attention in recent years, and increasingly researchers are building data-drive, end-to-end neural network models for the task. We will first review the recently released datasets and then some end-to-end models on this task. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.1 DATASETS ",
+        "text_level": 1,
+        "bbox": [
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+            362
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "A number of datasets for studying machine comprehension were created in Cloze style by removing a single token from a sentence in the original corpus, and the task is to predict the missing word. For example, Hermann et al. (2015) created questions in Cloze style from CNN and Daily Mail highlights. Hill et al. (2016) created the Children’s Book Test dataset, which is based on children’s stories. Cui et al. (2016) released two similar datasets in Chinese, the People Daily dataset and the Children’s Fairy Tale dataset. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Instead of creating questions in Cloze style, a number of other datasets rely on human annotators to create real questions. Richardson et al. (2013) created the well-known MCTest dataset and Tapaswi et al. (2016) created the MovieQA dataset. In these datasets, candidate answers are provided for each question. Similar to these two datasets, the SQuAD dataset (Rajpurkar et al., 2016) was also created by human annotators. Different from the previous two, however, the SQuAD dataset does not provide candidate answers, and thus all possible subsequences from the given passage have to be considered as candidate answers. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Besides the datasets above, there are also a few other datasets created for machine comprehension, such as WikiReading dataset (Hewlett et al., 2016) and bAbI dataset (Weston et al., 2016), but they are quite different from the datasets above in nature. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.2 END-TO-END NEURAL NETWORK MODELS FOR MACHINE COMPREHENSION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "There have been a number of studies proposing end-to-end neural network models for machine comprehension. A common approach is to use recurrent neural networks (RNNs) to process the given text and the question in order to predict or generate the answers (Hermann et al., 2015). Attention mechanism is also widely used on top of RNNs in order to match the question with the given passage (Hermann et al., 2015; Chen et al., 2016). Given that answers often come from the given passage, Pointer Network has been adopted in a few studies in order to copy tokens from the given passage as answers (Kadlec et al., 2016; Trischler et al., 2016). Compared with existing work, we use match-LSTM to match a question and a given passage, and we use Pointer Network in a different way such that we can generate answers that contain multiple tokens from the given passage. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Memory Networks (Weston et al., 2015) have also been applied to machine comprehension (Sukhbaatar et al., 2015; Kumar et al., 2016; Hill et al., 2016), but its scalability when applied to a large dataset is still an issue. In this work, we did not consider memory networks for the SQuAD/MSMARCO datasets. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "The setting of visual question answering (Antol et al., 2015) is quite similar to machine comprehension, while their answers are usually very short. So the sequence order of the word-level attention representation used to align the figure and the question(Xu & Saenko, 2016; Fukui et al., 2016; Lu et al., 2016), are not used in VQA. While our model focus on the word-by-word attention and use ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "LSTM to concatenate the aligned pairs and that would be helpful to generate a longer sequence as answer. ",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSIONS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In this paper, We developed two models for the machine comprehension problem defined in the Stanford Question Answering (SQuAD) and A Human-Generated MAchine Reading COmprehension (MSMARCO) datasets, both making use of match-LSTM and Pointer Network. Experiments on the SQuAD and MSMARCO datasets showed that our second model, the boundary model, could achieve a performance close to the state-of-the-art performance on the SQuAD dataset and achieved the state-of-the-art on the MSMARCO dataset. We also show the boundary model could overcome the early stop prediction problem of the sequence model. ",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In the future, we plan to look further into the different types of questions and focus on those questions which currently have low performance, such as the “why’ questions and multi-sentences related questions. We also plan to test how our models could be applied to other machine comprehension datasets. ",
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+    {
+        "type": "text",
+        "text": "6 ACKNOWLEDGMENTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This research is supported by the National Research Foundation, Prime Ministers Office, Singapore under its International Research Centres in Singapore Funding Initiative. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We thank Pranav Rajpurkar for testing our model on the hidden test dataset and Percy Liang for helping us with the Dockerfile for Codalab. ",
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+    {
+        "type": "text",
+        "text": "A APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            297,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We show the predictions our boundary and sequence models on two cases from two datasets in Table 5. It can be seen that the sequence model is more likely to predict a shorter sequence which is the problem of early stop prediction. ",
+        "bbox": [
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+            133,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/39d7f833d8f92ef64474da80edfe2befc97be4747fec0ea0c8880c1546f4ba15.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 5: Prediction samples for sequence and boundary models. The first case is sampled from SQuAD dataset and the second is sampled from MSMARCO dataset. "
+        ],
+        "table_body": "<table><tr><td>(1) Context</td><td>Asopposed to broadcasts of primetime series,CBS broadcast special episodes of its late night talk shows as its lead-out programs for Super Bowl 5O, beginning with a special episode of The Late Show with Stephen Colbert following the game.</td></tr><tr><td>Question (Syntactic) Golden Anwser match-LSTM (Sequence)</td><td>What CBS show followed the Super Bowl? The Late Show with Stephen Colbert The Late Show The Late Show with Stephen Colbert</td></tr><tr><td>match-LSTM (Boundary) (2) Context</td><td>Urinalysis is a test that evaluates a sample of your urine.Urinalysis is used to detect and assess a wide range of disorders,such as uri- nary tract infection, kidney disease and diabetes. Urinalysis involves examining the appearance,concentration and content of urine.Abnor- mal urinalysis results may point to a disease or illness.For example,</td></tr><tr><td>Query</td><td>a urinary tract infection can make urine look cloudy instead of clear. Increased levels of protein in urine can be a sign of kidney disease. what can urinalysis detect?</td></tr><tr><td>Golden Anwser</td><td>Detect and assess a wide range of disorders,such as urinary tract infec- tion, kidney disease and diabetes.</td></tr><tr><td>match-LSTM (Sequence) match-LSTM (Boundary)</td><td>Urinalysis Urinalysis is used to detect and assess a wide range of disorders,such as urinary tract infection,kidney disease and diabetes</td></tr></table>",
+        "bbox": [
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+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "B APPENDIX ",
+        "text_level": 1,
+        "bbox": [
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+            117
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "We show how four different models work on different type of questions in SQuAD dataset through Table 6. After the analysis of a hundred cases, we see that our models are not able to solve the questions that need multi-sentences reasoning. And the model without attention mechanism has less power to identify the important key word like the third case shown in Table 6. ",
+        "bbox": [
+            173,
+            133,
+            825,
+            189
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "table",
+        "img_path": "images/67bfb16ece01e51aa5431192d4d4d569a73f4ea205b3b1e600285fca4b21868b.jpg",
+        "table_caption": [
+            "Table 6: Different types of reasoning samples in SQuAD dataset. “match-LSTM” refers to the “match-LSTM with Ans-Ptr” and “LSTM” refers to the “LSTM with Ans-Ptr” which is the ablation of attention mechanism in match-LSTM. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>(1) Context</td><td>The Rankine cycle is sometimes referred to as a practical Carnot cycle be- cause,when an efficient turbine is used, the TS diagram begins to resemble the</td></tr><tr><td>Question (Synonymy) Golden Anwser</td><td>Carnot cycle. What is the Rankine cycle sometimes called? practical Carnot cycle</td></tr><tr><td>LSTM (Sequence) match-LSTM (Sequence)</td><td>Carnot cycle</td></tr><tr><td>LSTM (Boundary) match-LSTM (Boundary)</td><td>Carnot cycle practical Carnot cycle</td></tr><tr><td>(2) Context</td><td>Carnot cycle</td></tr><tr><td></td><td>While the Commission has a monopoly on initiating legislation,the European Parliament and the Council of the European Union have powers of amend-</td></tr><tr><td></td><td>ment and veto during the legislative process.</td></tr><tr><td>Question (Knowledge) Golden Anwser</td><td>Which two governing bodies have legislative veto power? the European Parliament and the Council of the European Union</td></tr><tr><td>LSTM (Sequence)</td><td>European Parliament and the Council of the European Union</td></tr><tr><td>match-LSTM (Sequence) LSTM (Boundary)</td><td>European Parliament and the Council of the European Union</td></tr><tr><td>match-LSTM (Boundary)</td><td>European Parliament and the Council of the European Union</td></tr><tr><td>(3) Context</td><td>European Parliament and the Council of the European Union</td></tr><tr><td></td><td>Current faculty include the anthropologist Marshall Sahlins, historian Dipesh Chakrabarty,... Shakespeare scholar David Bevington, and renowned political</td></tr><tr><td>Question (Syntactic) Golden Anwser</td><td>scientists John Mearsheimer and Robert Pape. What Shakespeare scholar is currently on the university&#x27;s faculty?</td></tr><tr><td>LSTM (Sequence)</td><td>David Bevington Marshall Sahlins</td></tr><tr><td>match-LSTM (Sequence) LSTM(Boundary)</td><td>David Bevington Marshall Sahlins</td></tr><tr><td>match-LSTM (Boundary) (4) Context</td><td>David Bevington</td></tr><tr><td></td><td>The V&amp;A Theatre &amp; Performance galleries,formerly the Theatre Museum, opened in March 2Oo9.The collections are stored by the V&amp;A,and are available for research,exhibitions and other shows.They hold the UK&#x27;s biggest national</td></tr><tr><td></td><td>collection of material about live performance in the UK since Shakespeare&#x27;s day,covering drama, dance,musical theatre, circus,music hall,rock and pop, and most other forms of live entertainment.</td></tr><tr><td>Question (Reasoning) Golden Anwser</td><td>What collection does the V&amp;A Theatre &amp; Performance galleries hold? material about live performance</td></tr><tr><td>LSTM (Sequence) match-LSTM (Sequence) LSTM (Boundary)</td><td>Theatre the Theatre Museum</td></tr><tr><td>match-LSTM (Boundary)</td><td>research,exhibitions and other shows</td></tr><tr><td></td><td>Theatre Museum</td></tr><tr><td></td><td></td></tr><tr><td>(5) Context</td><td>Along with giving the offender his &quot;just deserts&quot;,achieving crime control via</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td>Question (Ambiguous)</td><td>incapacitation and deterrence is a major goal of criminal punishment.</td></tr><tr><td></td><td></td></tr><tr><td>Golden Anwser</td><td>What is the main goal of criminal punishment of civil disobedients ?</td></tr><tr><td></td><td></td></tr><tr><td></td><td>achieving crime control via incapacitation and deterrence</td></tr><tr><td>LSTM (Sequence)</td><td></td></tr><tr><td></td><td>deterrence</td></tr><tr><td>match-LSTM (Sequence) LSTM (Boundary)</td><td>just deserts incapacitation and deterrence</td></tr></table>",
+        "bbox": [
+            174,
+            198,
+            826,
+            830
+        ],
+        "page_idx": 14
+    }
+]

parse/train/BJO-BuT1g/BJO-BuT1g.md

@@ -0,0 +1,357 @@
+# A LEARNED REPRESENTATION FOR ARTISTIC STYLE
+
+Vincent Dumoulin & Jonathon Shlens & Manjunath Kudlur
+
+Google Brain, Mountain View, CA
+
+vi.dumoulin@gmail.com, shlens@google.com, keveman@google.com
+
+# ABSTRACT
+
+The diversity of painting styles represents a rich visual vocabulary for the construction of an image. The degree to which one may learn and parsimoniously capture this visual vocabulary measures our understanding of the higher level features of paintings, if not images in general. In this work we investigate the construction of a single, scalable deep network that can parsimoniously capture the artistic style of a diversity of paintings. We demonstrate that such a network generalizes across a diversity of artistic styles by reducing a painting to a point in an embedding space. Importantly, this model permits a user to explore new painting styles by arbitrarily combining the styles learned from individual paintings. We hope that this work provides a useful step towards building rich models of paintings and offers a window on to the structure of the learned representation of artistic style.
+
+# 1 INTRODUCTION
+
+A pastiche is an artistic work that imitates the style of another one. Computer vision and more recently machine learning have a history of trying to automate pastiche, that is, render an image in the style of another one. This task is called style transfer, and is closely related to the texture synthesis task. While the latter tries to capture the statistical relationship between the pixels of a source image which is assumed to have a stationary distribution at some scale, the former does so while also attempting to preserve some notion of content.
+
+On the computer vision side, Efros & Leung (1999) and Wei & Levoy (2000) attempt to “grow” textures one pixel at a time using non-parametric sampling of pixels in an examplar image. Efros & Freeman (2001) and Liang et al. (2001) extend this idea to “growing” textures one patch at a time, and Efros & Freeman (2001) uses the approach to implement “texture transfer”, i.e. transfering the texture of an object onto another one. Kwatra et al. (2005) approaches the texture synthesis problem from an energy minimization perspective, progressively refining the texture using an EMlike algorithm. Hertzmann et al. (2001) introduces the concept of “image analogies”: given a pair of “unfiltered” and “filtered” versions of an examplar image, a target image is processed to create an analogous “filtered” result. More recently, Frigo et al. (2016) treats style transfer as a local texture transfer (using an adaptive patch partition) followed by a global color transfer, and Elad & Milanfar (2016) extends Kwatra’s energy-based method into a style transfer algorithm by taking content similarity into account.
+
+On the machine learning side, it has been shown that a trained classifier can be used as a feature extractor to drive texture synthesis and style transfer. Gatys et al. (2015a) uses the VGG-19 network (Simonyan & Zisserman, 2014) to extract features from a texture image and a synthesized texture. The two sets of features are compared and the synthesized texture is modified by gradient descent so that the two sets of features are as close as possible. Gatys et al. (2015b) extends this idea to style transfer by adding the constraint that the synthesized image also be close to a content image with respect to another set of features extracted by the trained VGG-19 classifier.
+
+While very flexible, this algorithm is expensive to run due to the optimization loop being carried. Ulyanov et al. (2016a), Li & Wand (2016) and Johnson et al. (2016) tackle this problem by introducing a feedforward style transfer network, which is trained to go from content to pastiche image in one pass. However, in doing so some of the flexibility of the original algorithm is lost: the style transfer network is tied to a single style, which means that separate networks have to be trained (a) With conditional instance normalization, a single style transfer network can capture 32 styles at the same time, five of which are shown here. All 32 styles in this single model are in the Appendix. Golden Gate Bridge photograph by Rich Niewiroski Jr.
+
+![](images/df8e77998ba668f5d97412f63335585b1a01cc4b4f8f262b9725f9f6146654c5.jpg)
+
+![](images/50a38ae6ebd099da9d49ab3f5cbfa8115049178cb65b68608a1bc48f441354bf.jpg)
+
+(b) The style representation learned via conditional instance normalization permits the arbitrary combination of artistic styles. Each pastiche in the sequence corresponds to a different step in interpolating between the $\gamma$ and $\beta$ values associated with two styles the model was trained on.
+
+Figure 1: Pastiches produced by a style transfer network trained on 32 styles chosen for their variety.
+
+for every style being modeled. Subsequent work has brought some performance improvements to style transfer networks, e.g. with respect to color preservation (Gatys et al., 2016a) or style transfer quality (Ulyanov et al., 2016b), but to our knowledge the problem of the single-purpose nature of style transfer networks remains untackled.
+
+We think this is an important problem that, if solved, would have both scientific and practical importance. First, style transfer has already found use in mobile applications, for which on-device processing is contingent upon the models having a reasonable memory footprint. More broadly, building a separate network for each style ignores the fact that individual paintings share many common visual elements and a true model that captures artistic style would be able to exploit and learn from such regularities. Furthermore, the degree to which an artistic styling model might generalize across painting styles would directly measure our ability to build systems that parsimoniously capture the higher level features and statistics of photographs and images (Simoncelli & Olshausen, 2001).
+
+In this work, we show that a simple modification of the style transfer network, namely the introduction of conditional instance normalization, allows it to learn multiple styles (Figure 1a).We demonstrate that this approach is flexible yet comparable to single-purpose style transfer networks, both qualitatively and in terms of convergence properties. This model reduces each style image into a point in an embedding space. Furthermore, this model provides a generic representation for artistic styles that seems flexible enough to capture new artistic styles much faster than a single-purpose network. Finally, we show that the embeddding space representation permits one to arbitrarily combine artistic styles in novel ways not previously observed (Figure 1b).
+
+![](images/23dbff951ee44413419bcb12434cdfe94df7fafcc770f5259c992a3cf285b0ff.jpg)  
+Figure 2: Style transfer network training diagram (Johnson et al., 2016; Ulyanov et al., 2016a). A pastiche image is produced by feeding a content image through the style transfer network. The two images, along with a style image, are passed through a trained classifier, and the resulting intermediate representations are used to compute the content loss $\mathcal { L } _ { c }$ and style loss $\mathcal { L } _ { s }$ . The parameters of the classifier are kept fixed throughout training.
+
+# 2 STYLE TRANSFER WITH DEEP NETWORKS
+
+Style transfer can be defined as finding a pastiche image $p$ whose content is similar to that of a content image $c$ but whose style is similar to that of a style image $s$ . This objective is by nature vaguely defined, because similarity in content and style are themselves vaguely defined.
+
+The neural algorithm of artistic style proposes the following definitions:
+
+• Two images are similar in content if their high-level features as extracted by a trained classifier are close in Euclidian distance.   
+• Two images are similar in style if their low-level features as extracted by a trained classifier share the same statistics or, more concretely, if the difference between the features’ Gram matrices has a small Frobenius norm.
+
+The first point is motivated by the empirical observation that high-level features in classifiers tend to correspond to higher levels of abstractions (see Zeiler & Fergus (2014) for visualizations; see Johnson et al. (2016) for style transfer features). The second point is motivated by the observation that the artistic style of a painting may be interpreted as a visual texture (Gatys et al., 2015a). A visual texture is conjectured to be spatially homogenous and consist of repeated structural motifs whose minimal sufficient statistics are captured by lower order statistical measurements (Julesz, 1962; Portilla & Simoncelli, 1999).
