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

Please answer the questions based on the text provided below. What other sentence embeddings methods are evaluated?
Context 1: Introduction
In this publication, we present Sentence-BERT (SBERT), a modification of the BERT network using siamese and triplet networks that is able to derive semantically meaningful sentence embeddings  This enables BERT to be used for certain new tasks, which up-to-now were not applicable for BERT  These tasks include large-scale semantic similarity comparison, clustering, and information retrieval via semantic search 
BERT set new state-of-the-art performance on various sentence classification and sentence-pair regression tasks  BERT uses a cross-encoder: Two sentences are passed to the transformer network and the target value is predicted  However, this setup is unsuitable for various pair regression tasks due to too many possible combinations  Finding in a collection of $n=10\,000$ sentences the pair with the highest similarity requires with BERT $n\cdot (n-1)/2=49\,995\,000$ inference computations  On a modern V100 GPU, this requires about 65 hours  Similar, finding which of the over 40 million existent questions of Quora is the most similar for a new question could be modeled as a pair-wise comparison with BERT, however, answering a single query would require over 50 hours 
A common method to address clustering and semantic search is to map each sentence to a vector space such that semantically similar sentences are close  Researchers have started to input individual sentences into BERT and to derive fixed-size sentence embeddings  The most commonly used approach is to average the BERT output layer (known as BERT embeddings) or by using the output of the first token (the [CLS] token)  As we will show, this common practice yields rather bad sentence embeddings, often worse than averaging GloVe embeddings BIBREF2 
To alleviate this issue, we developed SBERT  The siamese network architecture enables that fixed-sized vectors for input sentences can be derived  Using a similarity measure like cosine-similarity or Manhatten / Euclidean distance, semantically similar sentences can be found  These similarity measures can be performed extremely efficient on modern hardware, allowing SBERT to be used for semantic similarity search as well as for clustering  The complexity for finding the most similar sentence pair in a collection of 10,000 sentences is reduced from 65 hours with BERT to the computation of 10,000 sentence embeddings (5 seconds with SBERT) and computing cosine-similarity (0 01 seconds)  By using optimized index structures, finding the most similar Quora question can be reduced from 50 hours to a few milliseconds BIBREF3 
We fine-tune SBERT on NLI data, which creates sentence embeddings that significantly outperform other state-of-the-art sentence embedding methods like InferSent BIBREF4 and Universal Sentence Encoder BIBREF5  On seven Semantic Textual Similarity (STS) tasks, SBERT achieves an improvement of 11 7 points compared to InferSent and 5 5 points compared to Universal Sentence Encoder  On SentEval BIBREF6, an evaluation toolkit for sentence embeddings, we achieve an improvement of 2 1 and 2 6 points, respectively 
SBERT can be adapted to a specific task  It sets new state-of-the-art performance on a challenging argument similarity dataset BIBREF7 and on a triplet dataset to distinguish sentences from different sections of a Wikipedia article BIBREF8 
The paper is structured in the following way: Section SECREF3 presents SBERT, section SECREF4 evaluates SBERT on common STS tasks and on the challenging Argument Facet Similarity (AFS) corpus BIBREF7  Section SECREF5 evaluates SBERT on SentEval  In section SECREF6, we perform an ablation study to test some design aspect of SBERT  In section SECREF7, we compare the computational efficiency of SBERT sentence embeddings in contrast to other state-of-the-art sentence embedding methods 
Related Work
We first introduce BERT, then, we discuss state-of-the-art sentence embedding methods 
BERT BIBREF0 is a pre-trained transformer network BIBREF9, which set for various NLP tasks new state-of-the-art results, including question answering, sentence classification, and sentence-pair regression  The input for BERT for sentence-pair regression consists of the two sentences, separated by a special [SEP] token  Multi-head attention over 12 (base-model) or 24 layers (large-model) is applied and the output is passed to a simple regression function to derive the final label  Using this setup, BERT set a new state-of-the-art performance on the Semantic Textual Semilarity (STS) benchmark BIBREF10  RoBERTa BIBREF1 showed, that the performance of BERT can further improved by small adaptations to the pre-training process  We also tested XLNet BIBREF11, but it led in general to worse results than BERT 
A large disadvantage of the BERT network structure is that no independent sentence embeddings are computed, which makes it difficult to derive sentence embeddings from BERT  To bypass this limitations, researchers passed single sentences through BERT and then derive a fixed sized vector by either averaging the outputs (similar to average word embeddings) or by using the output of the special CLS token (for example: bertsentenceembeddings1,bertsentenceembeddings2,bertsentenceembeddings3)  These two options are also provided by the popular bert-as-a-service-repository  Up to our knowledge, there is so far no evaluation if these methods lead to useful sentence embeddings 
Sentence embeddings are a well studied area with dozens of proposed methods  Skip-Thought BIBREF12 trains an encoder-decoder architecture to predict the surrounding sentences  InferSent BIBREF4 uses labeled data of the Stanford Natural Language Inference dataset BIBREF13 and the Multi-Genre NLI dataset BIBREF14 to train a siamese BiLSTM network with max-pooling over the output  Conneau et al  showed, that InferSent consistently outperforms unsupervised methods like SkipThought  Universal Sentence Encoder BIBREF5 trains a transformer network and augments unsupervised learning with training on SNLI  hill-etal-2016-learning showed, that the task on which sentence embeddings are trained significantly impacts their quality  Previous work BIBREF4, BIBREF5 found that the SNLI datasets are suitable for training sentence embeddings  yang-2018-learning presented a method to train on conversations from Reddit using siamese DAN and siamese transformer networks, which yielded good results on the STS benchmark dataset 
polyencoders addresses the run-time overhead of the cross-encoder from BERT and present a method (poly-encoders) to compute a score between $m$ context vectors and pre-computed candidate embeddings using attention  This idea works for finding the highest scoring sentence in a larger collection  However, poly-encoders have the drawback that the score function is not symmetric and the computational overhead is too large for use-cases like clustering, which would require $O(n^2)$ score computations 
Previous neural sentence embedding methods started the training from a random initialization  In this publication, we use the pre-trained BERT and RoBERTa network and only fine-tune it to yield useful sentence embeddings  This reduces significantly the needed training time: SBERT can be tuned in less than 20 minutes, while yielding better results than comparable sentence embedding methods 
Model
SBERT adds a pooling operation to the output of BERT / RoBERTa to derive a fixed sized sentence embedding  We experiment with three pooling strategies: Using the output of the CLS-token, computing the mean of all output vectors (MEAN-strategy), and computing a max-over-time of the output vectors (MAX-strategy)  The default configuration is MEAN 
In order to fine-tune BERT / RoBERTa, we create siamese and triplet networks BIBREF15 to update the weights such that the produced sentence embeddings are semantically meaningful and can be compared with cosine-similarity 
The network structure depends on the available training data  We experiment with the following structures and objective functions 
Classification Objective Function  We concatenate the sentence embeddings $u$ and $v$ with the element-wise difference $|u-v|$ and multiply it with the trainable weight $W_t \in \mathbb {R}^{3n \times k}$:
where $n$ is the dimension of the sentence embeddings and $k$ the number of labels  We optimize cross-entropy loss  This structure is depicted in Figure FIGREF4 