+
+In its original formulation, the neural algorithm of artistic style proceeds as follows: starting from some initialization of $p$ (e.g. $c$ , or some random initialization), the algorithm adapts $p$ to minimize the loss function
+
+$$
+\begin{array} { r } { \mathcal { L } ( s , c , p ) = \lambda _ { s } \mathcal { L } _ { s } ( p ) + \lambda _ { c } \mathcal { L } _ { c } ( p ) , } \end{array}
+$$
+
+where $\mathcal { L } _ { s } ( p )$ is the style loss, $\mathcal { L } _ { c } ( p )$ is the content loss and $\lambda _ { s } , \lambda _ { c }$ are scaling hyperparameters. Given a set of “style layers” $s$ and a set of “content layers” $\mathcal { C }$ , the style and content losses are themselves defined as
+
+$$
+\begin{array} { c } { { \mathcal { L } _ { s } ( p ) = \displaystyle \sum _ { i \in \mathcal { S } } \frac { 1 } { U _ { i } } \parallel G ( \phi _ { i } ( p ) ) - G ( \phi _ { i } ( s ) ) \parallel _ { F } ^ { 2 } } } \\ { { \mathcal { L } _ { c } ( p ) = \displaystyle \sum _ { j \in \mathcal { C } } \frac { 1 } { U _ { j } } \parallel \phi _ { j } ( p ) - \phi _ { j } ( c ) \parallel _ { 2 } ^ { 2 } } } \end{array}
+$$
+
+where $\phi _ { l } ( x )$ are the classifier activations at layer $l$ , $U _ { l }$ is the total number of units at layer $l$ and $G ( \phi _ { l } ( x ) )$ is the Gram matrix associated with the layer $l$ activations. In practice, we set $\lambda _ { c } = 1 . 0$ and and leave $\lambda _ { s }$ as a free hyper-parameter.
+
+In order to speed up the procedure outlined above, a feed-forward convolutional network, termed a style transfer network $T$ , is introduced to learn the transformation (Johnson et al., 2016; Li & Wand, 2016; Ulyanov et al., 2016a). It takes as input a content image $c$ and outputs the pastiche image $p$ directly (Figure 2). The network is trained on many content images (Deng et al., 2009) using the same loss function as above, i.e.
+
+$$
+\begin{array} { r } { \mathcal { L } ( s , c ) = \lambda _ { s } \mathcal { L } _ { s } ( T ( c ) ) + \lambda _ { c } \mathcal { L } _ { c } ( T ( c ) ) . } \end{array}
+$$
+
+While feedforward style transfer networks solve the problem of speed at test-time, they also suffer from the fact that the network $T$ is tied to one specific painting style. This means that a separate network $T$ has to be trained for every style to be imitated. The real-world impact of this limitation is that it becomes prohibitive to implement a style transfer application on a memory-limited device, such as a smartphone.
+
+# 2.1 N-STYLES FEEDFORWARD STYLE TRANSFER NETWORKS
+
+Our work stems from the intuition that many styles probably share some degree of computation, and that this sharing is thrown away by training $N$ networks from scratch when building an $N .$ - styles style transfer system. For instance, many impressionist paintings share similar paint strokes but differ in the color palette being used. In that case, it seems very wasteful to treat a set of $N$ impressionist paintings as completely separate styles.
+
+To take this into account, we propose to train a single conditional style transfer network $T ( c , s )$ for $N$ styles. The conditional network is given both a content image and the identity of the style to apply and produces a pastiche corresponding to that style. While the idea is straightforward on paper, there remains the open question of how conditioning should be done. In exploring this question, we found a very surprising fact about the role of normalization in style transfer networks: to model a style, it is sufficient to specialize scaling and shifting parameters after normalization to each specific style. In other words, all convolutional weights of a style transfer network can be shared across many styles, and it is sufficient to tune parameters for an affine transformation after normalization for each style.
+
+We call this approach conditional instance normalization. The goal of the procedure is transform a layer’s activations $x$ into a normalized activation $z$ specific to painting style $s$ . Building off the instance normalization technique proposed in Ulyanov et al. (2016b), we augment the $\gamma$ and $\beta$ parameters so that they’re $N \times C$ matrices, where $N$ is the number of styles being modeled and $C$ is the number of output feature maps. Conditioning on a style is achieved as follows:
+
+$$
+z = \gamma _ { s } \left( \frac { x - \mu } { \sigma } \right) + \beta _ { s }
+$$
+
+where $\mu$ and $\sigma$ are $x$ ’s mean and standard deviation taken across spatial axes and $\gamma _ { s }$ and $\beta _ { s }$ are obtained by selecting the row corresponding to $s$ in the $\gamma$ and $\beta$ matrices (Figure 3). One added benefit of this approach is that one can stylize a single image into $N$ painting styles with a single feed forward pass of the network with a batch size of $N$ . In constrast, a single-style network requires $N$ feed forward passes to perform $N$ style transfers (Johnson et al., 2016; Li & Wand, 2016; Ulyanov et al., 2016a).
+
+Because conditional instance normalization only acts on the scaling and shifting parameters, training a style transfer network on $N$ styles requires fewer parameters than the naive approach of training $N$ separate networks. In a typical network setup, the model consists of roughly 1.6M parameters, only around 3K (or $0 . 2 \%$ ) of which specify individual artistic styles. In fact, because the size of $\gamma$ and $\beta$ grows linearly with respect to the number of feature maps in the network, this approach requires $O ( N \times L )$ parameters, where $L$ is the total number of feature maps in the network.
+
+In addition, as is discussed in subsection 3.4, conditional instance normalization presents the advantage that integrating an $N + 1 ^ { t h }$ style to the network is cheap because of the very small number of parameters to train.
+
+![](images/5d34eef4793ed46349bc8a8ae998f4fce40d761e4769158dcfb694d0ece57307.jpg)  
+Figure 3: Conditional instance normalization. The input activation $x$ is normalized across both spatial dimensions and subsequently scaled and shifted using style-dependent parameter vectors $\gamma _ { s } , \beta _ { s }$ where $s$ indexes the style label.
+
+# 3 EXPERIMENTAL RESULTS
+
+# 3.1 METHODOLOGY
+
+Unless noted otherwise, all style transfer networks were trained using the hyperparameters outlined in the Appendix’s Table 1.
+
+We used the same network architecture as in Johnson et al. (2016), except for two key details: zero-padding is replaced with mirror-padding, and transposed convolutions (also sometimes called deconvolutions) are replaced with nearest-neighbor upsampling followed by a convolution. The use of mirror-padding avoids border patterns sometimes caused by zero-padding in SAME-padded convolutions, while the replacement for transposed convolutions avoids checkerboard patterning, as discussed in in Odena et al. (2016). We find that with these two improvements training the network no longer requires a total variation loss that was previously employed to remove high frequency noise as proposed in Johnson et al. (2016).
+
+Our training procedure follows Johnson et al. (2016). Briefly, we employ the ImageNet dataset (Deng et al., 2009) as a corpus of training content images. We train the $N$ -style network with stochastic gradient descent using the Adam optimizer (Kingma & Ba, 2014). Details of the model architecture are in the Appendix. A complete implementation of the model in TensorFlow (Abadi et al., 2016) as well as a pretrained model are available for download 1. The evaluation images used for this work were resized such that their smaller side has size 512. Their stylized versions were then center-cropped to 512x512 pixels for display.
+
+# 3.2 TRAINING A SINGLE NETWORK ON N STYLES PRODUCES STYLIZATIONS COMPARABLETO INDEPENDENTLY-TRAINED MODELS
+
+As a first test, we trained a 10-styles model on stylistically similar images, namely 10 impressionist paintings from Claude Monet. Figure 4 shows the result of applying the trained network on evaluation images for a subset of the styles, with the full results being displayed in the Appendix. The model captures different color palettes and textures. We emphasize that $9 9 . 8 \%$ of the parameters are shared across all styles in contrast to $0 . 2 \%$ of the parameters which are unique to each painting style.
+
+To get a sense of what is being traded off by folding 10 styles into a single network, we trained a separate, single-style network on each style and compared them to the 10-styles network in terms of style transfer quality and training speed (Figure 5).
+
+The left column compares the learning curves for style and content losses between the single-style networks and the 10-styles network. The losses were averaged over 32 random batches of content images. By visual inspection, we observe that the 10-styles network converges as quickly as the single-style networks in terms of style loss, but lags slightly behind in terms of content loss.
+
+In order to quantify this observation, we compare the final losses for 10-styles and single-style models (center column). The 10-styles network’s content loss is around $8 . 7 \pm 3 . 9 \%$ higher than its single-style counterparts, while the difference in style losses $( 8 . 9 \pm 1 6 . 5 \%$ lower) is insignificant. While the $N$ -styles network suffers from a slight decrease in content loss convergence speed, this may not be a fair comparison, given that it takes $N$ times more parameter updates to train $N$ singlestyle networks separately than to train them with an $N$ -styles network.
+
+![](images/3c5729c7b2bbd4a39f2057d4bf138e57b2e103bb7ee497a54c2ee0d1a0ff906c.jpg)  
+Figure 4: A single style transfer network was trained to capture the style of 10 Monet paintings, five of which are shown here. All 10 styles in this single model are in the Appendix. Golden Gate Bridge photograph by Rich Niewiroski Jr.
+
+The right column shows a comparison between the pastiches produced by the 10-styles network and the ones produced by the single-style networks. We see that both results are qualitatively similar.
+
+# 3.3 THE N-STYLES MODEL IS FLEXIBLE ENOUGH TO CAPTURE VERY DIFFERENT STYLES
+
+We evaluated the flexibility of the $N$ -styles model by training a style transfer network on 32 works of art chosen for their diversity. Figure 1a shows the result of applying the trained network on evaluation images for a subset of the styles. Once again, the full results are displayed in the Appendix. The model appears to be capable of modeling all 32 styles in spite of the tremendous variation in color palette and the spatial scale of the painting styles.
+
+# 3.4 THE TRAINED NETWORK GENERALIZES ACROSS PAINTING STYLES
+
+Since all weights in the transformer network are shared between styles, one way to incorporate a new style to a trained network is to keep the trained weights fixed and learn a new set of $\gamma$ and $\beta$ parameters. To test the efficiency of this approach, we used it to incrementally incorporate Monet’s Plum Trees in Blossom painting to the network trained on 32 varied styles. Figure 6 shows that doing so is much faster than training a new network from scratch (left) while yielding comparable pastiches: even after eight times fewer parameter updates than its single-style counterpart, the finetuned model produces comparable pastiches (right).
+
+# 3.5 THE TRAINED NETWORK CAN ARBITRARILY COMBINE PAINTING STYLES
+
+The conditional instance normalization approach raises some interesting questions about style representation. In learning a different set of $\gamma$ and $\beta$ parameters for every style, we are in some sense learning an embedding of styles.
+
+![](images/43fb7c853f97127dad9e4e0405b6f98bfe1d3a2006653d22136ceb81910ffd64.jpg)  
+Figure 5: The $N$ -styles model exhibits learning dynamics comparable to individual models. (Left column) The N-styles model converges slightly slower in terms of content loss (top) and as fast in terms of style loss (bottom) than individual models. Training on a single Monet painting is represented by two curves with the same color. The dashed curve represents the $N$ -styles model, and the full curves represent individual models. Emphasis has been added on the styles for Vetheuil (1902) (teal) and Water Lilies (purple) for visualization purposes; remaining colors correspond to other Monet paintings (see Appendix). (Center column) The N-styles model reaches a slightly higher final content loss than (top, $8 . 7 \pm 3 . 9 \%$ increase) and a final style loss comparable to (bottom, $8 . 9 \pm 1 6 . 5 \%$ decrease) individual models. (Right column) Pastiches produced by the $N$ -styles network are qualitatively comparable to those produced by individual networks.
+
+![](images/8899f6aa7fa60a1c9656b32856001f87278c6c1e7c9bed920d5bd7fd2235a517.jpg)  
+Figure 6: The trained network is efficient at learning new styles. (Left column) Learning $\gamma$ and $\beta$ from a trained style transfer network converges much faster than training a model from scratch. (Right) Learning $\gamma$ and $\beta$ for 5,000 steps from a trained style transfer network produces pastiches comparable to that of a single network trained from scratch for 40,000 steps. Conversely, 5,000 step of training from scratch produces leads to a poor pastiche.
+
+Previous work suggested that cleverly balancing optimization strategies offers an opportunity to blend painting styles 2. To probe the utility of this embedding, we tried convex combinations of the $\gamma$ and $\beta$ values to blend very distinct painting styles (Figure 1b; Figure 7, left column). Employing a single convex combination produces a smooth transition from one style to the other. Suppose $( \gamma _ { 1 } , \beta _ { 1 } )$ and $( \gamma _ { 2 } , \beta _ { 2 } )$ are the parameters corresponding to two different styles. We use $\gamma = \alpha \times \gamma _ { 1 } +$ $( 1 - \alpha ) \times \gamma _ { 2 }$ and $\beta = \alpha \times \beta _ { 1 } + ( 1 - \alpha ) \times \beta _ { 2 }$ to stylize an image. Employing convex combinations may be extended to an arbitrary number of styles 3. Figure 7 (right column) shows the style loss from the transformer network for a given source image, with respect to the Bicentennial Print and Head of a Clown paintings, as we vary $\alpha$ from 0 to 1. As $\alpha$ increases, the style loss with respect to Bicentennial Print increases, which explains the smooth fading out of that style’s artifact in the transformed image.
+
+![](images/bb45f4fb381de4e4436efa8b66c33a60449587edf33af2513d572b08d254a1d6.jpg)  
+Figure 7: The $N$ -styles network can arbitrarily combine artistic styles. (Left) Combining four styles, shown in the corners. Each pastiche corresponds to a different convex combination of the four styles’ $\gamma$ and $\beta$ values. (Right) As we transition from one style to another (Bicentennial Print and Head of a Clown in this case), the style losses vary monotonically.
+
+# 4 DISCUSSION
+
+It seems surprising that such a small proportion of the network’s parameters can have such an impact on the overall process of style transfer. A similar intuition has been observed in auto-regressive models of images (van den Oord et al., 2016b) and audio (van den Oord et al., 2016a) where the conditioning process is mediated by adjusting the biases for subsequent samples from the model. That said, in the case of art stylization when posed as a feedforward network, it could be that the specific network architecture is unable to take full advantage of its capacity. We see evidence for this behavior in that pruning the architecture leads to qualitatively similar results. Another interpretation could be that the convolutional weights of the style transfer network encode transformations that represent “elements of style”. The scaling and shifting factors would then provide a way for each style to inhibit or enhance the expression of various elements of style to form a global identity of style. While this work does not attempt to verify this hypothesis, we think that this would constitute a very promising direction of research in understanding the computation behind style transfer networks as well as the representation of images in general.
+
+Concurrent to this work, Gatys et al. (2016b) demonstrated exciting new methods for revising the loss to selectively adjust the spatial scale, color information and spatial localization of the artistic style information. These methods are complementary to the results in this paper and present an interesting direction for exploring how spatial and color information uniquely factor into artistic style representation.
+
+The question of how predictive each style image is of its corresponding style representation is also of great interest. If it is the case that the style representation can easily be predicted from a style image, one could imagine building a transformer network which skips learning an individual conditional embedding and instead learn to produce a pastiche directly from a style and a content image, much like in the original neural algorithm of artistic style, but without any optimization loop at test time.
+
+Finally, the learned style representation opens the door to generative models of style: by modeling enough paintings of a given artistic movement (e.g. impressionism), one could build a collection of style embeddings upon which a generative model could be trained. At test time, a style representation would be sampled from the generative model and used in conjunction with the style transfer network to produce a random pastiche of that artistic movement.
+
+In summary, we demonstrated that conditional instance normalization constitutes a simple, efficient and scalable modification of style transfer networks that allows them to model multiple styles at the same time. A practical consequence of this approach is that a new painting style may be transmitted to and stored on a mobile device with a small number of parameters. We showed that despite its simplicity, the method is flexible enough to capture very different styles while having very little impact on training time and final performance of the trained network. Finally, we showed that the learned representation of style is useful in arbitrarily combining artistic styles. This work suggests the existence of a learned representation for artistic styles whose vocabulary is flexible enough to capture a diversity of the painted world.
+
+# ACKNOWLEDGMENTS
+
+We would like to thank Fred Bertsch, Douglas Eck, Cinjon Resnick and the rest of the Google Magenta team for their feedback; Peyman Milanfar, Michael Elad, Feng Yang, Jon Barron, Bhavik Singh, Jennifer Daniel as well as the the Google Brain team for their crucial suggestions and advice; an anonymous reviewer for helpful suggestions about applying this model in a mobile domain. Finally, we would like to thank the Google Cultural Institute, whose curated collection of art photographs was very helpful in finding exciting style images to train on.
+
+# REFERENCES
+
+Martın Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, et al. Tensorflow: Large-scale machine learning on heterogeneous distributed systems. arXiv preprint arXiv:1603.04467, 2016.
+
+Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on, pp. 248–255. IEEE, 2009.
+
+Alexei A Efros and William T Freeman. Image quilting for texture synthesis and transfer. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pp. 341–346. ACM, 2001.
+
+Alexei A Efros and Thomas K Leung. Texture synthesis by non-parametric sampling. In Computer Vision, 1999. The Proceedings of the Seventh IEEE International Conference on, volume 2, pp. 1033–1038. IEEE, 1999.
+
+Michael Elad and Peyman Milanfar. Style-transfer via texture-synthesis. arXiv preprint arXiv:1609.03057, 2016.
+
+Oriel Frigo, Neus Sabater, Julie Delon, and Pierre Hellier. Split and match: Example-based adaptive patch sampling for unsupervised style transfer. 2016.
+
+Leon Gatys, Alexander S Ecker, and Matthias Bethge. Texture synthesis using convolutional neural networks. In Advances in Neural Information Processing Systems, pp. 262–270, 2015a.
+
+Leon A Gatys, Alexander S Ecker, and Matthias Bethge. A neural algorithm of artistic style. arXiv preprint arXiv:1508.06576, 2015b.
+
+Leon A Gatys, Matthias Bethge, Aaron Hertzmann, and Eli Shechtman. Preserving color in neural artistic style transfer. arXiv preprint arXiv:1606.05897, 2016a.
+
+Leon A. Gatys, Alexander S. Ecker, Matthias Bethge, Aaron Hertzmann, and Eli Shechtman. Controlling perceptual factors in neural style transfer. CoRR, abs/1611.07865, 2016b. URL http://arxiv.org/abs/1611.07865.
+
+Aaron Hertzmann, Charles E Jacobs, Nuria Oliver, Brian Curless, and David H Salesin. Image analogies. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pp. 327–340. ACM, 2001.
+
+Justin Johnson, Alexandre Alahi, and Li Fei-Fei. Perceptual losses for real-time style transfer and super-resolution. arXiv preprint arXiv:1603.08155, 2016.
+
+Bela Julesz. Visual pattern discrimination. IRE Trans. Info Theory, 8:84–92, 1962.
+
+Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
+
+Vivek Kwatra, Irfan Essa, Aaron Bobick, and Nipun Kwatra. Texture optimization for examplebased synthesis. ACM Transactions on Graphics (ToG), 24(3):795–802, 2005.
+
+Chuan Li and Michael Wand. Precomputed real-time texture synthesis with markovian generative adversarial networks. ECCV, 2016. URL http://arxiv.org/abs/1604.04382.
+
+Lin Liang, Ce Liu, Ying-Qing Xu, Baining Guo, and Heung-Yeung Shum. Real-time texture synthesis by patch-based sampling. ACM Transactions on Graphics (ToG), 20(3):127–150, 2001.
+
+Augustus Odena, Christopher Olah, and Vincent Dumoulin. Avoiding checkerboard artifacts in neural networks. Distill, 2016.
+
+Javier Portilla and Eero Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. International Journal of Computer Vision, 40:49–71, 1999.
+
+Eero Simoncelli and Bruno Olshausen. Natural image statistics and neural representation. Annual Review of Neuroscience, 24:1193–1216, 2001.   
+Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556, 2014.   
+Dmitry Ulyanov, Vadim Lebedev, Andrea Vedaldi, and Victor Lempitsky. Texture networks: Feedforward synthesis of textures and stylized images. arXiv preprint arXiv:1603.03417, 2016a.   
+Dmitry Ulyanov, Andrea Vedaldi, and Victor Lempitsky. Instance normalization: The missing ingredient for fast stylization. arXiv preprint arXiv:1607.08022, 2016b.   
+Aaron van den Oord, Sander Dieleman, Heiga Zen, Karen Simonyan, Oriol Vinyals, Alex Graves, ¨ Nal Kalchbrenner, Andrew W. Senior, and Koray Kavukcuoglu. Wavenet: A generative model for raw audio. CoRR, abs/1609.03499, 2016a. URL http://arxiv.org/abs/1609.03499.   
+Aaron van den Oord, Nal Kalchbrenner, Oriol Vinyals, Lasse Espeholt, Alex Graves, and Koray ¨ Kavukcuoglu. Conditional image generation with pixelcnn decoders. CoRR, abs/1606.05328, 2016b. URL http://arxiv.org/abs/1606.05328.   
+Li-Yi Wei and Marc Levoy. Fast texture synthesis using tree-structured vector quantization. In Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pp. 479–488. ACM Press/Addison-Wesley Publishing Co., 2000.   
+Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In European Conference on Computer Vision, pp. 818–833. Springer, 2014.
+
+# APPENDIX
+
+HYPERPARAMETERS   
+Table 1: Style transfer network hyperparameters.   
+
+<table><tr><td></td><td></td><td></td><td>OperationKernel sizeStrideFeature mapsPaddingNonlinearity</td><td></td><td></td></tr><tr><td>Network-256 × 256× 3 input</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Convolution</td><td>9</td><td>1</td><td>32</td><td>SAME</td><td>ReLU</td></tr><tr><td>Convolution</td><td>3</td><td>2</td><td>64</td><td>SAME</td><td>ReLU</td></tr><tr><td>Convolution</td><td>3</td><td>2</td><td>128</td><td>SAME</td><td>ReLU</td></tr><tr><td>Residual block</td><td></td><td></td><td>128</td><td></td><td></td></tr><tr><td>Residual block</td><td></td><td></td><td>128</td><td></td><td></td></tr><tr><td>Residual block</td><td></td><td></td><td>128</td><td></td><td></td></tr><tr><td>Residual block</td><td></td><td></td><td>128</td><td></td><td></td></tr><tr><td>Residual block</td><td></td><td></td><td>128</td><td></td><td></td></tr><tr><td>Upsampling</td><td></td><td></td><td>64</td><td></td><td></td></tr><tr><td>Upsampling</td><td></td><td></td><td>32</td><td></td><td></td></tr><tr><td>Convolution</td><td>9</td><td>1</td><td>3</td><td>SAME</td><td>Sigmoid</td></tr><tr><td>Residual block - C feature maps</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Convolution</td><td>3</td><td>1</td><td>C</td><td>SAME</td><td>ReLU</td></tr><tr><td>Convolution</td><td>3</td><td>1</td><td>C</td><td>SAME</td><td>Linear</td></tr><tr><td></td><td>Add the input and the output</td><td></td><td></td><td></td><td></td></tr><tr><td>Upsampling- C feature maps</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td>Nearest-neighbor interpolation,factor 2</td><td></td><td></td></tr><tr><td>Convolution</td><td>3</td><td>1</td><td>C</td><td>SAME</td><td>ReLU</td></tr><tr><td></td><td>Padding mode REFLECT</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>Normalization Conditional instance normalization after every convolution</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>Optimizer Adam (Kingma &amp; Ba,2014) (α = 0.001, β1 = 0.9, β2 = 0.999)</td><td></td><td></td><td></td><td></td></tr><tr><td>Parameter updates 40,000</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Batch size 16</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Weight initialization Isotropic gaussian (μ = O,σ = 0.01)</td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+# MONET PASTICHES
+
+![](images/0e4556708d012d8c03990061a3cafe8f68b3ab1e44354ecc5714a2622aedb1d9.jpg)
+
+Claude Monet, Grainstacks at Giverny; the Evening Sun (1888/1889).
+
+![](images/b7254fddd8bb880a9cca9ac60f89235fdb0a0736c6e7381ca9c297e52b17a1db.jpg)  
+Claude Monet, Plum Trees in Blossom (1879).
+
+![](images/a2e313a3a4f12fde5bcf051a0d174a2e23d551a4603428751061e757025d0657.jpg)  
+Claude Monet, Poppy Field (1873).
+
+![](images/4891c29a27c99ebf04263a4b424d986551678694203947ac3167f85dd9a2cfb0.jpg)  
+Claude Monet, Rouen Cathedral, West Fac¸ade (1894).
+
+![](images/f87f9a01d727ed3fd886459b2f2fc6528ddfbe26f6b369aaabeb4b6a59da81b0.jpg)  
+Claude Monet, Sunrise (Marine) (1873).
+
+![](images/66c2010409c795a148438cd1774f77619391db28812e3b857eca819bcd49cd05.jpg)
+
+![](images/34c7c91b120f90b21c7fdf66a5c012723cbe1de590063844abdb6955a596a25f.jpg)  
+Claude Monet, Three Fishing Boats (1886).
+
+![](images/45729b6fb394ffb8ea4701b8bd4d129d61029e1190fe4c05ef66e18d13d30648.jpg)
+
+Claude Monet, Vetheuil ´ (1879).
+
+![](images/f21ea787fabbbfadb568bb1fae8efa65c277461eb4f858c9e8cd6fc5d11ca0f8.jpg)
+
+Claude Monet, Vetheuil ´ (1902).
+
+![](images/406592e80ffbc54f6bb256b789f453add25661aeaf5c8a154db81f59f57e5b14.jpg)
+
+Claude Monet, Water Lilies (ca. 1914-1917).
+
+# VARIED PASTICHES
+
+![](images/ddf369be3257ec67a10cee94e4421018a5a6ee03be33f58fef8614987cefd4bc.jpg)
+
+Roy Lichtenstein, Bicentennial Print (1975).
+
+![](images/bd56df5fa654a61edc5e351c2bd82891e3be2e3aacda1aa7e38b64e455c10778.jpg)
+
+Ernst Ludwig Kirchner, Boy with Sweets (1918).
+
+![](images/04107561e76a5bb1a3fb4130f76cb708478bf5ccf667d1a3659c2b4829195684.jpg)  
+Paul Signac, Cassis, Cap Lombard, Opus 196 (1889).
+
+![](images/045360bf319faa0982d5730b29f2cbf50c2a76b14fe44610be553dbbd298ee82.jpg)  
+Paul Klee, Colors from a Distance (1932).
+
+![](images/8e7c8a36c8702938118ee84cc263df7ad99e2076e0f40530e712c20030c8c975.jpg)
+
+![](images/b479702380b1e31e4ed2649e780bde4c4c157d09c4cbc68b546f842e1f788b5d.jpg)
+
+Jamini Roy, Crucifixion.
+
+![](images/1aa9ddf24a34631abe1674f83130c91d35b568d3d0d654d7610d3796bed8b13b.jpg)  
+Henri de Toulouse-Lautrec, Divan Japonais (1893).
+
+![](images/8db50798d1e09fb4e972beef82a027e82a9e0651c51545566047567ed6c20b44.jpg)  
+Egon Schiele, Edith with Striped Dress, Sitting (1915).
+
+![](images/a33f87a848646f87ba72325ab751ac96c5df0d57ea53117f3671ebe1de14e0fe.jpg)
+
+Georges Rouault, Head of a Clown (ca. 1907-1908).
+
+![](images/df9b824a0b36fe04b9ce379134c2aa45d66d9e559d95f31a3153c18c17285043.jpg)  
+William Hoare, Henry Hoare, ”The Magnificent”, of Stourhead (about 1750-1760).
+
+![](images/460b228369bbb89aa8dff56c44f516e39813126e32fec9e763f5866ee8728ada.jpg)
+
+Giorgio de Chirico, Horses on the seashore (1927/1928).
+
+![](images/af7deef7c21d10a457dbb91f97859ac1a108f9649b9c5efc89f11207501a9980.jpg)  
+Vincent van Gogh, Landscape at Saint-Remy (Enclosed Field with Peasant) ´ (1889).
+
+![](images/0599a340ed95b4a6040d04a7fbfbccb9f897c820cc95b4c1af981f90845f1492.jpg)  
+Nicolas Poussin, Landscape with a Calm (1650-1651).
+
+![](images/9fb38d435921abebe2f7264c52ce12bbe5287e3574b41ae47f9768254053aad1.jpg)
+
+Bernardino Fungai, Madonna and Child with Two Hermit Saints (early 1480s).
+
+![](images/92067baf1f3204359d5334e2c46086d49d8dd861abd2e925248eb758f502e5bd.jpg)  
+Max Hermann Maxy, Portrait of a Friend (1926).
+
+![](images/01c20b642e993dd683a0c6e8052a926b9ca3f7ae66faab3c7b0159b1f8c2c9b6.jpg)  
+Juan Gris, Portrait of Pablo Picasso (1912).
+
+![](images/fe55c4cb28770f07aab4a671691897bfdef1efadfb92dae9e02d23bec383611f.jpg)
+
+Severini Gino, Ritmo plastico del 14 luglio (1913).
+
+![](images/4225e73062f595a40a94cfa20a22cc16629d1b43be4654aa0af9899369381885.jpg)
+
+Richard Diebenkorn, Seawall (1957).
+
+![](images/74c01f952f0982ebeac9fae6cb9ff593de3c83b5c0c103ec226c85fcccc5f6c4.jpg)  
+Alice Bailly, Self-Portrait (1917).
+
+![](images/f21a187de27a5142d27677b472b958358ed7853fc7646193e342e987920d57b4.jpg)  
+Grayson Perry, The Annunciation of the Virgin Deal (2012).
+
+![](images/903da496e3db87e2012346c87f4816fd9372dc668e773e01cc79c3cfb68ed6f4.jpg)  
+William Glackens, The Green Boathouse (ca. 1922).
+
+![](images/4f7d375006c2bf53abe818fc35bc6ccdc0e6ecee534762b852717efcfa873fb2.jpg)
+
+Edvard Munch, The Scream (1910).
+
+![](images/81556932d65a0c19f02c5e8380b827ea8b094e4cdd47068b7b0220d48e57539f.jpg)
+
+Vincent van Gogh, The Starry Night (1889).
+
+![](images/d366cad0d6630f6007be03e804bf10baf92ff3ccf1d5253a1751c915caa8dc3c.jpg)  
+Pieter Bruegel the Elder, The Tower of Babel (1563).
+
+![](images/efd7b9cb43a41042fa3860d0842da69410debf099af75af1395ee562e7bd4daf.jpg)  
+Wolfgang Lettl, The Trial (1981).
+
+![](images/01de4975074ea1d9b2043d923a431a92718bf6f097e7be213e5d3a9389cba382.jpg)
+
+Douglas Coupland, Thomson No. 5 (Yellow Sunset) (2011).
+
+![](images/cc04e10b127e71be8d5784e160452ea3ca1aded59942c7f191a7174df4aa4e50.jpg)  
+Claude Monet, Three Fishing Boats (1886).
+
+![](images/b015deece7dfd358b1434f3a0cd791d6ce10020c4bc47899f77a5c75e84af8f9.jpg)  
+John Ruskin, Trees in a Lane (1847).
+
+![](images/e1f16dbfad13419a156f64328ef972c932af16e621ebf4f18cfc13cd960ca66b.jpg)  
+Giuseppe Cades, Tullia about to Ride over the Body of Her Father in Her Chariot (about 1770-1775).
+
+![](images/cf4cc7bd4476d956a5ab500311b22a922a59caa742b649cb5a4853541ef87bf6.jpg)  
+Berthe Morisot, Under the Orange Tree (1889).
+
+![](images/b28313326333f961b7c8b07c4a94f3e292b1aca7f257a36472f303cc48a59c61.jpg)
+
+Giulio Romano (Giulio Pippi), Victory, Janus, Chronos and Gaea (about 1532-1534).
+
+![](images/c8509f80be29c0b0b52e1ff299215653d6a6641991962417029d6fbaf3e56f05.jpg)
+
+Wassily Kandinsky, White Zig Zags (1922).