Regression Objective Function  The cosine-similarity between the two sentence embeddings $u$ and $v$ is computed (Figure FIGREF5)  We use mean-squared-error loss as the objective function 
Triplet Objective Function  Given an anchor sentence $a$, a positive sentence $p$, and a negative sentence $n$, triplet loss tunes the network such that the distance between $a$ and $p$ is smaller than the distance between $a$ and $n$  Mathematically, we minimize the following loss function:
with $s_x$ the sentence embedding for $a$/$n$/$p$, $||\cdot ||$ a distance metric and margin $\epsilon $  Margin $\epsilon $ ensures that $s_p$ is at least $\epsilon $ closer to $s_a$ than $s_n$  As metric we use Euclidean distance and we set $\epsilon =1$ in our experiments 
Model ::: Training Details
We train SBERT on the combination of the SNLI BIBREF13 and the Multi-Genre NLI BIBREF14 dataset  The SNLI is a collection of 570,000 sentence pairs annotated with the labels contradiction, eintailment, and neutral  MultiNLI contains 430,000 sentence pairs and covers a range of genres of spoken and written text  We fine-tune SBERT with a 3-way softmax-classifier objective function for one epoch  We used a batch-size of 16, Adam optimizer with learning rate $2\mathrm {e}{-5}$, and a linear learning rate warm-up over 10% of the training data  Our default pooling strategy is MEAN 
Evaluation - Semantic Textual Similarity
We evaluate the performance of SBERT for common Semantic Textual Similarity (STS) tasks  State-of-the-art methods often learn a (complex) regression function that maps sentence embeddings to a similarity score  However, these regression functions work pair-wise and due to the combinatorial explosion those are often not scalable if the collection of sentences reaches a certain size  Instead, we always use cosine-similarity to compare the similarity between two sentence embeddings  We ran our experiments also with negative Manhatten and negative Euclidean distances as similarity measures, but the results for all approaches remained roughly the same 
Evaluation - Semantic Textual Similarity ::: Unsupervised STS
We evaluate the performance of SBERT for STS without using any STS specific training data  We use the STS tasks 2012 - 2016 BIBREF16, BIBREF17, BIBREF18, BIBREF19, BIBREF20, the STS benchmark BIBREF10, and the SICK-Relatedness dataset BIBREF21  These datasets provide labels between 0 and 5 on the semantic relatedness of sentence pairs  We showed in BIBREF22 that Pearson correlation is badly suited for STS  Instead, we compute the Spearman's rank correlation between the cosine-similarity of the sentence embeddings and the gold labels  The setup for the other sentence embedding methods is equivalent, the similarity is computed by cosine-similarity  The results are depicted in Table TABREF6 
The results shows that directly using the output of BERT leads to rather poor performances  Averaging the BERT embeddings achieves an average correlation of only 54 81, and using the CLS-token output only achieves an average correlation of 29 19  Both are worse than computing average GloVe embeddings 
Using the described siamese network structure and fine-tuning mechanism substantially improves the correlation, outperforming both InferSent and Universal Sentence Encoder substantially  The only dataset where SBERT performs worse than Universal Sentence Encoder is SICK-R  Universal Sentence Encoder was trained on various datasets, including news, question-answer pages and discussion forums, which appears to be more suitable to the data of SICK-R  In contrast, SBERT was pre-trained only on Wikipedia (via BERT) and on NLI data 
While RoBERTa was able to improve the performance for several supervised tasks, we only observe minor difference between SBERT and SRoBERTa for generating sentence embeddings 
Evaluation - Semantic Textual Similarity ::: Supervised STS
The STS benchmark (STSb) BIBREF10 provides is a popular dataset to evaluate supervised STS systems  The data includes 8,628 sentence pairs from the three categories captions, news, and forums  It is divided into train (5,749), dev (1,500) and test (1,379)  BERT set a new state-of-the-art performance on this dataset by passing both sentences to the network and using a simple regression method for the output 
We use the training set to fine-tune SBERT using the regression objective function  At prediction time, we compute the cosine-similarity between the sentence embeddings  All systems are trained with 10 random seeds to counter variances BIBREF23 
The results are depicted in Table TABREF10  We experimented with two setups: Only training on STSb, and first training on NLI, then training on STSb  We observe that the later strategy leads to a slight improvement of 1-2 points  This two-step approach had an especially large impact for the BERT cross-encoder, which improved the performance by 3-4 points  We do not observe a significant difference between BERT and RoBERTa 
Evaluation - Semantic Textual Similarity ::: Argument Facet Similarity
We evaluate SBERT on the Argument Facet Similarity (AFS) corpus by MisraEW16  The AFS corpus annotated 6,000 sentential argument pairs from social media dialogs on three controversial topics: gun control, gay marriage, and death penalty  The data was annotated on a scale from 0 (“different topic") to 5 (“completely equivalent")  The similarity notion in the AFS corpus is fairly different to the similarity notion in the STS datasets from SemEval  STS data is usually descriptive, while AFS data are argumentative excerpts from dialogs  To be considered similar, arguments must not only make similar claims, but also provide a similar reasoning  Further, the lexical gap between the sentences in AFS is much larger  Hence, simple unsupervised methods as well as state-of-the-art STS systems perform badly on this dataset BIBREF24 
We evaluate SBERT on this dataset in two scenarios: 1) As proposed by Misra et al , we evaluate SBERT using 10-fold cross-validation  A draw-back of this evaluation setup is that it is not clear how well approaches generalize to different topics  Hence, 2) we evaluate SBERT in a cross-topic setup  Two topics serve for training and the approach is evaluated on the left-out topic  We repeat this for all three topics and average the results 
SBERT is fine-tuned using the Regression Objective Function  The similarity score is computed using cosine-similarity based on the sentence embeddings  We also provide the Pearson correlation $r$ to make the results comparable to Misra et al  However, we showed BIBREF22 that Pearson correlation has some serious drawbacks and should be avoided for comparing STS systems  The results are depicted in Table TABREF12 
Unsupervised methods like tf-idf, average GloVe embeddings or InferSent perform rather badly on this dataset with low scores  Training SBERT in the 10-fold cross-validation setup gives a performance that is nearly on-par with BERT 
However, in the cross-topic evaluation, we observe a performance drop of SBERT by about 7 points Spearman correlation  To be considered similar, arguments should address the same claims and provide the same reasoning  BERT is able to use attention to compare directly both sentences (e g  word-by-word comparison), while SBERT must map individual sentences from an unseen topic to a vector space such that arguments with similar claims and reasons are close  This is a much more challenging task, which appears to require more than just two topics for training to work on-par with BERT 
Evaluation - Semantic Textual Similarity ::: Wikipedia Sections Distinction
ein-dor-etal-2018-learning use Wikipedia to create a thematically fine-grained train, dev and test set for sentence embeddings methods  Wikipedia articles are separated into distinct sections focusing on certain aspects  Dor et al  assume that sentences in the same section are thematically closer than sentences in different sections  They use this to create a large dataset of weakly labeled sentence triplets: The anchor and the positive example come from the same section, while the negative example comes from a different section of the same article  For example, from the Alice Arnold article: Anchor: Arnold joined the BBC Radio Drama Company in 1988 , positive: Arnold gained media attention in May 2012 , negative: Balding and Arnold are keen amateur golfers 
We use the dataset from Dor et al  We use the Triplet Objective, train SBERT for one epoch on the about 1 8 Million training triplets and evaluate it on the 222,957 test triplets  Test triplets are from a distinct set of Wikipedia articles  As evaluation metric, we use accuracy: Is the positive example closer to the anchor than the negative example?