parse/train/BJO-BuT1g/BJO-BuT1g_content_list.json

@@ -0,0 +1,1951 @@
+[
+    {
+        "type": "text",
+        "text": "A LEARNED REPRESENTATION FOR ARTISTIC STYLE ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            99,
+            808,
+            121
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Vincent Dumoulin & Jonathon Shlens & Manjunath Kudlur ",
+        "bbox": [
+            183,
+            143,
+            604,
+            160
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Google Brain, Mountain View, CA ",
+        "bbox": [
+            184,
+            162,
+            415,
+            178
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "vi.dumoulin@gmail.com, shlens@google.com, keveman@google.com ",
+        "bbox": [
+            186,
+            183,
+            772,
+            195
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            233,
+            544,
+            248
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The diversity of painting styles represents a rich visual vocabulary for the construction of an image. The degree to which one may learn and parsimoniously capture this visual vocabulary measures our understanding of the higher level features of paintings, if not images in general. In this work we investigate the construction of a single, scalable deep network that can parsimoniously capture the artistic style of a diversity of paintings. We demonstrate that such a network generalizes across a diversity of artistic styles by reducing a painting to a point in an embedding space. Importantly, this model permits a user to explore new painting styles by arbitrarily combining the styles learned from individual paintings. We hope that this work provides a useful step towards building rich models of paintings and offers a window on to the structure of the learned representation of artistic style. ",
+        "bbox": [
+            233,
+            263,
+            764,
+            429
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            454,
+            336,
+            469
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "A pastiche is an artistic work that imitates the style of another one. Computer vision and more recently machine learning have a history of trying to automate pastiche, that is, render an image in the style of another one. This task is called style transfer, and is closely related to the texture synthesis task. While the latter tries to capture the statistical relationship between the pixels of a source image which is assumed to have a stationary distribution at some scale, the former does so while also attempting to preserve some notion of content. ",
+        "bbox": [
+            174,
+            484,
+            825,
+            569
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "On the computer vision side, Efros & Leung (1999) and Wei & Levoy (2000) attempt to “grow” textures one pixel at a time using non-parametric sampling of pixels in an examplar image. Efros & Freeman (2001) and Liang et al. (2001) extend this idea to “growing” textures one patch at a time, and Efros & Freeman (2001) uses the approach to implement “texture transfer”, i.e. transfering the texture of an object onto another one. Kwatra et al. (2005) approaches the texture synthesis problem from an energy minimization perspective, progressively refining the texture using an EMlike algorithm. Hertzmann et al. (2001) introduces the concept of “image analogies”: given a pair of “unfiltered” and “filtered” versions of an examplar image, a target image is processed to create an analogous “filtered” result. More recently, Frigo et al. (2016) treats style transfer as a local texture transfer (using an adaptive patch partition) followed by a global color transfer, and Elad & Milanfar (2016) extends Kwatra’s energy-based method into a style transfer algorithm by taking content similarity into account. ",
+        "bbox": [
+            174,
+            575,
+            825,
+            742
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "On the machine learning side, it has been shown that a trained classifier can be used as a feature extractor to drive texture synthesis and style transfer. Gatys et al. (2015a) uses the VGG-19 network (Simonyan & Zisserman, 2014) to extract features from a texture image and a synthesized texture. The two sets of features are compared and the synthesized texture is modified by gradient descent so that the two sets of features are as close as possible. Gatys et al. (2015b) extends this idea to style transfer by adding the constraint that the synthesized image also be close to a content image with respect to another set of features extracted by the trained VGG-19 classifier. ",
+        "bbox": [
+            174,
+            750,
+            823,
+            847
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "While very flexible, this algorithm is expensive to run due to the optimization loop being carried. Ulyanov et al. (2016a), Li & Wand (2016) and Johnson et al. (2016) tackle this problem by introducing a feedforward style transfer network, which is trained to go from content to pastiche image in one pass. However, in doing so some of the flexibility of the original algorithm is lost: the style transfer network is tied to a single style, which means that separate networks have to be trained (a) With conditional instance normalization, a single style transfer network can capture 32 styles at the same time, five of which are shown here. All 32 styles in this single model are in the Appendix. Golden Gate Bridge photograph by Rich Niewiroski Jr. ",
+        "bbox": [
+            176,
+            854,
+            823,
+            924
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
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+        "type": "text",
+        "text": "(b) The style representation learned via conditional instance normalization permits the arbitrary combination of artistic styles. Each pastiche in the sequence corresponds to a different step in interpolating between the $\\gamma$ and $\\beta$ values associated with two styles the model was trained on. ",
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+        "text": "Figure 1: Pastiches produced by a style transfer network trained on 32 styles chosen for their variety. ",
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+        "type": "text",
+        "text": "for every style being modeled. Subsequent work has brought some performance improvements to style transfer networks, e.g. with respect to color preservation (Gatys et al., 2016a) or style transfer quality (Ulyanov et al., 2016b), but to our knowledge the problem of the single-purpose nature of style transfer networks remains untackled. ",
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+        "text": "We think this is an important problem that, if solved, would have both scientific and practical importance. First, style transfer has already found use in mobile applications, for which on-device processing is contingent upon the models having a reasonable memory footprint. More broadly, building a separate network for each style ignores the fact that individual paintings share many common visual elements and a true model that captures artistic style would be able to exploit and learn from such regularities. Furthermore, the degree to which an artistic styling model might generalize across painting styles would directly measure our ability to build systems that parsimoniously capture the higher level features and statistics of photographs and images (Simoncelli & Olshausen, 2001). ",
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+        "text": "In this work, we show that a simple modification of the style transfer network, namely the introduction of conditional instance normalization, allows it to learn multiple styles (Figure 1a).We demonstrate that this approach is flexible yet comparable to single-purpose style transfer networks, both qualitatively and in terms of convergence properties. This model reduces each style image into a point in an embedding space. Furthermore, this model provides a generic representation for artistic styles that seems flexible enough to capture new artistic styles much faster than a single-purpose network. Finally, we show that the embeddding space representation permits one to arbitrarily combine artistic styles in novel ways not previously observed (Figure 1b). ",
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+        "img_path": "images/23dbff951ee44413419bcb12434cdfe94df7fafcc770f5259c992a3cf285b0ff.jpg",
+        "image_caption": [
+            "Figure 2: Style transfer network training diagram (Johnson et al., 2016; Ulyanov et al., 2016a). A pastiche image is produced by feeding a content image through the style transfer network. The two images, along with a style image, are passed through a trained classifier, and the resulting intermediate representations are used to compute the content loss $\\mathcal { L } _ { c }$ and style loss $\\mathcal { L } _ { s }$ . The parameters of the classifier are kept fixed throughout training. "
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+        "type": "text",
+        "text": "2 STYLE TRANSFER WITH DEEP NETWORKS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Style transfer can be defined as finding a pastiche image $p$ whose content is similar to that of a content image $c$ but whose style is similar to that of a style image $s$ . This objective is by nature vaguely defined, because similarity in content and style are themselves vaguely defined. ",
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+        "type": "text",
+        "text": "The neural algorithm of artistic style proposes the following definitions: ",
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+        "text": "• Two images are similar in content if their high-level features as extracted by a trained classifier are close in Euclidian distance.   \n• Two images are similar in style if their low-level features as extracted by a trained classifier share the same statistics or, more concretely, if the difference between the features’ Gram matrices has a small Frobenius norm. ",
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+        "text": "The first point is motivated by the empirical observation that high-level features in classifiers tend to correspond to higher levels of abstractions (see Zeiler & Fergus (2014) for visualizations; see Johnson et al. (2016) for style transfer features). The second point is motivated by the observation that the artistic style of a painting may be interpreted as a visual texture (Gatys et al., 2015a). A visual texture is conjectured to be spatially homogenous and consist of repeated structural motifs whose minimal sufficient statistics are captured by lower order statistical measurements (Julesz, 1962; Portilla & Simoncelli, 1999). ",
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+        "type": "text",
+        "text": "In its original formulation, the neural algorithm of artistic style proceeds as follows: starting from some initialization of $p$ (e.g. $c$ , or some random initialization), the algorithm adapts $p$ to minimize the loss function ",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/00a00421cbe5977097c28f53806d2a74917843cf5305459a6dde91a509304bb1.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } ( s , c , p ) = \\lambda _ { s } \\mathcal { L } _ { s } ( p ) + \\lambda _ { c } \\mathcal { L } _ { c } ( p ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where $\\mathcal { L } _ { s } ( p )$ is the style loss, $\\mathcal { L } _ { c } ( p )$ is the content loss and $\\lambda _ { s } , \\lambda _ { c }$ are scaling hyperparameters. Given a set of “style layers” $s$ and a set of “content layers” $\\mathcal { C }$ , the style and content losses are themselves defined as ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/83019f2d4a5722e35a4285b39a6ded4edce52137c536b9ac64da50c8ea5de18f.jpg",
+        "text": "$$\n\\begin{array} { c } { { \\mathcal { L } _ { s } ( p ) = \\displaystyle \\sum _ { i \\in \\mathcal { S } } \\frac { 1 } { U _ { i } } \\parallel G ( \\phi _ { i } ( p ) ) - G ( \\phi _ { i } ( s ) ) \\parallel _ { F } ^ { 2 } } } \\\\ { { \\mathcal { L } _ { c } ( p ) = \\displaystyle \\sum _ { j \\in \\mathcal { C } } \\frac { 1 } { U _ { j } } \\parallel \\phi _ { j } ( p ) - \\phi _ { j } ( c ) \\parallel _ { 2 } ^ { 2 } } } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\phi _ { l } ( x )$ are the classifier activations at layer $l$ , $U _ { l }$ is the total number of units at layer $l$ and $G ( \\phi _ { l } ( x ) )$ is the Gram matrix associated with the layer $l$ activations. In practice, we set $\\lambda _ { c } = 1 . 0$ and and leave $\\lambda _ { s }$ as a free hyper-parameter. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In order to speed up the procedure outlined above, a feed-forward convolutional network, termed a style transfer network $T$ , is introduced to learn the transformation (Johnson et al., 2016; Li & Wand, 2016; Ulyanov et al., 2016a). It takes as input a content image $c$ and outputs the pastiche image $p$ directly (Figure 2). The network is trained on many content images (Deng et al., 2009) using the same loss function as above, i.e. ",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "equation",
+        "img_path": "images/1de61632c3286fdd3971e31bc03a0d04d4856ad89a06a63e72af98508d8e7ddf.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } ( s , c ) = \\lambda _ { s } \\mathcal { L } _ { s } ( T ( c ) ) + \\lambda _ { c } \\mathcal { L } _ { c } ( T ( c ) ) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "While feedforward style transfer networks solve the problem of speed at test-time, they also suffer from the fact that the network $T$ is tied to one specific painting style. This means that a separate network $T$ has to be trained for every style to be imitated. The real-world impact of this limitation is that it becomes prohibitive to implement a style transfer application on a memory-limited device, such as a smartphone. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.1 N-STYLES FEEDFORWARD STYLE TRANSFER NETWORKS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our work stems from the intuition that many styles probably share some degree of computation, and that this sharing is thrown away by training $N$ networks from scratch when building an $N .$ - styles style transfer system. For instance, many impressionist paintings share similar paint strokes but differ in the color palette being used. In that case, it seems very wasteful to treat a set of $N$ impressionist paintings as completely separate styles. ",
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+    {
+        "type": "text",
+        "text": "To take this into account, we propose to train a single conditional style transfer network $T ( c , s )$ for $N$ styles. The conditional network is given both a content image and the identity of the style to apply and produces a pastiche corresponding to that style. While the idea is straightforward on paper, there remains the open question of how conditioning should be done. In exploring this question, we found a very surprising fact about the role of normalization in style transfer networks: to model a style, it is sufficient to specialize scaling and shifting parameters after normalization to each specific style. In other words, all convolutional weights of a style transfer network can be shared across many styles, and it is sufficient to tune parameters for an affine transformation after normalization for each style. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We call this approach conditional instance normalization. The goal of the procedure is transform a layer’s activations $x$ into a normalized activation $z$ specific to painting style $s$ . Building off the instance normalization technique proposed in Ulyanov et al. (2016b), we augment the $\\gamma$ and $\\beta$ parameters so that they’re $N \\times C$ matrices, where $N$ is the number of styles being modeled and $C$ is the number of output feature maps. Conditioning on a style is achieved as follows: ",
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+    {
+        "type": "equation",
+        "img_path": "images/8903aee416ada28dd7ba8bfc886485d76c4f96f6f14434e6ca9c93143592e6b6.jpg",
+        "text": "$$\nz = \\gamma _ { s } \\left( \\frac { x - \\mu } { \\sigma } \\right) + \\beta _ { s }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where $\\mu$ and $\\sigma$ are $x$ ’s mean and standard deviation taken across spatial axes and $\\gamma _ { s }$ and $\\beta _ { s }$ are obtained by selecting the row corresponding to $s$ in the $\\gamma$ and $\\beta$ matrices (Figure 3). One added benefit of this approach is that one can stylize a single image into $N$ painting styles with a single feed forward pass of the network with a batch size of $N$ . In constrast, a single-style network requires $N$ feed forward passes to perform $N$ style transfers (Johnson et al., 2016; Li & Wand, 2016; Ulyanov et al., 2016a). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Because conditional instance normalization only acts on the scaling and shifting parameters, training a style transfer network on $N$ styles requires fewer parameters than the naive approach of training $N$ separate networks. In a typical network setup, the model consists of roughly 1.6M parameters, only around 3K (or $0 . 2 \\%$ ) of which specify individual artistic styles. In fact, because the size of $\\gamma$ and $\\beta$ grows linearly with respect to the number of feature maps in the network, this approach requires $O ( N \\times L )$ parameters, where $L$ is the total number of feature maps in the network. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In addition, as is discussed in subsection 3.4, conditional instance normalization presents the advantage that integrating an $N + 1 ^ { t h }$ style to the network is cheap because of the very small number of parameters to train. ",
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+    {
+        "type": "image",
+        "img_path": "images/5d34eef4793ed46349bc8a8ae998f4fce40d761e4769158dcfb694d0ece57307.jpg",
+        "image_caption": [
+            "Figure 3: Conditional instance normalization. The input activation $x$ is normalized across both spatial dimensions and subsequently scaled and shifted using style-dependent parameter vectors $\\gamma _ { s } , \\beta _ { s }$ where $s$ indexes the style label. "
+        ],
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+    {
+        "type": "text",
+        "text": "3 EXPERIMENTAL RESULTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1 METHODOLOGY ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Unless noted otherwise, all style transfer networks were trained using the hyperparameters outlined in the Appendix’s Table 1. ",
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+    {
+        "type": "text",
+        "text": "We used the same network architecture as in Johnson et al. (2016), except for two key details: zero-padding is replaced with mirror-padding, and transposed convolutions (also sometimes called deconvolutions) are replaced with nearest-neighbor upsampling followed by a convolution. The use of mirror-padding avoids border patterns sometimes caused by zero-padding in SAME-padded convolutions, while the replacement for transposed convolutions avoids checkerboard patterning, as discussed in in Odena et al. (2016). We find that with these two improvements training the network no longer requires a total variation loss that was previously employed to remove high frequency noise as proposed in Johnson et al. (2016). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our training procedure follows Johnson et al. (2016). Briefly, we employ the ImageNet dataset (Deng et al., 2009) as a corpus of training content images. We train the $N$ -style network with stochastic gradient descent using the Adam optimizer (Kingma & Ba, 2014). Details of the model architecture are in the Appendix. A complete implementation of the model in TensorFlow (Abadi et al., 2016) as well as a pretrained model are available for download 1. The evaluation images used for this work were resized such that their smaller side has size 512. Their stylized versions were then center-cropped to 512x512 pixels for display. ",
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+    {
+        "type": "text",
+        "text": "3.2 TRAINING A SINGLE NETWORK ON N STYLES PRODUCES STYLIZATIONS COMPARABLETO INDEPENDENTLY-TRAINED MODELS",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "As a first test, we trained a 10-styles model on stylistically similar images, namely 10 impressionist paintings from Claude Monet. Figure 4 shows the result of applying the trained network on evaluation images for a subset of the styles, with the full results being displayed in the Appendix. The model captures different color palettes and textures. We emphasize that $9 9 . 8 \\%$ of the parameters are shared across all styles in contrast to $0 . 2 \\%$ of the parameters which are unique to each painting style. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To get a sense of what is being traded off by folding 10 styles into a single network, we trained a separate, single-style network on each style and compared them to the 10-styles network in terms of style transfer quality and training speed (Figure 5). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The left column compares the learning curves for style and content losses between the single-style networks and the 10-styles network. The losses were averaged over 32 random batches of content images. By visual inspection, we observe that the 10-styles network converges as quickly as the single-style networks in terms of style loss, but lags slightly behind in terms of content loss. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In order to quantify this observation, we compare the final losses for 10-styles and single-style models (center column). The 10-styles network’s content loss is around $8 . 7 \\pm 3 . 9 \\%$ higher than its single-style counterparts, while the difference in style losses $( 8 . 9 \\pm 1 6 . 5 \\%$ lower) is insignificant. While the $N$ -styles network suffers from a slight decrease in content loss convergence speed, this may not be a fair comparison, given that it takes $N$ times more parameter updates to train $N$ singlestyle networks separately than to train them with an $N$ -styles network. ",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/3c5729c7b2bbd4a39f2057d4bf138e57b2e103bb7ee497a54c2ee0d1a0ff906c.jpg",
+        "image_caption": [
+            "Figure 4: A single style transfer network was trained to capture the style of 10 Monet paintings, five of which are shown here. All 10 styles in this single model are in the Appendix. Golden Gate Bridge photograph by Rich Niewiroski Jr. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The right column shows a comparison between the pastiches produced by the 10-styles network and the ones produced by the single-style networks. We see that both results are qualitatively similar. ",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.3 THE N-STYLES MODEL IS FLEXIBLE ENOUGH TO CAPTURE VERY DIFFERENT STYLES ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We evaluated the flexibility of the $N$ -styles model by training a style transfer network on 32 works of art chosen for their diversity. Figure 1a shows the result of applying the trained network on evaluation images for a subset of the styles. Once again, the full results are displayed in the Appendix. The model appears to be capable of modeling all 32 styles in spite of the tremendous variation in color palette and the spatial scale of the painting styles. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.4 THE TRAINED NETWORK GENERALIZES ACROSS PAINTING STYLES ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Since all weights in the transformer network are shared between styles, one way to incorporate a new style to a trained network is to keep the trained weights fixed and learn a new set of $\\gamma$ and $\\beta$ parameters. To test the efficiency of this approach, we used it to incrementally incorporate Monet’s Plum Trees in Blossom painting to the network trained on 32 varied styles. Figure 6 shows that doing so is much faster than training a new network from scratch (left) while yielding comparable pastiches: even after eight times fewer parameter updates than its single-style counterpart, the finetuned model produces comparable pastiches (right). ",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "3.5 THE TRAINED NETWORK CAN ARBITRARILY COMBINE PAINTING STYLES ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The conditional instance normalization approach raises some interesting questions about style representation. In learning a different set of $\\gamma$ and $\\beta$ parameters for every style, we are in some sense learning an embedding of styles. ",
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+        "img_path": "images/43fb7c853f97127dad9e4e0405b6f98bfe1d3a2006653d22136ceb81910ffd64.jpg",
+        "image_caption": [
+            "Figure 5: The $N$ -styles model exhibits learning dynamics comparable to individual models. (Left column) The N-styles model converges slightly slower in terms of content loss (top) and as fast in terms of style loss (bottom) than individual models. Training on a single Monet painting is represented by two curves with the same color. The dashed curve represents the $N$ -styles model, and the full curves represent individual models. Emphasis has been added on the styles for Vetheuil (1902) (teal) and Water Lilies (purple) for visualization purposes; remaining colors correspond to other Monet paintings (see Appendix). (Center column) The N-styles model reaches a slightly higher final content loss than (top, $8 . 7 \\pm 3 . 9 \\%$ increase) and a final style loss comparable to (bottom, $8 . 9 \\pm 1 6 . 5 \\%$ decrease) individual models. (Right column) Pastiches produced by the $N$ -styles network are qualitatively comparable to those produced by individual networks. "
+        ],
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+        "image_caption": [
+            "Figure 6: The trained network is efficient at learning new styles. (Left column) Learning $\\gamma$ and $\\beta$ from a trained style transfer network converges much faster than training a model from scratch. (Right) Learning $\\gamma$ and $\\beta$ for 5,000 steps from a trained style transfer network produces pastiches comparable to that of a single network trained from scratch for 40,000 steps. Conversely, 5,000 step of training from scratch produces leads to a poor pastiche. "
+        ],
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+    {
+        "type": "text",
+        "text": "Previous work suggested that cleverly balancing optimization strategies offers an opportunity to blend painting styles 2. To probe the utility of this embedding, we tried convex combinations of the $\\gamma$ and $\\beta$ values to blend very distinct painting styles (Figure 1b; Figure 7, left column). Employing a single convex combination produces a smooth transition from one style to the other. Suppose $( \\gamma _ { 1 } , \\beta _ { 1 } )$ and $( \\gamma _ { 2 } , \\beta _ { 2 } )$ are the parameters corresponding to two different styles. We use $\\gamma = \\alpha \\times \\gamma _ { 1 } +$ $( 1 - \\alpha ) \\times \\gamma _ { 2 }$ and $\\beta = \\alpha \\times \\beta _ { 1 } + ( 1 - \\alpha ) \\times \\beta _ { 2 }$ to stylize an image. Employing convex combinations may be extended to an arbitrary number of styles 3. Figure 7 (right column) shows the style loss from the transformer network for a given source image, with respect to the Bicentennial Print and Head of a Clown paintings, as we vary $\\alpha$ from 0 to 1. As $\\alpha$ increases, the style loss with respect to Bicentennial Print increases, which explains the smooth fading out of that style’s artifact in the transformed image. ",
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+    },
+    {
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+        "img_path": "images/bb45f4fb381de4e4436efa8b66c33a60449587edf33af2513d572b08d254a1d6.jpg",
+        "image_caption": [
+            "Figure 7: The $N$ -styles network can arbitrarily combine artistic styles. (Left) Combining four styles, shown in the corners. Each pastiche corresponds to a different convex combination of the four styles’ $\\gamma$ and $\\beta$ values. (Right) As we transition from one style to another (Bicentennial Print and Head of a Clown in this case), the style losses vary monotonically. "
+        ],
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "4 DISCUSSION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "It seems surprising that such a small proportion of the network’s parameters can have such an impact on the overall process of style transfer. A similar intuition has been observed in auto-regressive models of images (van den Oord et al., 2016b) and audio (van den Oord et al., 2016a) where the conditioning process is mediated by adjusting the biases for subsequent samples from the model. That said, in the case of art stylization when posed as a feedforward network, it could be that the specific network architecture is unable to take full advantage of its capacity. We see evidence for this behavior in that pruning the architecture leads to qualitatively similar results. Another interpretation could be that the convolutional weights of the style transfer network encode transformations that represent “elements of style”. The scaling and shifting factors would then provide a way for each style to inhibit or enhance the expression of various elements of style to form a global identity of style. While this work does not attempt to verify this hypothesis, we think that this would constitute a very promising direction of research in understanding the computation behind style transfer networks as well as the representation of images in general. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Concurrent to this work, Gatys et al. (2016b) demonstrated exciting new methods for revising the loss to selectively adjust the spatial scale, color information and spatial localization of the artistic style information. These methods are complementary to the results in this paper and present an interesting direction for exploring how spatial and color information uniquely factor into artistic style representation. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The question of how predictive each style image is of its corresponding style representation is also of great interest. If it is the case that the style representation can easily be predicted from a style image, one could imagine building a transformer network which skips learning an individual conditional embedding and instead learn to produce a pastiche directly from a style and a content image, much like in the original neural algorithm of artistic style, but without any optimization loop at test time. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Finally, the learned style representation opens the door to generative models of style: by modeling enough paintings of a given artistic movement (e.g. impressionism), one could build a collection of style embeddings upon which a generative model could be trained. At test time, a style representation would be sampled from the generative model and used in conjunction with the style transfer network to produce a random pastiche of that artistic movement. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In summary, we demonstrated that conditional instance normalization constitutes a simple, efficient and scalable modification of style transfer networks that allows them to model multiple styles at the same time. A practical consequence of this approach is that a new painting style may be transmitted to and stored on a mobile device with a small number of parameters. We showed that despite its simplicity, the method is flexible enough to capture very different styles while having very little impact on training time and final performance of the trained network. Finally, we showed that the learned representation of style is useful in arbitrarily combining artistic styles. This work suggests the existence of a learned representation for artistic styles whose vocabulary is flexible enough to capture a diversity of the painted world. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We would like to thank Fred Bertsch, Douglas Eck, Cinjon Resnick and the rest of the Google Magenta team for their feedback; Peyman Milanfar, Michael Elad, Feng Yang, Jon Barron, Bhavik Singh, Jennifer Daniel as well as the the Google Brain team for their crucial suggestions and advice; an anonymous reviewer for helpful suggestions about applying this model in a mobile domain. Finally, we would like to thank the Google Cultural Institute, whose curated collection of art photographs was very helpful in finding exciting style images to train on. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
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+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            264,
+            117
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/af896040ba8cd5a50c4a1f80d0ca8836aec169802f0ad31f55ffee3bcf80092b.jpg",
+        "table_caption": [
+            "HYPERPARAMETERS ",
+            "Table 1: Style transfer network hyperparameters. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td></td><td>OperationKernel sizeStrideFeature mapsPaddingNonlinearity</td><td></td><td></td></tr><tr><td>Network-256 × 256× 3 input</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Convolution</td><td>9</td><td>1</td><td>32</td><td>SAME</td><td>ReLU</td></tr><tr><td>Convolution</td><td>3</td><td>2</td><td>64</td><td>SAME</td><td>ReLU</td></tr><tr><td>Convolution</td><td>3</td><td>2</td><td>128</td><td>SAME</td><td>ReLU</td></tr><tr><td>Residual block</td><td></td><td></td><td>128</td><td></td><td></td></tr><tr><td>Residual block</td><td></td><td></td><td>128</td><td></td><td></td></tr><tr><td>Residual block</td><td></td><td></td><td>128</td><td></td><td></td></tr><tr><td>Residual block</td><td></td><td></td><td>128</td><td></td><td></td></tr><tr><td>Residual block</td><td></td><td></td><td>128</td><td></td><td></td></tr><tr><td>Upsampling</td><td></td><td></td><td>64</td><td></td><td></td></tr><tr><td>Upsampling</td><td></td><td></td><td>32</td><td></td><td></td></tr><tr><td>Convolution</td><td>9</td><td>1</td><td>3</td><td>SAME</td><td>Sigmoid</td></tr><tr><td>Residual block - C feature maps</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Convolution</td><td>3</td><td>1</td><td>C</td><td>SAME</td><td>ReLU</td></tr><tr><td>Convolution</td><td>3</td><td>1</td><td>C</td><td>SAME</td><td>Linear</td></tr><tr><td></td><td>Add the input and the output</td><td></td><td></td><td></td><td></td></tr><tr><td>Upsampling- C feature maps</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td>Nearest-neighbor interpolation,factor 2</td><td></td><td></td></tr><tr><td>Convolution</td><td>3</td><td>1</td><td>C</td><td>SAME</td><td>ReLU</td></tr><tr><td></td><td>Padding mode REFLECT</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>Normalization Conditional instance normalization after every convolution</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>Optimizer Adam (Kingma &amp; Ba,2014) (α = 0.001, β1 = 0.9, β2 = 0.999)</td><td></td><td></td><td></td><td></td></tr><tr><td>Parameter updates 40,000</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Batch size 16</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Weight initialization Isotropic gaussian (μ = O,σ = 0.01)</td><td></td><td></td><td></td><td></td><td></td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "MONET PASTICHES ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/0e4556708d012d8c03990061a3cafe8f68b3ab1e44354ecc5714a2622aedb1d9.jpg",
+        "image_caption": [],
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Claude Monet, Grainstacks at Giverny; the Evening Sun (1888/1889). ",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/b7254fddd8bb880a9cca9ac60f89235fdb0a0736c6e7381ca9c297e52b17a1db.jpg",
+        "image_caption": [
+            "Claude Monet, Plum Trees in Blossom (1879). "
+        ],
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+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/a2e313a3a4f12fde5bcf051a0d174a2e23d551a4603428751061e757025d0657.jpg",
+        "image_caption": [
+            "Claude Monet, Poppy Field (1873). "
+        ],
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+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/4891c29a27c99ebf04263a4b424d986551678694203947ac3167f85dd9a2cfb0.jpg",
+        "image_caption": [
+            "Claude Monet, Rouen Cathedral, West Fac¸ade (1894). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
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+        "img_path": "images/f87f9a01d727ed3fd886459b2f2fc6528ddfbe26f6b369aaabeb4b6a59da81b0.jpg",
+        "image_caption": [
+            "Claude Monet, Sunrise (Marine) (1873). "
+        ],
+        "image_footnote": [],
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+    },
+    {
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+        "image_caption": [
+            "Claude Monet, Three Fishing Boats (1886). "
+        ],
+        "image_footnote": [],
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+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Claude Monet, Vetheuil ´ (1879). ",
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
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+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Claude Monet, Vetheuil ´ (1902). ",
+        "bbox": [
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+        "page_idx": 14
+    },
+    {
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+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Claude Monet, Water Lilies (ca. 1914-1917). ",
+        "bbox": [
+            351,
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+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "VARIED PASTICHES ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 15
+    },
+    {
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+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Roy Lichtenstein, Bicentennial Print (1975). ",
+        "bbox": [
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+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
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+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Ernst Ludwig Kirchner, Boy with Sweets (1918). ",
+        "bbox": [
+            339,
+            810,
+            658,
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+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
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+        "image_caption": [
+            "Paul Signac, Cassis, Cap Lombard, Opus 196 (1889). "
+        ],
+        "image_footnote": [],
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+        "image_caption": [
+            "Paul Klee, Colors from a Distance (1932). "
+        ],
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+    {
+        "type": "text",
+        "text": "Jamini Roy, Crucifixion. ",
+        "bbox": [
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+        "page_idx": 17
+    },
+    {
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+        "image_caption": [
+            "Henri de Toulouse-Lautrec, Divan Japonais (1893). "
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+        "image_caption": [
+            "Egon Schiele, Edith with Striped Dress, Sitting (1915). "
+        ],
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+    {
+        "type": "text",
+        "text": "Georges Rouault, Head of a Clown (ca. 1907-1908). ",
+        "bbox": [
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+        "page_idx": 18
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+    {
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+        "image_caption": [
+            "William Hoare, Henry Hoare, ”The Magnificent”, of Stourhead (about 1750-1760). "
+        ],
+        "image_footnote": [],
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+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "Giorgio de Chirico, Horses on the seashore (1927/1928). ",
+        "bbox": [
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+        "page_idx": 18
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+        "image_caption": [
+            "Vincent van Gogh, Landscape at Saint-Remy (Enclosed Field with Peasant) ´ (1889). "
+        ],
+        "image_footnote": [],
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+        "image_caption": [
+            "Nicolas Poussin, Landscape with a Calm (1650-1651). "
+        ],
+        "image_footnote": [],
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+        "page_idx": 19
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+    {
+        "type": "text",
+        "text": "Bernardino Fungai, Madonna and Child with Two Hermit Saints (early 1480s). ",
+        "bbox": [
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+        "page_idx": 19
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+    {
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+        "image_caption": [
+            "Max Hermann Maxy, Portrait of a Friend (1926). "
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+        "image_caption": [
+            "Juan Gris, Portrait of Pablo Picasso (1912). "
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+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "Severini Gino, Ritmo plastico del 14 luglio (1913). ",
+        "bbox": [
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+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "image",
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+        "page_idx": 21
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+    {
+        "type": "text",
+        "text": "Richard Diebenkorn, Seawall (1957). ",
+        "bbox": [
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+        "page_idx": 21
+    },
+    {
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+        "image_caption": [
+            "Alice Bailly, Self-Portrait (1917). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "image_caption": [
+            "Grayson Perry, The Annunciation of the Virgin Deal (2012). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "image_caption": [
+            "William Glackens, The Green Boathouse (ca. 1922). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+        "page_idx": 22
+    },
+    {
+        "type": "text",
+        "text": "Edvard Munch, The Scream (1910). ",
+        "bbox": [
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+            551
+        ],
+        "page_idx": 22
+    },
+    {
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+        "page_idx": 22
+    },
+    {
+        "type": "text",
+        "text": "Vincent van Gogh, The Starry Night (1889). ",
+        "bbox": [
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+            643,
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+        ],
+        "page_idx": 22
+    },
+    {
+        "type": "image",
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+        "image_caption": [
+            "Pieter Bruegel the Elder, The Tower of Babel (1563). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+        "image_caption": [
+            "Wolfgang Lettl, The Trial (1981). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 23
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+        "page_idx": 23
+    },
+    {
+        "type": "text",
+        "text": "Douglas Coupland, Thomson No. 5 (Yellow Sunset) (2011). ",
+        "bbox": [
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+            789
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "image",
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+        "image_caption": [
+            "Claude Monet, Three Fishing Boats (1886). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    {
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+        "image_caption": [
+            "John Ruskin, Trees in a Lane (1847). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+        "image_caption": [
+            "Giuseppe Cades, Tullia about to Ride over the Body of Her Father in Her Chariot (about 1770-1775). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "image_caption": [
+            "Berthe Morisot, Under the Orange Tree (1889). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+        "page_idx": 25
+    },
+    {
+        "type": "text",
+        "text": "Giulio Romano (Giulio Pippi), Victory, Janus, Chronos and Gaea (about 1532-1534). ",
+        "bbox": [
+            215,
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+        ],
+        "page_idx": 25
+    },
+    {
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+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "text",
+        "text": "Wassily Kandinsky, White Zig Zags (1922). ",
+        "bbox": [
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+        ],
+        "page_idx": 25
+    }
+]

parse/train/UFGEelJkLu5/UFGEelJkLu5.md

@@ -0,0 +1,550 @@
+# MIXKD: TOWARDS EFFICIENT DISTILLATION OF LARGE-SCALE LANGUAGE MODELS
+
+Kevin J Liang1,2∗, Weituo $\mathbf { H a o ^ { 1 * } }$ , Dinghan Shen3, Yufan Zhou4, Weizhu Chen3,   
+Changyou Chen4, Lawrence Carin1   
+1Duke University 2Facebook AI 3Microsoft Dynamics 365 AI   
+4State University of New York at Buffalo   
+{kevin.liang, weituo.hao}@duke.edu
+
+# ABSTRACT
+
+Large-scale language models have recently demonstrated impressive empirical performance. Nevertheless, the improved results are attained at the price of bigger models, more power consumption, and slower inference, which hinder their applicability to low-resource (both memory and computation) platforms. Knowledge distillation (KD) has been demonstrated as an effective framework for compressing such big models. However, large-scale neural network systems are prone to memorize training instances, and thus tend to make inconsistent predictions when the data distribution is altered slightly. Moreover, the student model has few opportunities to request useful information from the teacher model when there is limited task-specific data available. To address these issues, we propose MixKD, a data-agnostic distillation framework that leverages mixup, a simple yet efficient data augmentation approach, to endow the resulting model with stronger generalization ability. Concretely, in addition to the original training examples, the student model is encouraged to mimic the teacher’s behavior on the linear interpolation of example pairs as well. We prove from a theoretical perspective that under reasonable conditions MixKD gives rise to a smaller gap between the generalization error and the empirical error. To verify its effectiveness, we conduct experiments on the GLUE benchmark, where MixKD consistently leads to significant gains over the standard KD training, and outperforms several competitive baselines. Experiments under a limited-data setting and ablation studies further demonstrate the advantages of the proposed approach.
+
+# 1 INTRODUCTION
+
+Recent language models (LM) pre-trained on large-scale unlabeled text corpora in a self-supervised manner have significantly advanced the state of the art across a wide variety of natural language processing (NLP) tasks (Devlin et al., 2018; Liu et al., 2019c; Yang et al., 2019; Joshi et al., 2020; Sun et al., 2019b; Clark et al., 2020; Lewis et al., 2019; Bao et al., 2020). After the LM pretraining stage, the resulting parameters can be fine-tuned to different downstream tasks. While these models have yielded impressive results, they typically have millions, if not billions, of parameters, and thus can be very expensive from storage and computational standpoints. Additionally, during deployment, such large models can require a lot of time to process even a single sample. In settings where computation may be limited (e.g. mobile, edge devices), such characteristics may preclude such powerful models from deployment entirely.
+
+One promising strategy to compress and accelerate large-scale language models is knowledge distillation (Zhao et al., 2019; Tang et al., 2019; Sun et al., 2020). The key idea is to train a smaller model (a “student”) to mimic the behavior of the larger, stronger-performing, but perhaps less practical model (the “teacher”), thus achieving similar performance with a faster, lighter-weight model. A simple but powerful method of achieving this is to use the output probability logits produced by the teacher model as soft labels for training the student (Hinton et al., 2015). With higher entropy than one-hot labels, these soft labels contain more information for the student model to learn from.
+
+Previous efforts on distilling large-scale LMs mainly focus on designing better training objectives, such as matching intermediate representations (Sun et al., 2019a; Mukherjee & Awadallah, 2019), learning multiple tasks together (Liu et al., 2019a), or leveraging the distillation objective during the pre-training stage (Jiao et al., 2019; Sanh et al., 2019). However, much less effort has been made to enrich task-specific data, a potentially vital component of the knowledge distillation procedure. In particular, tasks with fewer data samples provide less opportunity for the student model to learn from the teacher. Even with a well-designed training objective, the student model is still prone to overfitting, despite effectively mimicking the teacher network on the available data.
+
+In response to these limitations, we propose improving the value of knowledge distillation by using data augmentation to generate additional samples from the available task-specific data. These augmented samples are further processed by the teacher network to produce additional soft labels, providing the student model more data to learn from a large-scale LM. Intuitively, this is akin to a student learning more from a teacher by asking more questions to further probe the teacher’s answers and thoughts. In particular, we demonstrate that mixup (Zhang et al., 2018) can significantly improve knowledge distillation’s effectiveness, and we show with a theoretical framework why this is the case. We call our framework MixKD.
+
+We conduct experiments on 6 GLUE datasets (Wang et al., 2019) across a variety of task types, demonstrating that MixKD significantly outperforms knowledge distillation (Hinton et al., 2015) and other previous methods that compress large-scale language models. In particular, we show that our method is especially effective when the number of available task data samples is small, substantially improving the potency of knowledge distillation. We also visualize representations learned with and without MixKD to show the value of interpolated distillation samples, perform a series of ablation and hyperparameter sensitivity studies, and demonstrate the superiority of MixKD over other BERT data augmentation strategies.