Results are presented in Table TABREF14  Dor et al  fine-tuned a BiLSTM architecture with triplet loss to derive sentence embeddings for this dataset  As the table shows, SBERT clearly outperforms the BiLSTM approach by Dor et al 
Evaluation - SentEval
SentEval BIBREF6 is a popular toolkit to evaluate the quality of sentence embeddings  Sentence embeddings are used as features for a logistic regression classifier  The logistic regression classifier is trained on various tasks in a 10-fold cross-validation setup and the prediction accuracy is computed for the test-fold 
The purpose of SBERT sentence embeddings are not to be used for transfer learning for other tasks  Here, we think fine-tuning BERT as described by devlin2018bert for new tasks is the more suitable method, as it updates all layers of the BERT network  However, SentEval can still give an impression on the quality of our sentence embeddings for various tasks 
We compare the SBERT sentence embeddings to other sentence embeddings methods on the following seven SentEval transfer tasks:
MR: Sentiment prediction for movie reviews snippets on a five start scale BIBREF25 
CR: Sentiment prediction of customer product reviews BIBREF26 
SUBJ: Subjectivity prediction of sentences from movie reviews and plot summaries BIBREF27 
MPQA: Phrase level opinion polarity classification from newswire BIBREF28 
SST: Stanford Sentiment Treebank with binary labels BIBREF29 
TREC: Fine grained question-type classification from TREC BIBREF30 
MRPC: Microsoft Research Paraphrase Corpus from parallel news sources BIBREF31 
The results can be found in Table TABREF15  SBERT is able to achieve the best performance in 5 out of 7 tasks  The average performance increases by about 2 percentage points compared to InferSent as well as the Universal Sentence Encoder  Even though transfer learning is not the purpose of SBERT, it outperforms other state-of-the-art sentence embeddings methods on this task 
It appears that the sentence embeddings from SBERT capture well sentiment information: We observe large improvements for all sentiment tasks (MR, CR, and SST) from SentEval in comparison to InferSent and Universal Sentence Encoder 
The only dataset where SBERT is significantly worse than Universal Sentence Encoder is the TREC dataset  Universal Sentence Encoder was pre-trained on question-answering data, which appears to be beneficial for the question-type classification task of the TREC dataset 
Average BERT embeddings or using the CLS-token output from a BERT network achieved bad results for various STS tasks (Table TABREF6), worse than average GloVe embeddings  However, for SentEval, average BERT embeddings and the BERT CLS-token output achieves decent results (Table TABREF15), outperforming average GloVe embeddings  The reason for this are the different setups  For the STS tasks, we used cosine-similarity to estimate the similarities between sentence embeddings  Cosine-similarity treats all dimensions equally  In contrast, SentEval fits a logistic regression classifier to the sentence embeddings  This allows that certain dimensions can have higher or lower impact on the classification result 
We conclude that average BERT embeddings / CLS-token output from BERT return sentence embeddings that are infeasible to be used with cosine-similarity or with Manhatten / Euclidean distance  For transfer learning, they yield slightly worse results than InferSent or Universal Sentence Encoder  However, using the described fine-tuning setup with a siamese network structure on NLI datasets yields sentence embeddings that achieve a new state-of-the-art for the SentEval toolkit 
Ablation Study
We have demonstrated strong empirical results for the quality of SBERT sentence embeddings  In this section, we perform an ablation study of different aspects of SBERT in order to get a better understanding of their relative importance 
We evaluated different pooling strategies (MEAN, MAX, and CLS)  For the classification objective function, we evaluate different concatenation methods  For each possible configuration, we train SBERT with 10 different random seeds and average the performances 
The objective function (classification vs  regression) depends on the annotated dataset  For the classification objective function, we train SBERT-base on the SNLI and the Multi-NLI dataset  For the regression objective function, we train on the training set of the STS benchmark dataset  Performances are measured on the development split of the STS benchmark dataset  Results are shown in Table TABREF23 
When trained with the classification objective function on NLI data, the pooling strategy has a rather minor impact  The impact of the concatenation mode is much larger  InferSent BIBREF4 and Universal Sentence Encoder BIBREF5 both use $(u, v, |u-v|, u*v)$ as input for a softmax classifier  However, in our architecture, adding the element-wise $u*v$ decreased the performance 
The most important component is the element-wise difference $|u-v|$  Note, that the concatenation mode is only relevant for training the softmax classifier  At inference, when predicting similarities for the STS benchmark dataset, only the sentence embeddings $u$ and $v$ are used in combination with cosine-similarity  The element-wise difference measures the distance between the dimensions of the two sentence embeddings, ensuring that similar pairs are closer and dissimilar pairs are further apart 
When trained with the regression objective function, we observe that the pooling strategy has a large impact  There, the MAX strategy perform significantly worse than MEAN or CLS-token strategy  This is in contrast to BIBREF4, who found it beneficial for the BiLSTM-layer of InferSent to use MAX instead of MEAN pooling 
Computational Efficiency
Sentence embeddings need potentially be computed for Millions of sentences, hence, a high computation speed is desired  In this section, we compare SBERT to average GloVe embeddings, InferSent BIBREF4, and Universal Sentence Encoder BIBREF5 
For our comparison we use the sentences from the STS benchmark BIBREF10  We compute average GloVe embeddings using a simple for-loop with python dictionary lookups and NumPy  InferSent is based on PyTorch  For Universal Sentence Encoder, we use the TensorFlow Hub version, which is based on TensorFlow  SBERT is based on PyTorch  For improved computation of sentence embeddings, we implemented a smart batching strategy: Sentences with similar lengths are grouped together and are only padded to the longest element in a mini-batch  This drastically reduces computational overhead from padding tokens 
Performances were measured on a server with Intel i7-5820K CPU @ 3 30GHz, Nvidia Tesla V100 GPU, CUDA 9 2 and cuDNN  The results are depicted in Table TABREF26 
On CPU, InferSent is about 65% faster than SBERT  This is due to the much simpler network architecture  InferSent uses a single BiLSTM layer, while BERT uses 12 stacked transformer layers  However, an advantage of transformer networks is the computational efficiency on GPUs  There, SBERT with smart batching is about 9% faster than InferSent and about 55% faster than Universal Sentence Encoder  Smart batching achieves a speed-up of 89% on CPU and 48% on GPU  Average GloVe embeddings is obviously by a large margin the fastest method to compute sentence embeddings 
Conclusion
We showed that BERT out-of-the-box maps sentences to a vector space that is rather unsuitable to be used with common similarity measures like cosine-similarity  The performance for seven STS tasks was below the performance of average GloVe embeddings 
To overcome this shortcoming, we presented Sentence-BERT (SBERT)  SBERT fine-tunes BERT in a siamese / triplet network architecture  We evaluated the quality on various common benchmarks, where it could achieve a significant improvement over state-of-the-art sentence embeddings methods  Replacing BERT with RoBERTa did not yield a significant improvement in our experiments 
SBERT is computationally efficient  On a GPU, it is about 9% faster than InferSent and about 55% faster than Universal Sentence Encoder  SBERT can be used for tasks which are computationally not feasible to be modeled with BERT  For example, clustering of 10,000 sentences with hierarchical clustering requires with BERT about 65 hours, as around 50 Million sentence combinations must be computed  With SBERT, we were able to reduce the effort to about 5 seconds 
Acknowledgments
This work has been supported by the German Research Foundation through the German-Israeli Project Cooperation (DIP, grant DA 1600/1-1 and grant GU 798/17-1)  It has been co-funded by the German Federal Ministry of Education and Research (BMBF) under the promotional references 03VP02540 (ArgumenText) 
Context 3: Introduction
Text summarization generates summaries from input documents while keeping salient information  It is an important task and can be applied to several real-world applications  Many methods have been proposed to solve the text summarization problem BIBREF0 , BIBREF1 , BIBREF2 , BIBREF3   There are two main text summarization techniques: extractive and abstractive  Extractive summarization generates summary by selecting salient sentences or phrases from the source text, while abstractive methods paraphrase and restructure sentences to compose the summary  We focus on abstractive summarization in this work as it is more flexible and thus can generate more diverse summaries 
Recently, many abstractive approaches are introduced based on neural sequence-to-sequence framework BIBREF4 , BIBREF0 , BIBREF3 , BIBREF5   Based on the sequence-to-sequence model with copy mechanism BIBREF6 , BIBREF0 incorporates a coverage vector to track and control attention scores on source text  BIBREF4 introduce intra-temporal attention processes in the encoder and decoder to address the repetition and incoherent problem 
There are two issues in previous abstractive methods: 1) these methods use left-context-only decoder, thus do not have complete context when predicting each word  2) they do not utilize the pre-trained contextualized language models on the decoder side, so it is more difficult for the decoder to learn summary representations, context interactions and language modeling together 
Recently, BERT has been successfully used in various natural language processing tasks, such as textual entailment, name entity recognition and machine reading comprehensions  In this paper, we present a novel natural language generation model based on pre-trained language models (we use BERT in this work)  As far as we know, this is the first work to extend BERT to the sequence generation task  To address the above issues of previous abstractive methods, in our model, we design a two-stage decoding process to make good use of BERT's context modeling ability  On the first stage, we generate the summary using a left-context-only-decoder  On the second stage, we mask each word of the summary and predict the refined word one-by-one using a refine decoder  To further improve the naturalness of the generated sequence, we cooperate reinforcement objective with the refine decoder 
The main contributions of this work are:
1  We propose a natural language generation model based on BERT, making good use of the pre-trained language model in the encoder and decoder process, and the model can be trained end-to-end without handcrafted features 
2  We design a two-stage decoder process  In this architecture, our model can generate each word of the summary considering both sides' context information 
3  We conduct experiments on the benchmark datasets CNN/Daily Mail and New York Times  Our model achieves a 33 33 average of ROUGE-1, ROUGE-2 and ROUGE-L on the CNN/Daily Mail, which is state-of-the-art  On the New York Times dataset, our model achieves about 5 6% relative improvement over ROUGE-1 
Text Summarization
In this paper, we focus on single-document multi-sentence summarization and propose a supervised abstractive model based on the neural attentive sequence-to-sequence framework which consists of two parts: a neural network for the encoder and another network for the decoder  The encoder encodes the input sequence to intermediate representation and the decoder predicts one word at a time step given the input sequence representation vector and previous decoded output  The goal of the model is to maximize the probability of generating the correct target sequences  In the encoding and generation process, the attention mechanism is used to concentrate on the most important positions of text  The learning objective of most sequence-to-sequence models is to minimize the negative log likelihood of the generated sequence as following equation shows, where $y^*_i$ is the i-th ground-truth summary token 
$$Loss = - \log \sum _{t=1}^N P(y_t^*|y_{<t}^*, X)$$   (Eq  3)
However, with this objective, traditional sequence generation models consider only one direction context in the decoding process, which could cause performance degradation since complete context of one token contains preceding and following tokens, thus feeding only preceded decoded words to the decoder so that the model may generate unnatural sequences  For example, attentive sequence-to-sequence models often generate sequences with repeated phrases which harm the naturalness  Some previous works mitigate this problem by improving the attention calculation process, but in this paper we show that feeding bi-directional context instead of left-only-context can better alleviate this problem 
Text summarization models are usually classified to abstractive and extractive ones  Recently, extractive models like DeepChannel BIBREF8 , rnn-ext+RL BIBREF9 and NeuSUM BIBREF2 achieve higher performances using well-designed structures  For example, DeepChannel propose a salience estimation network and iteratively extract salient sentences  BIBREF16 train a sentence compression model to teach another latent variable extractive model 
Also, several recent works focus on improving abstractive methods  BIBREF3 design a content selector to over-determine phrases in a source document that should be part of the summary  BIBREF11 introduce inconsistency loss to force words in less attended sentences(which determined by extractive model) to have lower generation probabilities  BIBREF5 extend seq2seq model with an information selection network to generate more informative summaries 
Bi-Directional Pre-Trained Context Encoders
Recently, context encoders such as ELMo, GPT, and BERT have been widely used in many NLP tasks  These models are pre-trained on a huge unlabeled corpus and can generate better contextualized token embeddings, thus the approaches built on top of them can achieve better performance 
Since our method is based on BERT, we illustrate the process briefly here  BERT consists of several layers  In each layer there is first a multi-head self-attention sub-layer and then a linear affine sub-layer with the residual connection  In each self-attention sub-layer the attention scores $e_{ij}$ are first calculated as Eq  ( 5 ) () shows, in which $d_e$ is output dimension, and $W^Q, W^K, W^V$ are parameter matrices 
$$&a_{ij} = \cfrac{(h_iW_Q)(h_jW_K)^T}{\sqrt{d_e}}  \\ &e_{ij} = \cfrac{\exp {e_{ij}}}{\sum _{k=1}^N\exp {e_{ik}}} $$   (Eq  5)
Then the output is calculated as Eq  ( 6 ) shows, which is the weighted sum of previous outputs $h$ added by previous output $h_i$   The last layer outputs is context encoding of input sequence 
$$o_i = h_i + \sum _{j=1}^{N} e_{ij}(h_j W_V) $$   (Eq  6)
Despite the wide usage and huge success, there is also a mismatch problem between these pre-trained context encoders and sequence-to-sequence models  The issue is that while using a pre-trained context encoder like GPT or BERT, they model token-level representations by conditioning on both direction context  During pre-training, they are fed with complete sequences  However, with a left-context-only decoder, these pre-trained language models will suffer from incomplete and inconsistent context and thus cannot generate good enough context-aware word representations, especially during the inference process 
Model
In this section, we describe the structure of our model, which learns to generate an abstractive multi-sentence summary from a given source document 
Based on the sequence-to-sequence framework built on top of BERT, we first design a refine decoder at word-level to tackle the two problems described in the above section  We also introduce a discrete objective for the refine decoders to reduce the exposure bias problem  The overall structure of our model is illustrated in Figure 1  
Problem Formulation
We denote the input document as $X = \lbrace x_1, \ldots , x_m\rbrace $ where $x_i \in \mathcal {X}$ represents one source token  The corresponding summary is denoted as $Y = \lbrace y_1, \ldots , y_L\rbrace $ , $L$ represents the summary length 