+
+# 2 RELATED WORK
+
+# 2.1 MODEL COMPRESSION
+
+Compressing large-scale language models, such as BERT, has attracted significant attention recently. Knowledge distillation has been demonstrated as an effective approach, which can be leveraged during both the pre-training and task-specific fine-tuning stages. Prior research efforts mainly focus on improving the training objectives to benefit the distillation process. Specifically, Turc et al. (2019) advocate that task-specific knowledge distillation can be improved by first pre-training the student model. It is shown by Clark et al. (2019) that a multi-task BERT model can be learned by distilling from multiple single-task teachers. Liu et al. (2019b) propose learning a stronger student model by distilling knowledge from an ensemble of BERT models. Patient knowledge distillation (PKD), introduced by Sun et al. (2019a), encourages the student model to mimic the teacher’s intermediate layers in addition to output logits. DistilBERT (Sanh et al., 2019) reduces the depth of BERT model by a factor of 2 via knowledge distillation during the pre-training stage. In this work, we evaluate MixKD on the case of task-specific knowledge distillation. Notably, it can be extended to the pre-training stage as well, which we leave for future work. Moreover, our method can be flexibly integrated with different KD training objectives (described above) to obtain even better results. However, we utilize the BERT-base model as the testbed in this paper without loss of generality.
+
+# 2.2 DATA AUGMENTATION IN NLP
+
+Data augmentation (DA) has been studied extensively in computer vision as a powerful technique to incorporate prior knowledge of invariances and improve the robustness of learned models (Simard et al., 1998; 2003; Krizhevsky et al., 2012). Recently, it has also been applied and shown effective on natural language data. Many approaches can be categorized as label-preserving transformations, which essentially produce neighbors around a training example that maintain its original label. For example, EDA (Wei & Zou, 2019) propose using various rule-based operations such as synonym replacement, word insertion, swap or deletion to obtain augmented samples. Back-translation (Yu et al., 2018; Xie et al., 2019) is another popular approach belonging to this type, which relies on pre-trained translation models. Additionally, methods based on paraphrase generation have also been leveraged from the data augmentation perspective (Kumar et al., 2019). On the other hand, label-altering techniques like mixup (Zhang et al., 2018) have also been proposed for language (Guo et al., 2019; Chen et al., 2020), producing interpolated inputs and labels for the models predict. The proposed MixKD framework leverages the ability of mixup to facilitate the student learning more information from the teacher. It is worth noting that MixKD can be combined with arbitrary labelpreserving DA modules. Back-translation is employed as a special case here, and we believe other advanced label-preserving transformations developed in the future can benefit the MixKD approach as well.
+
+# 2.3 MIXUP
+
+Mixup (Zhang et al., 2018) is a popular data augmentation strategy to increase model generalizability and robustness by training on convex combinations of pairs of inputs and labels $( x _ { i } , y _ { i } )$ and $( x _ { j } , y _ { j } )$
+
+$$
+\begin{array} { l } { { x ^ { \prime } = \lambda x _ { i } + ( 1 - \lambda ) x _ { j } } } \\ { { y ^ { \prime } = \lambda y _ { i } + ( 1 - \lambda ) y _ { j } } } \end{array}
+$$
+
+with $\lambda \in [ 0 , 1 ]$ and $( x ^ { \prime } , y ^ { \prime } )$ being the resulting virtual training example. This concept of interpolating samples was later generalized with Manifold mixup (Verma et al., 2019a) and also found to be effective in semi-supervised learning settings (Verma et al., 2019b;c; Berthelot et al., 2019b;a). Other strategies include mixing together samples resulting from chaining together other augmentation techniques (Hendrycks et al., 2020), or replacing linear interpolation with the cutting and pasting of patches (Yun et al., 2019).
+
+# 3 METHODOLOGY
+
+# 3.1 PRELIMINARIES
+
+In NLP, an input sample $i$ is often represented as a vector of tokens $\mathbf { w } _ { i } = \{ w _ { i , 1 } , w _ { i , 2 } , . . . , w _ { i , T } \}$ , with each token $w _ { i , t } \in \mathbb { R } ^ { V }$ a one-hot vector often representing words (but also possibly subwords, punctuation, or special tokens) and $V$ being the vocabulary size. These discrete tokens are then mapped to word embeddings $\mathbf x _ { i } = \{ x _ { i , 1 } , x _ { i , 2 } , . . . , x _ { i , T } \}$ , which serve as input to the machine learning model $f$ . For supervised classification problems, a one-hot label $y _ { i } \in \mathbb { R } ^ { C }$ indicates the ground-truth class of $\mathbf { x } _ { i }$ out of $C$ possible classes. The parameters $\theta$ of $f$ are optimized with some form of stochastic gradient descent so that the output of the model $f ( \mathbf { x } _ { i } ) \in \mathbb { R } ^ { \dot { C } }$ is as close to $y _ { i }$ as possible, with cross-entropy as the most common loss function:
+
+$$
+\mathcal { L } _ { \mathrm { M L E } } = - \frac { 1 } { n } \sum _ { i } ^ { n } y _ { i } \cdot \log ( f ( \mathbf { x } _ { i } ) )
+$$
+
+where $n$ is the number of samples, and $\cdot$ is the dot product.
+
+# 3.2 KNOWLEDGE DISTILLATION FOR BERT
+
+Consider two models $f$ and $g$ parameterized by $\theta _ { T }$ and $\theta _ { S }$ , respectively, with $| \theta _ { T } | \gg | \theta _ { S } |$ . Given enough training data and sufficient optimization, $f$ is likely to yield better accuracy than $g$ , due to higher modeling capacity, but may be too bulky or slow for certain applications. Being smaller in size, $g$ is more likely to satisfy operational constraints, but its weaker performance can be seen as a disadvantage. To improve $g$ , we can use the output prediction $f ( \mathbf { x } _ { i } )$ on input $\mathbf { x } _ { i }$ as extra supervision for $g$ to learn from, seeking to match $g ( \mathbf { x } _ { i } )$ with $f ( \mathbf { x } _ { i } )$ . Given these roles, we refer to $g$ as the student model and $f$ as the teacher model.
+
+While there are a number of recent large-scale language models driving the state of the art, we focus here on BERT (Devlin et al., 2018) models. Following Sun et al. (2019a), we use the notation $\mathrm { B E R T } _ { k }$ to indicate a BERT model with $k$ Transformer (Vaswani et al., 2017) layers. While powerful, BERT models also tend to be quite large; for example, the default bert-base-uncased $\mathrm { ( B E R T _ { 1 2 } }$ ) has ${ \sim } 1 1 0 \mathbf { M }$ parameters. Reducing the number of layers (e.g. using $\mathrm { B E R T _ { 3 } }$ ) makes such models significantly more portable and efficient, but at the expense of accuracy. With a knowledge distillation set-up, however, we aim to reduce this loss in performance.
+
+# 3.3 MIXUP DATA AUGMENTATION FOR KNOWLEDGE DISTILLATION
+
+While knowledge distillation can be a powerful technique, if the size of the available data is small, then the student has only limited opportunities to learn from the teacher. This may make it much harder for knowledge distillation to close the gap between student and teacher model performance. To correct this, we propose using data augmentation for knowledge distillation. While data augmentation (Yu et al., 2018; Xie et al., 2019; Yun et al., 2019; Kumar et al., 2019; Hendrycks et al.,
+
+2020; Shen et al., 2020; Qu et al., 2020) is a commonly used technique across machine learning for increasing training samples, robustness, and overall performance, a limited modeling capacity constrains the representations the student is capable of learning on its own. Instead, we propose using the augmented samples to further query the teacher model, whose large size often allows it to learn more powerful features.
+
+While many different data augmentation strategies have been proposed for NLP, we focus on mixup (Zhang et al., 2018) for generating additional samples to learn from the teacher. Mixup’s vicinal risk minimization tends to result in smoother decision boundaries and better generalization, while also being cheaper to compute than methods such as backtranslation (Yu et al., 2018; Xie et al., 2019). Mixup was initially proposed for continuous data, where interpolations between data points remain in-domain; its efficacy was demonstrated primarily on image data, but examples in speech recognition and tabular data were also shown to demonstrate generality.
+
+Directly applying mixup to NLP is not quite as straightforward as it is for images, as language commonly consists of sentences of variable length, each comprised of discrete word tokens. Since performing mixup directly on the word tokens doesn’t result in valid language inputs, we instead perform mixup on the word embeddings at each time step $x _ { i , t }$ (Guo et al., 2019). This can be interpreted as a special case of Manifold mixup Verma et al. (2019a), where the mixing layer is set to the embedding layer. In other words, mixup samples are generated as:
+
+$$
+\begin{array} { r l } & { x _ { i , t } ^ { \prime } = \lambda x _ { i , t } + ( 1 - \lambda ) x _ { j , t } \quad \forall t } \\ & { \quad y _ { i } ^ { \prime } = \lambda y _ { i } + ( 1 - \lambda ) y _ { j } } \end{array}
+$$
+
+with $\lambda \in [ 0 , 1 ]$ ; random sampling of $\lambda$ from a Uniform or Beta distribution are common choices. Note that we index the augmented sample with $i$ regardless of the value of $\lambda$ . Sentence length variability can be mitigated by grouping mixup pairs by length. Alternatively, padding is a common technique for setting a consistent input length across samples; thus, if $\mathbf { x } ^ { ( i ) }$ contains more word tokens than $\mathbf { x } ^ { ( j ) }$ , then the extra word embeddings are mixed up with zero paddings. We find this approach to be effective, while also being much simpler to implement.
+
+We query the teacher model with the generated mixup sample $\mathbf { x } _ { i } ^ { \prime }$ , producing output prediction $f ( \mathbf { x } _ { i } ^ { \prime } )$ The student is encouraged to imitate this prediction on the same input, by minimizing the objective:
+
+$$
+\mathcal { L } _ { \mathrm { T M K D } } = d ( f ( \mathbf { x } _ { i } ^ { \prime } ) , g ( \mathbf { x } _ { i } ^ { \prime } ) )
+$$
+
+where $d ( \cdot , \cdot )$ is a distance metric for distillation, with temperature-adjusted cross-entropy and mean square error (MSE) being common choices.
+
+Since we have the mixup samples already generated (with an easy-to-generate interpolated pseudolabel $y _ { i } ^ { \prime } )$ , we can also train the student model on these augmented data samples in the usual way, with a cross-entropy objective:
+
+$$
+\mathcal { L } _ { \mathrm { S M } } = - \frac { 1 } { n } \sum _ { i } ^ { n } y _ { i } ^ { \prime } \cdot \log ( g ( \mathbf { x } _ { i } ^ { \prime } ) )
+$$
+
+Our final objective for $M i x K D$ is a sum of the original data cross-entropy loss, student cross-entropy loss on the mixup samples, and knowledge distillation from the teacher on the mixup samples:
+
+$$
+\mathcal { L } = \mathcal { L } _ { \mathrm { M L E } } + \alpha _ { \mathrm { S M } } \mathcal { L } _ { \mathrm { S M } } + \alpha _ { \mathrm { T M K D } } \mathcal { L } _ { \mathrm { T M K D } }
+$$
+
+where $\alpha _ { \mathrm { S M } }$ and $\alpha _ { \mathrm { T M K D } }$ are hyperparameters weighting the loss terms.
+
+# 3.4 THEORETICAL ANALYSIS
+
+We develop a theoretical foundation for the proposed framework. We wish to prove that by adopting data augmentation for knowledge distillation, one can achieve $\ddot { \iota }$ ) a smaller gap between generalization error and empirical error, and $\romannumeral 2$ ) better generalization.
+
+To this end, assume the original training data $\{ { \bf x } _ { i } \} _ { i = 1 } ^ { n }$ are sampled i.i.d. from the true data distribution $p ( \mathbf { x } )$ , and the augmented data distribution by mixup is denoted as $q ( \mathbf { x } )$ (apparently $p$ and $q$ are dependent). Let $f$ be the teacher function, and $g \in { \mathcal { G } }$ be the learnable student function. Denote the loss function to learn $g$ as $l ( \cdot , \cdot ) ^ { 1 }$ . The population risk w.r.t. $p ( \mathbf { x } )$ is defined as $\mathcal { R } ( f , g , p ) =$ $\mathbb { E } _ { \mathbf { x } \sim p ( \mathbf { x } ) } \left[ l ( f ( \mathbf { x } ) , g ( \mathbf { x } ) ) \right]$ , and the empirical risk as $\mathcal { R } _ { e m p } ( f , g , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { n } ) = \frac { 1 } { n } \sum _ { i = 1 } ^ { n } l ( f ( \mathbf { x } _ { i } ) , g ( \mathbf { x } _ { i } ) ) .$ A classic statement for generalization is the following: with at least $1 - \delta$ probability, we have
+
+$$
+\begin{array} { r } { \mathcal { R } ( f , g _ { p } , p ) - \mathcal { R } _ { e m p } ( f , g _ { p } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { n } ) \leq \epsilon , } \end{array}
+$$
+
+where $\epsilon > 0$ , and we have used $g _ { p }$ to indicate that the function is learned based on $p ( \mathbf { x } )$ . Note different training data would correspond to a different error $\epsilon$ in equation 9. We use $\epsilon _ { p }$ to denote the minimum value over all $\epsilon$ ’s satisfying equation 9. Similarly, we can replace $p$ with $q$ , and $\{ { \bf x } _ { i } \} _ { i = 1 } ^ { n }$ with $\{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b }$ in equation 9 in the data-augmentation case. In this case, the student function is learned based on both the training data and augmented data, which we denote as $g ^ { * }$ . Similarly, we also have a corresponding minimum error, which we denote as $\epsilon ^ { * }$ . Consequently, our goal of better generalization corresponds to proving $\mathcal { R } ( f , g ^ { \ast } , p ) \leq \mathcal { R } ( f , g _ { p } , p )$ , and the goal of a smaller gap corresponds to proving $\epsilon ^ { * } \leq \epsilon _ { p }$ . In our theoretical results, we will give conditions when these goals are achievable. First, we consider the following three cases about the joint data $\mathbf { X } \triangleq \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b }$ and the function class $\mathcal { G }$ :
+
+• Case 1: There exists a distribution $\tilde { p }$ such that $\mathbf { X }$ are i.i.d. samples from it2; $\mathcal { G }$ is a finite set.   
+• Case 2: There exists $\tilde { p }$ such that $\mathbf { X }$ are i.i.d. samples from it; $\mathcal { G }$ is an infinite set.   
+• Case 3: There does not exist a distribution $\tilde { p }$ such that $\mathbf { X }$ are i.i.d. samples from it.
+
+Our theoretical results are summarized in Theorems 1-3, which state that with enough augmented data, our method can achieve smaller generalization errors. Proofs are given in the Appendix.
+
+Theorem 1 Assume the loss function $l ( \cdot , \cdot )$ is upper bounded by $M > 0$ . Under Case 1, there exists a constant $c > 0$ such that if
+
+$$
+b \geq \frac { M ^ { 2 } \log ( | \mathcal { G } | / \delta ) } { c } - a
+$$
+
+then
+
+$$
+\epsilon ^ { * } \leq \epsilon _ { p }
+$$
+
+where $\epsilon ^ { * }$ and $\epsilon _ { p }$ denote the minimal generalization gaps one can achieve with or without augmented data, with at least $1 - \delta$ probability. If further assuming a better empirical risk with data augmentation (which is usually the case in practice), i.e., $\begin{array} { r } { \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a ^ { - } } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) \leq } \end{array}$ $\mathcal { R } _ { e m p } ( \bar { f } , g _ { p } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { n } )$ , we have
+
+$$
+\mathcal { R } ( f , g ^ { * } , p ) \leq \mathcal { R } ( f , g _ { p } , p )
+$$
+
+Theorem 2 Assume the loss function $l ( \cdot , \cdot )$ is upper bounded by $M > 0$ and Lipschitz continuous. Fix the probability parameter $\delta$ . Under Case 2, there exists a constant $c > 0$ such that if
+
+$$
+b \ge \frac { M ^ { 2 } \log ( 1 / \delta ) } { c } - a
+$$
+
+then
+
+$$
+\epsilon ^ { * } \leq \epsilon _ { p }
+$$
+
+where $\epsilon ^ { * }$ and $\epsilon _ { p }$ denote the minimal generalization gaps one can achieve with or without augmented data, with at least $1 - \delta$ probability. If further assuming a better empirical risk with data augmentation, i.e., $\mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) \leq \mathcal { R } _ { e m p } ( f , g _ { p } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { n } )$ , we have
+
+$$
+\mathcal { R } ( f , g ^ { * } , p ) \leq \mathcal { R } ( f , g _ { p } , p )
+$$
+
+A more interesting setting is Case 3. Our result is based on Baxter (2000), which studies learning from different and possibly correlated distributions.