Given input document $X$ , we first predict the summary draft by a left-context-only decoder, and then using the generated summary draft we can condition on both context sides and refine the content of the summary  The draft will guide and constrain the refine process of summary 
Summary Draft Generation
The summary draft is based on the sequence-to-sequence model  On the encoder side the input document $X$ is encoded into representation vectors $H = \lbrace h_1, \ldots , h_m\rbrace $ , and then fed to the decoder to generate the summary draft $A = \lbrace a_1, \ldots , a_{|a|}\rbrace $  
We simply use BERT as the encoder  It first maps the input sequence to word embeddings and then computes document embeddings as the encoder's output, denoted by following equation 
$$H = BERT(x_1, \ldots , x_m)$$   (Eq  10)
In the draft decoder, we first introduce BERT's word embedding matrix to map the previous summary draft outputs $\lbrace y_1, \ldots , y_{t-1}\rbrace $ into embeddings vectors $\lbrace q_1, \ldots , q_{t-1}\rbrace $ at t-th time step  Note that as the input sequence of the decoder is not complete, we do not use the BERT network to predict the context vectors here 
Then we introduce an $N$ layer Transformer decoder to learn the conditional probability $P(A|H)$   Transformer's decoder-encoder multi-head attention helps the decoder learn soft alignments between summary and source document  At the t-th time step, the draft decoder predicts output probability conditioned on previous outputs and encoder hidden representations as Eq  ( 13 ) shows, in which $q_{<t} = \lbrace q_1, \ldots , q_{t-1}\rbrace $   Each generated sequence will be truncated in the first position of a special token '[PAD]' 
$$&P^{vocab}_t(w) = f_{dec}(q_{<t}, H)  \\ &L_{dec} = \sum _{i=1}^{|a|} -\log P(a_i = y_i^*|a_{< i}, H) $$   (Eq  13)
As Eq  () shows, the decoder's learning objective is to minimize negative likelihood of conditional probability, in which $y_i^*$ is the i-th ground truth word of summary 
However a decoder with this structure is not sufficient enough: if we use the BERT network in this decoder, then during training and inference, in-complete context(part of sentence) is fed into the BERT module, and although we can fine-tune BERT's parameters, the input distribution is quite different from the pre-train process, and thus harms the quality of generated context representations 
If we just use the embedding matrix here, it will be more difficult for the decoder with fresh parameters to learn to model representations as well as vocabulary probabilities, from a relative small corpus compared to BERT's huge pre-training corpus  In a word, the decoder cannot utilize BERT's ability to generate high quality context vectors, which will also harm performance 
This issue exists when using any other contextualized word representations, so we design a refine process to mitigate it in our approach which will be described in the next sub-section 
As some summary tokens are out-of-vocabulary words and occurs in input document, we incorporate copy mechanism BIBREF6 based on the Transformer decoder, we will describe it briefly 
At decoder time step $t$ , we first calculate the attention probability distribution over source document $X$ using the bi-linear dot product of the last layer decoder output of Transformer $o_t$ and the encoder output $h_j$ , as Eq  ( 15 ) () shows 
$$u_t^j =& o_t W_c h_j \\ \alpha _t^j =& \cfrac{\exp {u_t^j}}{\sum _{k=1}^N\exp {u_t^k}} $$   (Eq  15)
We then calculate copying gate $g_t\in [0, 1]$ , which makes a soft choice between selecting from source and generating from vocabulary, $W_c, W_g, b_g$ are parameters:
$$g_t = sigmoid(W_g \cdot [o_t, h] + b_g) $$   (Eq  16)
Using $g_t$ we calculate the weighted sum of copy probability and generation probability to get the final predicted probability of extended vocabulary $\mathcal {V} + \mathcal {X}$ , where $\mathcal {X}$ is the set of out of vocabulary words from the source document  The final probability is calculated as follow:
$$P_t(w) = (1-g_t)P_t^{vocab}(w) + g_t\sum _{i:w_i=w} \alpha _t^i$$   (Eq  17)
Summary Refine Process
The main reason to introduce the refine process is to enhance the decoder using BERT's contextualized representations, so we do not modify the encoder and reuse it during this process 
On the decoder side, we propose a new word-level refine decoder  The refine decoder receives a generated summary draft as input, and outputs a refined summary  It first masks each word in the summary draft one by one, then feeds the draft to BERT to generate context vectors  Finally it predicts a refined summary word using an $N$ layer Transformer decoder which is the same as the draft decoder  At t-th time step the n-th word of input summary is masked, and the decoder predicts the n-th refined word given other words of the summary 
The learning objective of this process is shown in Eq  ( 19 ), $y_i$ is the i-th summary word and $y_{i}^*$ for the ground-truth summary word, and $a_{\ne i} = \lbrace a_1, \ldots , a_{i-1}, a_{i+1}, \ldots , a_{|y|}\rbrace $  
$$L_{refine} = \sum _{i=1}^{|y|} -\log P(y_i = y_i^*|a_{\ne i}, H) $$   (Eq  19)
From the view of BERT or other contextualized embeddings, the refine decoding process provides a more complete input sequence which is consistent with their pre-training processes  Intuitively, this process works as follows: first the draft decoder writes a summary draft based on a document, and then the refine decoder edits the draft  It concentrates on one word at a time, based on the source document as well as other words 
We design the word-level refine decoder because this process is similar to the cloze task in BERT's pre-train process, therefore by using the ability of the contextual language model the decoder can generate more fluent and natural sequences 
The parameters are shared between the draft decoder and refine decoder, as we find that using individual parameters the model's performance degrades a lot  The reason may be that we use teach-forcing during training, and thus the word-level refine decoder learns to predict words given all the other ground-truth words of summary  This objective is similar to the language model's pre-train objective, and is probably not enough for the decoder to learn to generate refined summaries  So in our model all decoders share the same parameters 
Researchers usually use ROUGE as the evaluation metric for summarization, however during sequence-to-sequence model training, the objective is to maximize the log likelihood of generated sequences  This mis-match harms the model's performance, so we add a discrete objective to the model, and optimize it by introducing the policy gradient method  For example, the discrete objective for the summary draft process is as Eq  ( 21 ) shows, where $a^s$ is the draft summary sampled from predicted distribution, and $R(a^s)$ is the reward score compared with the ground-truth summary, we use ROUGE-L in our experiment  To balance between optimizing the discrete objective and generating readable sequences, we mix the discrete objective with maximum-likelihood objective  As Eq  () shows, minimizing $\hat{L}_{dec}$ is the final objective for the draft process, note here $L_{dec}$ is $-logP(a|x)$   In the refine process we introduce similar objectives 
$$L^{rl}_{dec} = R(a^s)\cdot [-\log (P(a^s|x))]  \\ \hat{L}_{dec} = \gamma * L^{rl}_{dec} + (1 - \gamma ) * L_{dec} $$   (Eq  21)
Learning and Inference
During model training, the objective of our model is sum of the two processes, jointly trained using "teacher-forcing" algorithm  During training we feed the ground-truth summary to each decoder and minimize the objective 
$$L_{model} = \hat{L}_{dec} + \hat{L}_{refine}$$   (Eq  23)
At test time, each time step we choose the predicted word by $\hat{y} = argmax_{y^{\prime }} P(y^{\prime }|x)$ , use beam search to generate the draft summaries, and use greedy search to generate the refined summaries 
Settings
In this work, all of our models are built on $BERT_{BASE}$ , although another larger pre-trained model with better performance ( $BERT_{LARGE}$ ) has published but it costs too much time and GPU memory  We use WordPiece embeddings with a 30,000 vocabulary which is the same as BERT  We set the layer of transformer decoders to 12(8 on NYT50), and set the attention heads number to 12(8 on NYT50), set fully-connected sub-layer hidden size to 3072  We train the model using an Adam optimizer with learning rate of $3e-4$ , $\beta _1=0 9$ , $\beta _2=0 999$ and $\epsilon =10^{-9}$ and use a dynamic learning rate during the training process  For regularization, we use dropout BIBREF13 and label smoothing BIBREF14 in our models and set the dropout rate to 0 15, and the label smoothing value to 0 1  We set the RL objective factor $\gamma $ to 0 99 