+
+Theorem 3 Assume the loss function $l ( \cdot , \cdot )$ is upper bounded. Under Case 3, there exists constants $c _ { 1 } , c _ { 2 } , c _ { 3 } > 0$ such that if
+
+$$
+b \geq { \frac { a \log ( 4 / \delta ) } { c _ { 1 } a - c _ { 2 } } } a n d a \geq c _ { 3 }
+$$
+
+<table><tr><td>Model</td><td>SST-2</td><td>MRPC</td><td>QQP</td><td>MNLI-m</td><td>QNLI</td><td>RTE</td></tr><tr><td>BERT12</td><td>92.20</td><td>90.53/86.52</td><td>88.21/91.25</td><td>84.12</td><td>91.32</td><td>77.98</td></tr><tr><td>DistilBERT6</td><td>91.3</td><td>87.5/82.4</td><td>-/88.5</td><td>82.2</td><td>89.2</td><td>59.9</td></tr><tr><td>BERT6-FT</td><td>90.94</td><td>88.54/83.82</td><td>87.16/90.43</td><td>81.28</td><td>88.25</td><td>66.43</td></tr><tr><td>BERT6-TMKD</td><td>91.63</td><td>88.93/83.82</td><td>86.60/90.27</td><td>81.49</td><td>88.71</td><td>65.34</td></tr><tr><td>BERT6-SM+TMKD</td><td>91.17</td><td>89.30/84.31</td><td>87.19/90.56</td><td>82.02</td><td>88.63</td><td>65.34</td></tr><tr><td>BERT6-FT+BT</td><td>91.74</td><td>89.60/84.80</td><td>87.06/90.39</td><td>82.10</td><td>87.68</td><td>67.51</td></tr><tr><td>BERT6-TMKD+BT</td><td>91.86</td><td>89.52/84.56</td><td>87.15/90.59</td><td>82.17</td><td>88.38</td><td>69.98</td></tr><tr><td>BERT6-SM+TMKD+BT</td><td>92.09</td><td>89.22/84.07</td><td>87.57/90.78</td><td>82.53</td><td>88.82</td><td>67.87</td></tr><tr><td>BERT3-FT</td><td>87.16</td><td>81.68/71.08</td><td>84.99/88.65</td><td>75.55</td><td>83.98</td><td>58.48</td></tr><tr><td>BERT3-TMKD</td><td>88.76</td><td>81.62/71.08</td><td>83.27/87.80</td><td>75.73</td><td>84.26</td><td>58.48</td></tr><tr><td>BERT3-SM+TMKD</td><td>88.99</td><td>81.73/71.08</td><td>84.47/88.37</td><td>75.52</td><td>84.24</td><td>59.57</td></tr><tr><td>BERT3-FT+BT</td><td>88.88</td><td>83.36/74.26</td><td>85.31/88.81</td><td>76.88</td><td>83.67</td><td>59.21</td></tr><tr><td>BERT3-TMKD+BT</td><td>89.79</td><td>84.46/75.74</td><td>85.17/89.00</td><td>77.19</td><td>84.68</td><td>62.82</td></tr><tr><td>BERT3-SM+TMKD+BT</td><td>90.37</td><td>84.14/75.25</td><td>85.56/89.09</td><td>77.52</td><td>84.83</td><td>60.65</td></tr></table>
+
+Table 1: GLUE dev set results. We report the results of our $\mathrm { B E R T _ { 1 2 } }$ teacher model, the 6-layer DistilBERT, and 3- and 6-layer MixKD student models with various ablations. DistilBERT results taken from Sanh et al. (2019). For MRPC and QQP, we report F1/Accuracy.
+
+then
+
+$$
+\epsilon ^ { * } \leq \epsilon _ { p }
+$$
+
+where $\epsilon ^ { * }$ and $\epsilon _ { p }$ denote the minimal generalization gaps one can achieve with or without augmented data, with at least $1 - \delta$ probability. If further assuming a better empirical risk with data augmentation, i.e., $\mathcal { R } _ { e m p } ( f , g ^ { * } , \bar { \{ }  \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) \leq \mathcal { R } _ { e m p } ( \bar { f } , g _ { p } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { n } )$ , we have
+
+$$
+\mathcal { R } ( f , g ^ { * } , p ) \leq \mathcal { R } ( f , g _ { p } , p )
+$$
+
+Remark 4 For Theorem $^ 3$ to hold, based on Baxter (2000), it is enough to ensure $\{ \mathbf { x } _ { i } , \mathbf { x } _ { i } ^ { \prime } \}$ and $\{ \mathbf { x } _ { j } , \mathbf { x } _ { j } ^ { \prime } \}$ to be independent for $i \neq j$ . We achieve this by constructing $\mathbf { x } _ { i } ^ { \prime }$ with $\mathbf { x } _ { i }$ and an extra random sample from the training data. Since all $\left( \mathbf { x } _ { i } , \mathbf { x } _ { j } \right)$ and the extra random samples are independent, the resulting concatenation will also be independent.
+
+# 4 EXPERIMENTS
+
+We demonstrate the effectiveness of MixKD on a number of GLUE (Wang et al., 2019) dataset tasks: Stanford Sentiment Treebank (SST-2) (Socher et al., 2013), Microsoft Research Paraphrase Corpus (MRPC) (Dolan & Brockett, 2005), Quora Question Pairs $( \mathrm { Q Q P } ) ^ { 3 }$ , Multi-Genre Natural Language Inference (MNLI) (Williams et al., 2018), Question Natural Language Inference (QNLI) (Rajpurkar et al., 2016), and Recognizing Textual Entailment (RTE) (Dagan et al., 2005; Haim et al., 2006; Giampiccolo et al., 2007; Bentivogli et al., 2009). Note that MNLI contains both an in-domain (MNLI-m) and cross-domain (MNLI-mm) evaluation set. These datasets span sentiment analysis, paraphrase similarity matching, and natural language inference types of tasks. We use the Hugging Face Transformers4 implementation of BERT for our experiments.
+
+# 4.1 GLUE DATASET EVALUATION
+
+We first analyze the contributions of each component of our method, evaluating on the dev set of the GLUE datasets. For the teacher model, we fine-tune a separate 12 Transformer-layer bert-base-uncased $( \mathrm { B E R T _ { 1 2 } } )$ ) for each task. We use the smaller $\mathrm { B E R T _ { 3 } }$ and $\mathrm { B E R T _ { 6 } }$ as the student model. We find that initializing the embeddings and Transformer layers of the student model from the first $k$ layers of the teacher model provides a significant boost to final performance. We use MSE as the knowledge distillation distance metric $d ( \cdot , \cdot )$ . We generate one mixup sample for each original sample in each minibatch (mixup ratio of 1), with $\lambda \sim \operatorname { B e t a } ( 0 . 4 , 0 . 4 )$ . We set hyperparameters weighting the components in the loss term in equation 8 as $\alpha _ { \mathrm { S M } } = \alpha _ { \mathrm { T M K D } } = 1$ .
+
+Table 3: GLUE test server results. We show results for the full variants of the 3- and 6-layer MixKD student models $( \mathbf { S } \mathbf { M } \mathbf { + } \mathbf { T } \mathbf { M } \mathbf { K } \mathbf { D } \mathbf { + } \mathbf { B } \mathbf { T } )$ . Knowledge distillation (KD) and Patient Knowledge Distillation (PKD) results are from Sun et al. (2019a).   
+
+<table><tr><td>Model</td><td>SST-2</td><td>MRPC</td><td>QQP</td><td>MNLI-m</td><td>MNLI-mm</td><td>QNLI</td><td>RTE</td></tr><tr><td>BERT12</td><td>93.5</td><td>88.9/84.8</td><td>71.2/89.2</td><td>84.6</td><td>83.4</td><td>90.5</td><td>66.4</td></tr><tr><td>BERT6-FT</td><td>90.7</td><td>85.9/80.2</td><td>69.2/88.2</td><td>80.4</td><td>79.7</td><td>86.7</td><td>63.6</td></tr><tr><td>BERT6-KD</td><td>91.5</td><td>86.2/80.6</td><td>70.1/88.8</td><td>80.2</td><td>79.8</td><td>88.3</td><td>64.7</td></tr><tr><td>BERT6-PKD</td><td>92.0</td><td>85.0/79.9</td><td>70.7/88.9</td><td>81.5</td><td>81.0</td><td>89.0</td><td>65.5</td></tr><tr><td>BERT6-MixKD</td><td>92.5</td><td>86.4/81.9</td><td>70.5/89.1</td><td>82.2</td><td>81.2</td><td>88.2</td><td>68.3</td></tr><tr><td>BERT3-FT</td><td>86.4</td><td>80.5/72.6</td><td>65.8/86.9</td><td>74.8</td><td>74.3</td><td>84.3</td><td>55.2</td></tr><tr><td>BERT3-KD</td><td>86.9</td><td>79.5/71.1</td><td>67.3/87.6</td><td>75.4</td><td>74.8</td><td>84.0</td><td>56.2</td></tr><tr><td>BERT3-PKD</td><td>87.5</td><td>80.7/72.5</td><td>68.1/87.8</td><td>76.7</td><td>76.3</td><td>84.7</td><td>58.2</td></tr><tr><td>BERT3-MixKD</td><td>89.5</td><td>83.3/75.2</td><td>67.2/87.4</td><td>77.2</td><td>76.8</td><td>84.4</td><td>62.0</td></tr></table>
+
+As a baseline, we fine-tune the student model on the task dataset without any distillation or augmentation, which we denote as $\mathrm { B E R T } _ { k }$ -FT. We compare this against MixKD, with both knowledge distillation on the teacher’s predictions $( \mathcal { L } _ { \mathrm { T M K D } } )$ and mixup for the student $( \mathcal { L } _ { \mathrm { S M } } )$ , which we call $\mathrm { B E R T } _ { k }$ -SM+TMKD. We also evaluate an ablated version without the student mixup loss $( \mathrm { B E R T } _ { k }$ - TMKD) to highlight the knowledge distillation component specifically. We note that our method can also easily be combined with other forms of data augmentation. For example, backtranslation (translating an input sequence to the data space of another language and then translating back to the original language) tends to generate varied but semantically similar sequences; these sentences also tend to be of higher quality than masking or word-dropping approaches. We show that our method has an additive effect with other techniques by also testing our method with the dataset augmented with German backtranslation, using the fairseq (Ott et al., 2019) neural machine translation codebase to generate these additional samples. We also compare all of the aforementioned variants with backtranslation samples augmenting the data; we denote these variants with an additional $+ \mathbf { B } \mathrm { T }$ .
+
+We report the model accuracy (and $F _ { 1 }$ score, for MRPC and QQP) in Table 1. We also show the performance of the full-scale teacher model $\mathrm { ( B E R T _ { 1 2 } ) }$ ) and DistilBERT (Sanh et al., 2019), which performs basic knowledge distillation during BERT pre-training to a 6-layer model. For our method, we observe that a combination of data augmentation and knowledge
+
+Table 2: Computation cost comparison of teacher and student models on SST-2 with batch size of 16 on a Nvidia TITAN X GPU.   
+
+<table><tr><td>Model</td><td>Inference Speed (samples/second)</td><td># of Parameters</td></tr><tr><td>BERT12Teacher</td><td>115</td><td>109,483,778</td></tr><tr><td>BERT6 Student</td><td>252</td><td>66,956,546</td></tr><tr><td>BERT3 Student</td><td>397</td><td>45,692,930</td></tr></table>
+
+distillation leads to significant gains in performance, with the best variant often being the combination of teacher mixup knowledge distillation, student mixup, and backtranslation. In the case of SST-2, for example, $\mathrm { B E R T _ { 6 } }$ - $\mathbf { \cdot S M { + } T M K D { + } B T }$ is able to capture $9 9 . 8 8 \%$ of the performance of the teacher model, closing $9 1 . 2 7 \%$ of the gap between the fine-tuned student model and the teacher, despite using far fewer parameters and having a much faster inference speed (Table 2).
+
+After analyzing the contributions of the components of our model on the dev set, we find the $\mathbf { S M + T M K D + B T }$ variant to have the best performance overall and thus focus on this variant. We submit this version of MixKD to the GLUE test server, reporting its results in comparison with fine-tuning (FT), vanilla knowledge distillation (KD) (Hinton et al., 2015), and patient knowledge distillation (PKD) (Sun et al., 2019a) in Table 3. Once again, we observe that our model outperforms the baseline methods on most tasks.
+
+# 4.2 LIMITED-DATA SETTINGS
+
+One of the primary motivations for using data augmentation for knowledge distillation is to give the student more opportunities to query the teacher model. For datasets with a large enough number of samples relative to the task’s complexity, the original dataset may provide enough chances to learn from the teacher, reducing the relative value of data augmentation.
+
+As such, we also evaluate MixKD with a $\mathrm { B E R T _ { 3 } }$ student on downsampled versions of QQP, MNLI (matched and mismatched), and QNLI in Figure 1. We randomly select $\mathrm { \bar { 1 0 \% } }$ and $1 \%$ of the data from these datasets to train both the teacher and student models, using the same subset for all experiments for fair comparison. In this data limited setting, we observe substantial gains from MixKD over the fine-tuned model for QQP $( + 2 . 0 \%$ , $+ 3 . 0 \%$ ), MNLI-m $( + 3 . 9 \%$ , $+ 3 . 4 \%$ ), MNLI-mm $( + 4 . 4 \%$ , $+ 3 . 3 \% )$ , and QNLI $( + 2 . 4 \%$ , $+ 4 . 1 \% )$ for $1 0 \%$ and $1 \%$ of the training data.
+
+![](images/c5bcdcd1a0c59614f736754e18078ae259700123df7980256d42f9f620505099.jpg)  
+Figure 1: Results of limited data case, where both the teacher and student models are learned with only $10 \%$ (left) or $1 \%$ of the training data (right).
+
+# 4.3 EMBEDDINGS VISUALIZATION
+
+We perform a qualitative examination of the effect of the proposed MixKD by visualizing the latent space between positive and negative samples as encoded by the student model with tSNE plots (Maaten & Hinton, 2008). In Figure 2, we show the shift of the transformer features at the [CLS] token position, with and without mixup data augmentation from the teacher. We randomly select a batch of 100 sentences from the SST-2 dataset, of which 50 are positive sentiment (blue square) and 50 are negative sentiment (red circle). The intermediate mixup neighbours are indicated by triangles with color determined by the closeness to the positive group or negative group. From Figure 2(a) to Figure 2(b), MixKD forces the lin
+
+![](images/d6991a5e3c137e2e71d05bf54381a199dfeeb9862f2ae8d771c9ffdb0a9fc98a.jpg)  
+Figure 2: Latent space of randomly sampled training data and their mixup neighbours encoded by student model (a) learned by standard finetuning (b) learned with MixKD.
+
+early interpolated samples to be aligned with the manifold formed by the real training data and leads the student model to explore meaningful regions of the feature space effectively.
+
+# 4.4 HYPERPARAMETER SENSITIVITY & FURTHER ANALYSIS
+
+Loss Hyperparameters Our final objective in equation 8 has hyperparameters $\alpha _ { \mathrm { S M } }$ and $\alpha _ { \mathrm { T M K D } }$ , which control the weight of the student model’s cross-entropy loss for the mixup samples and the knowledge distillation loss with the teacher’s predictions on the mixup samples, respectively. We demonstrate that the model is fairly stable over a wide range by sweeping both $\alpha _ { \mathrm { S M } }$ and $\alpha _ { \mathrm { T M K D } }$ over the range $\{ 0 . 1 , 0 . 5 , 1 . 0 , 2 . 0 , 1 0 . 0 \}$ . We do this for a $\mathrm { B E R T _ { 3 } }$ student and $\mathrm { B E R T _ { 1 2 } }$ teacher, with SST-2 as the task; we show the results of this sensitivity study, both with and without German backtranslation, in Figure 3. Given the overall consistency, we observe that our method is stable over a wide range of settings.
+
+Mixup Ratio We also investigate the effect of the mixup ratio: the number of mixup samples generated for each sample in a minibatch. We run a smaller sweep of $\alpha _ { \mathrm { S M } }$ and $\alpha _ { \mathrm { T M K D } }$ over the range $\{ 0 . 5 , 1 . 0 , 2 . 0 \}$ for mixup ratios of 2 and 3 for a $\mathrm { B E R T _ { 3 } }$ student SST-2, with and without German backtranslation, in Figure 3. We conclude that the mixup ratio does not have a strong effect on overall performance. Given that higher mixup ratio requires more computation (due to more samples over which to compute the forward and backward pass), we find a mixup ratio of 1 to be enough.
+
+![](images/4d565200ecf3aece19166b7c4c3f00505dd0f5dad6d7f5604a5cf75ccab94b25.jpg)  
+Figure 3: Hyperparameter sensitivity analysis regarding the MixKD approach, with different choices of $\alpha _ { \mathrm { T M K D } }$ , $\alpha _ { \mathrm { S M } }$ and the ratio of mixup samples (w.r.t. the original training data).
+
+Comparing with TinyBERT’s DA module TinyBERT (Jiao et al., 2019) also utilizes data augmentation for knowledge distillation. Specifically, they adopt a conditional BERT contextual augmentation (Wu et al., 2019) strategy. To further verify the effectiveness of our approach, we use TinyBERT’s released codebase5 to generate augmented samples and make
+
+<table><tr><td>Methods</td><td>MNLI</td><td>SST-2</td></tr><tr><td>BERT6</td><td>81.3</td><td>90.9</td></tr><tr><td>BERT6+ TinyBERTDA module</td><td>81.5</td><td>91.3</td></tr><tr><td>BERT6+MixKD</td><td>82.5</td><td>92.1</td></tr></table>
+
+Table 4: We compare our approach with the data augmentation module proposed by TinyBert (Jiao et al., 2019).
+
+a direct comparison with MixKD. As shown in Table 4, our approach exhibits much stronger results for distilling a 6-layer BERT model (on both MNLI and SST-2 datasets). Notably, TinyBERT’s data augmentation module is much less efficient than mixup’s simple operation, generating 20 times the original data as augmented samples, thus leading to massive computation overhead.
+
+# 5 CONCLUSIONS
+
+We introduce MixKD, a method that uses data augmentation to significantly increase the value of knowledge distillation for compressing large-scale language models. Intuitively, MixKD allows the student model additional queries to the teacher model, granting it more opportunities to absorb the latter’s richer representations. We analyze MixKD from a theoretical standpoint, proving that our approach results in a smaller gap between generalization error and empirical error, as well as better generalization, under appropriate conditions. Our approach’s success on a variety of GLUE tasks demonstrates its broad applicability, with a thorough set of experiments for validation. We also believe that the MixKD framework can further reduce the gap between student and teacher models with the incorporation of more recent mixup and knowledge distillation techniques (Lee et al., 2020; Wang et al., 2020; Mirzadeh et al., 2019), and we leave this to future work.
+
+# ACKNOWLEDGMENTS
+
+CC is partly supported by the Verizon Media FREP program.