During training, we set the batch size to 36, and train for 4 epochs(8 epochs for NYT50 since it has many fewer training samples), after training the best model are selected from last 10 models based on development set performance  Due to GPU memory limit, we use gradient accumulation, set accumulate step to 12 and feed 3 samples at each step  We use beam size 4 and length penalty of 1 0 to generate logical form sequences 
We filter repeated tri-grams in beam-search process by setting word probability to zero if it will generate an tri-gram which exists in the existing summary  It is a nice method to avoid phrase repetition since the two datasets seldom contains repeated tri-grams in one summary  We also fine tune the generated sequences using another two simple rules  When there are multi summary sentences with exactly the same content, we keep the first one and remove the other sentences; we also remove sentences with less than 3 words from the result 
To evaluate the performance of our model, we conduct experiments on CNN/Daily Mail dataset, which is a large collection of news articles and modified for summarization  Following BIBREF0 we choose the non-anonymized version of the dataset, which consists of more than 280,000 training samples and 11490 test set samples 
We also conduct experiments on the New York Times(NYT) dataset which also consists of many news articles  The original dataset can be applied here  In our experiment, we follow the dataset splits and other pre-process settings of BIBREF15   We first filter all samples without a full article text or abstract and then remove all samples with summaries shorter than 50 words  Then we choose the test set based on the date of publication(all examples published after January 1, 2007)  The final dataset contains 22,000 training samples and 3,452 test samples and is called NYT50 since all summaries are longer than 50 words 
We tokenize all sequences of the two datasets using the WordPiece tokenizer  After tokenizing, the average article length and summary length of CNN/Daily Mail are 691 and 51, and NYT50's average article length and summary length are 1152 and 75  We truncate the article length to 512, and the summary length to 100 in our experiment(max summary length is set to 150 on NYT50 as its average golden summary length is longer) 
On CNN/Daily Mail dataset, we report the full-length F-1 score of the ROUGE-1, ROUGE-2 and ROUGE-L metrics, calculated using PyRouge package and the Porter stemmer option  On NYT50, following BIBREF4 we evaluate limited length ROUGE recall score(limit the generated summary length to the ground truth length)  We split NYT50 summaries into sentences by semicolons to calculate the ROUGE scores 
Results and Analysis
Table 1 shows the results on CNN/Daily Mail dataset, we compare the performance of many recent approaches with our model  We classify them to two groups based on whether they are extractive or abstractive models  As the last line of the table shows, the ROUGE-1 and ROUGE-2 score of our full model is comparable with DCA, and outperforms on ROUGE-L  Also, compared to extractive models NeuSUM and MASK- $LM^{global}$ , we achieve slight higher ROUGE-1  Except the four scores, our model outperforms these models on all the other scores, and since we have 95% confidence interval of at most $\pm $ 0 20, these improvements are statistically significant 
As the last four lines of Table 1 show, we conduct an ablation study on our model variants to analyze the importance of each component  We use three ablation models for the experiments  One-Stage: A sequence-to-sequence model with copy mechanism based on BERT; Two-Stage: Adding the word-refine decoder to the One-Stage model; Two-Stage + RL: Full model with refine process cooperated with RL objective 
First, we compare the Two-Stage+RL model with Two-Stage ablation, we observe that the full model outperforms by 0 30 on average ROUGE, suggesting that the reinforcement objective helps the model effectively  Then we analyze the effect of refine process by removing word-level refine from the Two-Stage model, we observe that without the refine process the average ROUGE score drops by 1 69  The ablation study shows that each module is necessary for our full model, and the improvements are statistically significant on all metrics 
To evaluate the impact of summary length on model performance, we compare the average rouge score improvements of our model with different length of ground-truth summaries  As the above sub-figure of Figure 2 shows, compared to Pointer-Generator with Coverage, on length interval 40-80(occupies about 70% of test set) the improvements of our model are higher than shorter samples, confirms that with better context representations, in longer documents our model can achieve higher performance 
As the below sub-figure of Figure 2 shows, compared to extractive baseline: Lead-3 BIBREF0 , the advantage of our model will fall when golden summary length is greater than 80  This probably because that we truncate the long documents and golden summaries and cannot get full information, it could also because that the training data in these intervals is too few to train an abstractive model, so simple extractive method will not fall too far behind 
Additional Results on NYT50
Table 2 shows experiments on the NYT50 corpus  Since the short summary samples are filtered, NYT50 has average longer summaries than CNN/Daily Mail  So the model needs to catch long-term dependency of the sequences to generate good summaries 
The first two lines of Table 2 show results of the two baselines introduced by BIBREF15 : these baselines select first n sentences, or select the first k words from the original document  Also we compare performance of our model with two recent models, we see 2 39 ROUGE-1 improvements compared to the ML+RL with intra-attn approach(previous SOTA) carries over to this dataset, which is a large margin  On ROUGE-2, our model also get an improvement of 0 51  The experiment proves that our approach can outperform competitive methods on different data distributions 
Pre-trained language models
Pre-trained word vectors BIBREF17 , BIBREF18 , BIBREF19 have been widely used in many NLP tasks  More recently, pre-trained language models (ELMo, GPT and BERT), have also achieved great success on several NLP problems such as textual entailment, semantic similarity, reading comprehension, and question answering BIBREF20 , BIBREF21 , BIBREF22  
Some recent works also focus on leveraging pre-trained language models in summarization  BIBREF23 pretrain a language model and use it as the sentiment analyser when generating reviews of goods  BIBREF24 train a language model on golden summaries, and then use it on the decoder side to incorporate prior knowledge 
In this work, we use BERT(which is a pre-trained language model using large scale unlabeled data) on the encoder and decoder of a seq2seq model, and by designing a two stage decoding structure we build a competitive model for abstractive text summarization 
Conclusion and Future Work
In this work, we propose a two-stage model based on sequence-to-sequence paradigm  Our model utilize BERT on both encoder and decoder sides, and introduce reinforce objective in learning process  We evaluate our model on two benchmark datasets CNN/Daily Mail and New York Times, the experimental results show that compared to previous systems our approach effectively improves performance 
Although our experiments are conducted on summarization task, our model can be used in most natural language generation tasks, such as machine translation, question generation and paraphrasing  The refine decoder and mixed objective can also be applied on other sequence generation tasks, and we will investigate on them in future work 

ground_truth: GloVe, BERT, Universal Sentence Encoder, TF-IDF, InferSent

Avg. GloVe embeddings, Avg. fast-text embeddings, Avg. BERT embeddings, BERT CLS-vector, InferSent - GloVe and Universal Sentence Encoder.

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

Please answer the questions based on the text provided below. How does their model improve interpretability compared to softmax transformers?