+
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+
+# A PROOFS
+
+Proof [Proof of Theorem 1] First of all, $\{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b }$ can be regarded as drawn from distribution $r ( \mathbf { x } ) = \frac { a p ( \mathbf { x } ) + b q ( \mathbf { x } ) } { a + b }$
+
+Given $\mathcal { G }$ is finite, we have the following theorem
+
+Theorem 5 (Mohri et al., 2018) Let $l$ be a bounded loss function, hypothesis set $\mathcal { G }$ is finite. Then for any $\delta > 0$ , with probability at least $1 - \delta$ , the following inequality holds for all $g \in { \mathcal { G } }$ :
+
+$$
+\mathcal { R } ( f , g , p ) - \mathcal { R } _ { e m p } ( f , g , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { n } ) \leq M \sqrt { \frac { \log ( | \mathcal { G } | / \delta ) } { 2 n } }
+$$
+
+Thus we have in our case:
+
+$$
+\mathcal { R } ( f , g _ { p } , p ) - \mathcal { R } _ { e m p } ( f , g _ { p } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { n } ) \leq \epsilon _ { p } \leq M \sqrt { \frac { { \log ( | \mathcal { G } | / \delta ) } } { 2 n } }
+$$
+
+and
+
+$$
+\begin{array} { r l } {  { \mathcal { R } ( f , g ^ { * } , p ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \big \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) } } \\ & { = \mathcal { R } ( f , g ^ { * } , r ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \big \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) + \int l ( f ( \mathbf { x } ) , g ^ { * } ( \mathbf { x } ) ) ( p ( \mathbf { x } ) - r ( \mathbf { x } ) ) d \mathbf { x } } \\ & { = \mathcal { R } ( f , g ^ { * } , r ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \big \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) + \frac { b } { a + b } \int l ( f ( \mathbf { x } ) , g ^ { * } ( \mathbf { x } ) ) ( p ( \mathbf { x } ) - q ( \mathbf { x } ) ) d \mathbf { x } } \\ & { \leq \mathcal { R } ( f , g ^ { * } , r ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \big \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) + \int l ( f ( \mathbf { x } ) , g ^ { * } ( \mathbf { x } ) ) ( p ( \mathbf { x } ) - q ( \mathbf { x } ) ) d \mathbf { x } } \\ & { { \overset { } { \leq } } M \sqrt { \frac { \log ( | \mathcal { G } | / \delta ) } { 2 ( a + b ) } } + \bigtriangleup } & { ( 1 } \end{array}
+$$
+
+where $\begin{array} { r } { \triangle = \int l ( f ( \mathbf { x } ) , g ^ { * } ( \mathbf { x } ) ) ( p ( \mathbf { x } ) - q ( \mathbf { x } ) ) d \mathbf { x } } \end{array}$ . If
+
+$$
+b \ge \frac { M ^ { 2 } \log ( | \mathcal { G } | / \delta ) } { 2 ( \epsilon _ { p } - \triangle ) ^ { 2 } } - a
+$$
+
+then
+
+$$
+\begin{array} { r l r } & { } & { 2 ( a + b ) \ge \frac { M ^ { 2 } \log ( | \mathcal { G } | / \delta ) } { ( \epsilon _ { p } - \triangle ) ^ { 2 } } } \\ & { } & { ( \epsilon _ { p } - \triangle ) ^ { 2 } \ge \frac { M ^ { 2 } \log ( | \mathcal { G } | / \delta ) } { 2 ( a + b ) } } \\ & { } & { \epsilon _ { p } \ge M \sqrt { \frac { \log ( | \mathcal { G } | / \delta ) } { 2 ( a + b ) } } + \triangle } \end{array}
+$$
+
+Substitute into equation 10, we have
+
+$$
+\begin{array} { r } { \mathcal { R } ( f , g ^ { * } , p ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) \leq \epsilon _ { p } } \end{array}
+$$
+
+Recall the definition of $\epsilon ^ { * }$ , which is the minimum value of all possible $\epsilon$ satisfying
+
+$$
+\mathcal { R } ( f , g ^ { * } , p ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) \leq \epsilon
+$$
+
+we know that $\epsilon ^ { * } \leq \epsilon _ { p }$ . Let $c = 2 ( \epsilon _ { p } - \triangle ) ^ { 2 }$ , we can conclude the theorem.
+
+Proof [Proof of Theorem 2] First of all, $\{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b }$ can be regarded as drawn from distribution $r ( \mathbf { x } ) = \frac { a p ( \mathbf { x } ) + b q ( \mathbf { x } ) } { a + b }$
+
+Theorem 6 (Mohri et al., 2018) Let $l$ be a non-negative loss function upper bounded by $M > 0$ , and for any fixed y, $l ( \mathbf { y } , \mathbf { y } ^ { \prime } )$ is $L$ -Lipschitz for some $L > 0$ , then with probability at least $1 - \delta$ ,
+
+$$
+\mathcal { R } ( f , g , p ) - \mathcal { R } _ { e m p } ( f , g , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { n } ) \leq 2 L \Re _ { p } ( \mathcal { G } ) + M \sqrt { \frac { l o g ( 1 / \delta ) } { 2 n } }
+$$
+
+Thus we have
+
+$$
+\mathcal { R } ( f , g , p ) - \mathcal { R } _ { e m p } ( f , g , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { n } ) \leq \epsilon _ { p } \leq 2 L \Re _ { p } ( \mathcal { G } ) + M \sqrt { \frac { l o g ( 1 / \delta ) } { 2 n } }
+$$
+
+where $\Re _ { p } ( \mathcal { G } )$ are Rademacher complexity over all samples of size $n$ samples from $p ( \mathbf { x } )$
+
+We also have
+
+$$
+\begin{array} { r l r } {  { \mathcal { R } ( f , g ^ { * } , p ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \big \{ \mathbf { x } _ { i } \big \} _ { i = 1 } ^ { a } \cup \big \{ \mathbf { x } _ { i } ^ { \prime } \big \} _ { i = 1 } ^ { b } ) } } \\ & { = \mathcal { R } ( f , g ^ { * } , r ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \big \{ \mathbf { x } _ { i } \big \} _ { i = 1 } ^ { a } \cup \big \{ \mathbf { x } _ { i } ^ { \prime } \big \} _ { i = 1 } ^ { b } ) + \int l ( f ( \mathbf { x } ) , g ^ { * } ( \mathbf { x } ) ) ( p ( \mathbf { x } ) - r ( \mathbf { x } ) ) d \mathbf { x } } \\ & { = \mathcal { R } ( f , g ^ { * } , r ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \big \{ \mathbf { x } _ { i } \big \} _ { i = 1 } ^ { a } \cup \big \{ \mathbf { x } _ { i } ^ { \prime } \big \} _ { i = 1 } ^ { b } ) + \frac { b } { a + b } \int l ( f ( \mathbf { x } ) , g ^ { * } ( \mathbf { x } ) ) ( p ( \mathbf { x } ) - q ( \mathbf { x } ) ) d \mathbf { x } } \\ & { \leq \mathcal { R } ( f , g ^ { * } , r ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \big \{ \mathbf { x } _ { i } \big \} _ { i = 1 } ^ { a } \cup \big \{ \mathbf { x } _ { i } ^ { \prime } \big \} _ { i = 1 } ^ { b } ) + \int l ( f ( \mathbf { x } ) , g ^ { * } ( \mathbf { x } ) ) ( p ( \mathbf { x } ) - q ( \mathbf { x } ) ) d \mathbf { x } } \\ & { \leq 2 L \mathfrak { R } _ { r } ( \mathcal { G } ) + M \sqrt { \frac { l o g ( 1 / \delta ) } { 2 ( a + b ) } } + \bigtriangleup } & { ( 1 } \end{array}
+$$
+
+where $\begin{array} { r } { \triangle = \int l ( f ( \mathbf { x } ) , g ^ { * } ( \mathbf { x } ) ) ( p ( \mathbf { x } ) - q ( \mathbf { x } ) ) d \mathbf { x } . \Re _ { r } ( \mathcal { G } ) } \end{array}$ are Rademacher complexity over all samples of size $( a + b )$ samples from $r ( \mathbf { x } ) = \frac { a p ( \mathbf { x } ) + b q ( \mathbf { x } ) } { a + b }$
+
+If
+
+then:
+
+$$
+\begin{array} { l } { { b \geq \displaystyle \frac { M ^ { 2 } \log ( 1 / \delta ) } { 2 ( \epsilon _ { p } - \bigtriangleup - 2 L \mathfrak { N } _ { r } ( \mathcal { G } ) ) ^ { 2 } } - a } } \\ { { \mathrm { } } } \\ { { 2 ( a + b ) \geq \displaystyle \frac { M ^ { 2 } \log ( 1 / \delta ) } { ( \epsilon _ { p } - \bigtriangleup - 2 L \mathfrak { N } _ { r } ( \mathcal { G } ) ) ^ { 2 } } } } \\ { { \epsilon _ { p } - \bigtriangleup - 2 L \mathfrak { N } _ { r } ( \mathcal { G } ) \geq M \sqrt { \displaystyle \frac { \log ( 1 / \delta ) } { 2 ( a + b ) } } } } \\ { { \epsilon _ { p } \geq M \sqrt { \displaystyle \frac { \log ( 1 / \delta ) } { 2 ( a + b ) } } + \bigtriangleup + 2 L \mathfrak { N } _ { r } ( \mathcal { G } ) } } \end{array}
+$$
+
+Substitute into equation 11, we have:
+
+$$
+\begin{array} { r } { \mathcal { R } ( f , g ^ { * } , p ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) \leq \epsilon _ { p } } \end{array}
+$$
+
+Recall the definition of $\epsilon ^ { * }$ , which is the minimum value of all possible $\epsilon$ satisfying
+
+$$
+\mathcal { R } ( f , g ^ { * } , p ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) \leq \epsilon
+$$
+
+we know that $\epsilon ^ { * } \leq \epsilon _ { p }$ . Let $c = 2 ( \epsilon _ { p } - \triangle - 2 L \Re _ { r } ( \mathcal { G } ) ) ^ { 2 }$ , we can conclude the theorem.
+
+Proof [Proof of Theorem 3] Similar to previous theorems, we write
+
+$$
+\begin{array} { l } { { \displaystyle \mathcal R ( f , g ^ { * } , p ) - \mathcal R _ { e m p } \big ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } \big ) } } \\ { { \displaystyle = \mathcal R \big ( f , g ^ { * } , \frac { a p + b q } { a + b } \big ) - \mathcal R _ { e m p } \big ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } \big ) + \int l ( f ( \mathbf { x } ) , g ^ { * } ( \mathbf { x } ) \big ) \big ( p ( \mathbf { x } ) - \frac { a p ( \mathbf { x } ) + b q ( \mathbf { x } ) } { a + b } \big ) \int l ( f ( \mathbf { x } ) - p ) \big ( f ( \mathbf { x } ) - p ) \big ( f ( \mathbf { x } ) - p \big ) ( f ( \mathbf { x } ) - q ( \mathbf { x } ) \big ) } } \\ { { \displaystyle = \mathcal R \big ( f , g ^ { * } , \frac { a p + b q } { a + b } \big ) - \mathcal R _ { e m p } \big ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \big \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } \big ) + \frac { b } { a + b } \int l ( f ( \mathbf { x } ) , g ^ { * } ( \mathbf { x } ) ) \big ( p ( \mathbf { x } ) - q ( \mathbf { x } ) \big ) d \mathbf { x } \ } } \\ { { \displaystyle \leq \mathcal R \big ( f , g ^ { * } , \frac { a p + b q } { a + b } \big ) - \mathcal R _ { e m p } \big ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \big \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } \big ) + \bigtriangleup } } \end{array}
+$$
+
+where $\begin{array} { r l r } { \triangle } & { { } = } & { \int l ( f ( \mathbf { x } ) , g ^ { * } ( \mathbf { x } ) ) ( p ( \mathbf { x } ) - \mathbf { \nabla } q ( \mathbf { x } ) ) d \mathbf { x } } \end{array}$ . For notation consistency, we write $\begin{array} { l } { \displaystyle \mathcal { R } ( f , g ^ { * } , \frac { a p + b q } { a + b } ) = \int l ( f ( \mathbf { x } ) - g ( \mathbf { x } ) ) \frac { a p ( \mathbf { x } ) + b q ( \mathbf { x } ) } { a + b } d \mathbf { x } } \end{array}$ ) d x. However, {xi}ai=1 ∪ {x0i}bi=1 are not drawn from the same distribution (which is r(x) = ap(x) + bq(x) i n previous cases).
+
+Let $\gamma = \lfloor \frac { a + b } { a } \rfloor$ , we split $\{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b }$ into $\gamma$ parts that don’t overlap with each other. The first part is $\{ { \bf x } _ { i } \} _ { i = 1 } ^ { a }$ , all the other parts has at least $a$ elements from $\{ { \bf x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b }$ .
+
+Let
+
+$$
+\lambda = \sqrt { \frac { 6 4 } { b } \log ( 4 / \delta ) + \frac { 6 4 } { a } \log C ( \mathcal { G } ) }
+$$
+
+where $C ( \mathcal G )$ is space capacity defined in Definition 4 in Baxter (2000), which depends on $\epsilon ^ { * }$ and $\mathcal { G }$ .
+
+By Theorem 4 in Baxter (2000),
+
+$$
+\left[ \mathcal { R } ( f , g ^ { * } , \frac { a p + b q } { a + b } ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) \right] ^ { 2 } \leq \operatorname* { m a x } \{ \frac { 6 4 } { \gamma a } \log ( \frac { 4 C ( \mathcal { G } ^ { \gamma } ) } { \delta } ) , \frac { 1 6 } { a } \}
+$$
+
+By Theorem 5 in Baxter (2000),
+
+$$
+\frac { 6 4 } { \gamma a } \log ( \frac { 4 C ( \mathcal { G } ^ { \gamma } ) } { \delta } ) = \frac { 6 4 } { \gamma a } ( \log ( \frac { 4 } { \delta } ) + \log ( C ( \mathcal { G } ^ { \gamma } ) ) ) \leq \frac { 6 4 } { \gamma a } ( \log ( \frac { 4 } { \delta } ) + \gamma \log ( C ( \mathcal { G } ) ) ) \leq \lambda ^ { 2 }
+$$
+
+The last inequality comes from $b \leq \gamma a$ , which is because of $\gamma = \lfloor \frac { a + b } { a } \rfloor$ . Then we have
+
+$$
+\mathcal { R } ( f , g ^ { * } , \frac { a p + b q } { a + b } ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) \bigg ] ^ { 2 } \leq \operatorname* { m a x } \{ \frac { 6 4 } { \gamma a } \log ( \frac { 4 C ( Q ^ { \gamma } ) } { \delta } ) , \frac { 1 6 } { a } \} \leq \operatorname* { m a x } \{ \lambda ^ { \gamma } \} ^ { \delta } .
+$$
+
+If
+
+$$
+b \ge \frac { 6 4 \log ( 4 / \delta ) } { ( \epsilon _ { p } - \triangle ) ^ { 2 } - 6 4 \log C ( \mathcal { G } ) / a }
+$$
+
+Then
+
+$$
+\lambda ^ { 2 } \leq \frac { 6 4 } { a } \log C ( \mathcal { G } ) + 6 4 \log ( \frac { 4 } { \delta } ) \frac { ( \epsilon _ { p } - \bigtriangleup ) ^ { 2 } - 6 4 \log C ( \mathcal { G } ) / a } { 6 4 \log ( 4 / \delta ) }
+$$
+
+$$
+\lambda ^ { 2 } \le ( \epsilon _ { p } - \triangle ) ^ { 2 }
+$$
+
+If
+
+$$
+\frac { 1 6 } { ( \epsilon _ { p } - \triangle ) ^ { 2 } } \leq a
+$$
+
+then
+
+$$
+\frac { 1 6 } { a } \leq ( \epsilon _ { p } - \triangle ) ^ { 2 }
+$$
+
+Combine equation 13 and equation 14, we have
+
+$$
+\mathcal { R } ( f , g ^ { * } , \frac { a p + b q } { a + b } ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) \leq \epsilon _ { p } - \bigtriangleup
+$$
+
+Substitute into equation 12, we have:
+
+$$
+\begin{array} { r } { \mathcal { R } ( f , g ^ { * } , p ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) \leq \epsilon _ { p } } \end{array}
+$$
+
+Recall the definition of $\epsilon ^ { * }$ , which is the minimum value of all possible $\epsilon$ satisfying
+
+$$
+\mathcal { R } ( f , g ^ { * } , p ) - \mathcal { R } _ { e m p } ( f , g ^ { * } , \{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { a } \cup \{ \mathbf { x } _ { i } ^ { \prime } \} _ { i = 1 } ^ { b } ) \leq \epsilon
+$$
+
+we know that $\epsilon ^ { * } \leq \epsilon _ { p }$
+
+# B VARIANCE ANALYSIS
+
+For the purpose of getting a sense of variance, we run experiments with additional random seeds on MRPC and RTE, which are relatively smaller datasets, and MNLI and QNLI, which are relatively larger datasets. Mean and standard deviation on the dev set of these GLUE datasets are reported in Table 5. We observe the variance of the same model’s performance to be small, especially on the relatively larger datasets.
+
+<table><tr><td>Model</td><td>MRPC</td><td>MNLI-m</td><td>QNLI</td><td>RTE</td></tr><tr><td>BERT6-TMKD+BT BERT6-SM+TMKD+BT</td><td>89.79±0.27/85.04±0.48 89.64±0.38/84.43±0.36</td><td>82.05±0.11 82.41±0.12</td><td>88.42±0.06</td><td>69.37±0.50</td></tr><tr><td>BERT3-TMKD+BT</td><td>84.79±0.33/75.82±0.48</td><td></td><td>88.76±0.15</td><td>68.02±0.11</td></tr><tr><td></td><td></td><td>77.16±0.03</td><td>84.60±0.07</td><td>62.47±0.36</td></tr><tr><td>BERT3-SM+TMKD+BT</td><td>84.53±0.39/75.85±0.60</td><td>77.42±0.11</td><td>84.88±0.06</td><td>60.83±0.18</td></tr></table>
+
+Table 5: Mean and variance reported for $\mathrm { B E R T _ { 6 } }$ -TMKD $^ +$ BT,BERT $^ 6$ -SM+TMKD $^ +$ BT,BERT3- TMKD+BT and $\mathrm { B E R T _ { 3 } }$ -SM $+$ TMKD+BT.