Context 2: Introduction
The Transformer architecture BIBREF0 for deep neural networks has quickly risen to prominence in NLP through its efficiency and performance, leading to improvements in the state of the art of Neural Machine Translation BIBREF1, BIBREF2, as well as inspiring other powerful general-purpose models like BERT BIBREF3 and GPT-2 BIBREF4  At the heart of the Transformer lie multi-head attention mechanisms: each word is represented by multiple different weighted averages of its relevant context  As suggested by recent works on interpreting attention head roles, separate attention heads may learn to look for various relationships between tokens BIBREF5, BIBREF6, BIBREF7, BIBREF8, BIBREF9 
The attention distribution of each head is predicted typically using the softmax normalizing transform  As a result, all context words have non-zero attention weight  Recent work on single attention architectures suggest that using sparse normalizing transforms in attention mechanisms such as sparsemax – which can yield exactly zero probabilities for irrelevant words – may improve performance and interpretability BIBREF12, BIBREF13, BIBREF14  Qualitative analysis of attention heads BIBREF0 suggests that, depending on what phenomena they capture, heads tend to favor flatter or more peaked distributions 
Recent works have proposed sparse Transformers BIBREF10 and adaptive span Transformers BIBREF11  However, the “sparsity" of those models only limits the attention to a contiguous span of past tokens, while in this work we propose a highly adaptive Transformer model that is capable of attending to a sparse set of words that are not necessarily contiguous  Figure FIGREF1 shows the relationship of these methods with ours 
Our contributions are the following:
We introduce sparse attention into the Transformer architecture, showing that it eases interpretability and leads to slight accuracy gains 
We propose an adaptive version of sparse attention, where the shape of each attention head is learnable and can vary continuously and dynamically between the dense limit case of softmax and the sparse, piecewise-linear sparsemax case 
We make an extensive analysis of the added interpretability of these models, identifying both crisper examples of attention head behavior observed in previous work, as well as novel behaviors unraveled thanks to the sparsity and adaptivity of our proposed model 
Background ::: The Transformer
In NMT, the Transformer BIBREF0 is a sequence-to-sequence (seq2seq) model which maps an input sequence to an output sequence through hierarchical multi-head attention mechanisms, yielding a dynamic, context-dependent strategy for propagating information within and across sentences  It contrasts with previous seq2seq models, which usually rely either on costly gated recurrent operations BIBREF15, BIBREF16 or static convolutions BIBREF17 
Given $n$ query contexts and $m$ sequence items under consideration, attention mechanisms compute, for each query, a weighted representation of the items  The particular attention mechanism used in BIBREF0 is called scaled dot-product attention, and it is computed in the following way:
where $\mathbf {Q} \in \mathbb {R}^{n \times d}$ contains representations of the queries, $\mathbf {K}, \mathbf {V} \in \mathbb {R}^{m \times d}$ are the keys and values of the items attended over, and $d$ is the dimensionality of these representations  The $\mathbf {\pi }$ mapping normalizes row-wise using softmax, $\mathbf {\pi }(\mathbf {Z})_{ij} = \operatornamewithlimits{\mathsf {softmax}}(\mathbf {z}_i)_j$, where
In words, the keys are used to compute a relevance score between each item and query  Then, normalized attention weights are computed using softmax, and these are used to weight the values of each item at each query context 
However, for complex tasks, different parts of a sequence may be relevant in different ways, motivating multi-head attention in Transformers  This is simply the application of Equation DISPLAY_FORM7 in parallel $H$ times, each with a different, learned linear transformation that allows specialization:
In the Transformer, there are three separate multi-head attention mechanisms for distinct purposes:
Encoder self-attention: builds rich, layered representations of each input word, by attending on the entire input sentence 
Context attention: selects a representative weighted average of the encodings of the input words, at each time step of the decoder 
Decoder self-attention: attends over the partial output sentence fragment produced so far 
Together, these mechanisms enable the contextualized flow of information between the input sentence and the sequential decoder 
Background ::: Sparse Attention
The softmax mapping (Equation DISPLAY_FORM8) is elementwise proportional to $\exp $, therefore it can never assign a weight of exactly zero  Thus, unnecessary items are still taken into consideration to some extent  Since its output sums to one, this invariably means less weight is assigned to the relevant items, potentially harming performance and interpretability BIBREF18  This has motivated a line of research on learning networks with sparse mappings BIBREF19, BIBREF20, BIBREF21, BIBREF22  We focus on a recently-introduced flexible family of transformations, $\alpha $-entmax BIBREF23, BIBREF14, defined as:
where $\triangle ^d \lbrace \mathbf {p}\in \mathbb {R}^d:\sum _{i} p_i = 1\rbrace $ is the probability simplex, and, for $\alpha \ge 1$, $\mathsf {H}^{\textsc {T}}_\alpha $ is the Tsallis continuous family of entropies BIBREF24:
This family contains the well-known Shannon and Gini entropies, corresponding to the cases $\alpha =1$ and $\alpha =2$, respectively 
Equation DISPLAY_FORM14 involves a convex optimization subproblem  Using the definition of $\mathsf {H}^{\textsc {T}}_\alpha $, the optimality conditions may be used to derive the following form for the solution (Appendix SECREF83):
where $[\cdot ]_+$ is the positive part (ReLU) function, $\mathbf {1}$ denotes the vector of all ones, and $\tau $ – which acts like a threshold – is the Lagrange multiplier corresponding to the $\sum _i p_i=1$ constraint 
Background ::: Sparse Attention ::: Properties of @!START@$\alpha $@!END@-entmax 
The appeal of $\alpha $-entmax for attention rests on the following properties  For $\alpha =1$ (i e , when $\mathsf {H}^{\textsc {T}}_\alpha $ becomes the Shannon entropy), it exactly recovers the softmax mapping (We provide a short derivation in Appendix SECREF89 )  For all $\alpha >1$ it permits sparse solutions, in stark contrast to softmax  In particular, for $\alpha =2$, it recovers the sparsemax mapping BIBREF19, which is piecewise linear  In-between, as $\alpha $ increases, the mapping continuously gets sparser as its curvature changes 
To compute the value of $\alpha $-entmax, one must find the threshold $\tau $ such that the r h s  in Equation DISPLAY_FORM16 sums to one  BIBREF23 propose a general bisection algorithm  BIBREF14 introduce a faster, exact algorithm for $\alpha =1 5$, and enable using $\mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}$ with fixed $\alpha $ within a neural network by showing that the $\alpha $-entmax Jacobian w r t  $\mathbf {z}$ for $\mathbf {p}^\star = \mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}(\mathbf {z})$ is
Our work furthers the study of $\alpha $-entmax by providing a derivation of the Jacobian w r t  the hyper-parameter $\alpha $ (Section SECREF3), thereby allowing the shape and sparsity of the mapping to be learned automatically  This is particularly appealing in the context of multi-head attention mechanisms, where we shall show in Section SECREF35 that different heads tend to learn different sparsity behaviors 
Adaptively Sparse Transformers with @!START@$\alpha $@!END@-entmax
We now propose a novel Transformer architecture wherein we simply replace softmax with $\alpha $-entmax in the attention heads  Concretely, we replace the row normalization $\mathbf {\pi }$ in Equation DISPLAY_FORM7 by
This change leads to sparse attention weights, as long as $\alpha >1$; in particular, $\alpha =1 5$ is a sensible starting point BIBREF14 
Adaptively Sparse Transformers with @!START@$\alpha $@!END@-entmax ::: Different @!START@$\alpha $@!END@ per head 
Unlike LSTM-based seq2seq models, where $\alpha $ can be more easily tuned by grid search, in a Transformer, there are many attention heads in multiple layers  Crucial to the power of such models, the different heads capture different linguistic phenomena, some of them isolating important words, others spreading out attention across phrases BIBREF0  This motivates using different, adaptive $\alpha $ values for each attention head, such that some heads may learn to be sparser, and others may become closer to softmax  We propose doing so by treating the $\alpha $ values as neural network parameters, optimized via stochastic gradients along with the other weights 
Adaptively Sparse Transformers with @!START@$\alpha $@!END@-entmax ::: Derivatives w r t  @!START@$\alpha $@!END@ 
In order to optimize $\alpha $ automatically via gradient methods, we must compute the Jacobian of the entmax output w r t  $\alpha $  Since entmax is defined through an optimization problem, this is non-trivial and cannot be simply handled through automatic differentiation; it falls within the domain of argmin differentiation, an active research topic in optimization BIBREF25, BIBREF26 
One of our key contributions is the derivation of a closed-form expression for this Jacobian  The next proposition provides such an expression, enabling entmax layers with adaptive $\alpha $  To the best of our knowledge, ours is the first neural network module that can automatically, continuously vary in shape away from softmax and toward sparse mappings like sparsemax 
Proposition 1 Let $\mathbf {p}^\star \mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}(\mathbf {z})$ be the solution of Equation DISPLAY_FORM14  Denote the distribution $\tilde{p}_i {(p_i^\star )^{2 - \alpha }}{ \sum _j(p_j^\star )^{2-\alpha }}$ and let $h_i -p^\star _i \log p^\star _i$  The $i$th component of the Jacobian $\mathbf {g} \frac{\partial \mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}(\mathbf {z})}{\partial \alpha }$ is
proof uses implicit function differentiation and is given in Appendix SECREF10 
Proposition UNKREF22 provides the remaining missing piece needed for training adaptively sparse Transformers  In the following section, we evaluate this strategy on neural machine translation, and analyze the behavior of the learned attention heads 
Experiments
We apply our adaptively sparse Transformers on four machine translation tasks  For comparison, a natural baseline is the standard Transformer architecture using the softmax transform in its multi-head attention mechanisms  We consider two other model variants in our experiments that make use of different normalizing transformations:
1 5-entmax: a Transformer with sparse entmax attention with fixed $\alpha =1 5$ for all heads  This is a novel model, since 1 5-entmax had only been proposed for RNN-based NMT models BIBREF14, but never in Transformers, where attention modules are not just one single component of the seq2seq model but rather an integral part of all of the model components 
$\alpha $-entmax: an adaptive Transformer with sparse entmax attention with a different, learned $\alpha _{i,j}^t$ for each head 
The adaptive model has an additional scalar parameter per attention head per layer for each of the three attention mechanisms (encoder self-attention, context attention, and decoder self-attention), i e ,
and we set $\alpha _{i,j}^t = 1 + \operatornamewithlimits{\mathsf {sigmoid}}(a_{i,j}^t) \in ]1, 2[$  All or some of the $\alpha $ values can be tied if desired, but we keep them independent for analysis purposes 
Experiments ::: Datasets 
Our models were trained on 4 machine translation datasets of different training sizes:
[itemsep= 5ex,leftmargin=2ex]
IWSLT 2017 German $\rightarrow $ English BIBREF27: 200K sentence pairs 
KFTT Japanese $\rightarrow $ English BIBREF28: 300K sentence pairs 
WMT 2016 Romanian $\rightarrow $ English BIBREF29: 600K sentence pairs 
WMT 2014 English $\rightarrow $ German BIBREF30: 4 5M sentence pairs 
All of these datasets were preprocessed with byte-pair encoding BIBREF31, using joint segmentations of 32k merge operations 
Experiments ::: Training 
We follow the dimensions of the Transformer-Base model of BIBREF0: The number of layers is $L=6$ and number of heads is $H=8$ in the encoder self-attention, the context attention, and the decoder self-attention  We use a mini-batch size of 8192 tokens and warm up the learning rate linearly until 20k steps, after which it decays according to an inverse square root schedule  All models were trained until convergence of validation accuracy, and evaluation was done at each 10k steps for ro$\rightarrow $en and en$\rightarrow $de and at each 5k steps for de$\rightarrow $en and ja$\rightarrow $en  The end-to-end computational overhead of our methods, when compared to standard softmax, is relatively small; in training tokens per second, the models using $\alpha $-entmax and $1 5$-entmax are, respectively, $75\%$ and $90\%$ the speed of the softmax model 
Experiments ::: Results 
We report test set tokenized BLEU BIBREF32 results in Table TABREF27  We can see that replacing softmax by entmax does not hurt performance in any of the datasets; indeed, sparse attention Transformers tend to have slightly higher BLEU, but their sparsity leads to a better potential for analysis  In the next section, we make use of this potential by exploring the learned internal mechanics of the self-attention heads 
Analysis
We conduct an analysis for the higher-resource dataset WMT 2014 English $\rightarrow $ German of the attention in the sparse adaptive Transformer model ($\alpha $-entmax) at multiple levels: we analyze high-level statistics as well as individual head behavior  Moreover, we make a qualitative analysis of the interpretability capabilities of our models 
Analysis ::: High-Level Statistics ::: What kind of @!START@$\alpha $@!END@ values are learned?
Figure FIGREF37 shows the learning trajectories of the $\alpha $ parameters of a selected subset of heads  We generally observe a tendency for the randomly-initialized $\alpha $ parameters to decrease initially, suggesting that softmax-like behavior may be preferable while the model is still very uncertain  After around one thousand steps, some heads change direction and become sparser, perhaps as they become more confident and specialized  This shows that the initialization of $\alpha $ does not predetermine its sparsity level or the role the head will have throughout  In particular, head 8 in the encoder self-attention layer 2 first drops to around $\alpha =1 3$ before becoming one of the sparsest heads, with $\alpha \approx 2$ 
The overall distribution of $\alpha $ values at convergence can be seen in Figure FIGREF38  We can observe that the encoder self-attention blocks learn to concentrate the $\alpha $ values in two modes: a very sparse one around $\alpha \rightarrow 2$, and a dense one between softmax and 1 5-entmax   However, the decoder self and context attention only learn to distribute these parameters in a single mode  We show next that this is reflected in the average density of attention weight vectors as well 
Analysis ::: High-Level Statistics ::: Attention weight density when translating 
For any $\alpha >1$, it would still be possible for the weight matrices in Equation DISPLAY_FORM9 to learn re-scalings so as to make attention sparser or denser  To visualize the impact of adaptive $\alpha $ values, we compare the empirical attention weight density (the average number of tokens receiving non-zero attention) within each module, against sparse Transformers with fixed $\alpha =1 5$ 
Figure FIGREF40 shows that, with fixed $\alpha =1 5$, heads tend to be sparse and similarly-distributed in all three attention modules  With learned $\alpha $, there are two notable changes: (i) a prominent mode corresponding to fully dense probabilities, showing that our models learn to combine sparse and dense attention, and (ii) a distinction between the encoder self-attention – whose background distribution tends toward extreme sparsity – and the other two modules, who exhibit more uniform background distributions  This suggests that perhaps entirely sparse Transformers are suboptimal 
The fact that the decoder seems to prefer denser attention distributions might be attributed to it being auto-regressive, only having access to past tokens and not the full sentence  We speculate that it might lose too much information if it assigned weights of zero to too many tokens in the self-attention, since there are fewer tokens to attend to in the first place 
Teasing this down into separate layers, Figure FIGREF41 shows the average (sorted) density of each head for each layer  We observe that $\alpha $-entmax is able to learn different sparsity patterns at each layer, leading to more variance in individual head behavior, to clearly-identified dense and sparse heads, and overall to different tendencies compared to the fixed case of $\alpha =1 5$ 
Analysis ::: High-Level Statistics ::: Head diversity 
To measure the overall disagreement between attention heads, as a measure of head diversity, we use the following generalization of the Jensen-Shannon divergence:
where $\mathbf {p}_j$ is the vector of attention weights assigned by head $j$ to each word in the sequence, and $\mathsf {H}^\textsc {S}$ is the Shannon entropy, base-adjusted based on the dimension of $\mathbf {p}$ such that $JS \le 1$  We average this measure over the entire validation set  The higher this metric is, the more the heads are taking different roles in the model 
Figure FIGREF44 shows that both sparse Transformer variants show more diversity than the traditional softmax one  Interestingly, diversity seems to peak in the middle layers of the encoder self-attention and context attention, while this is not the case for the decoder self-attention 
The statistics shown in this section can be found for the other language pairs in Appendix SECREF8 
Analysis ::: Identifying Head Specializations
Previous work pointed out some specific roles played by different heads in the softmax Transformer model BIBREF33, BIBREF5, BIBREF9  Identifying the specialization of a head can be done by observing the type of tokens or sequences that the head often assigns most of its attention weight; this is facilitated by sparsity 
Analysis ::: Identifying Head Specializations ::: Positional heads 
One particular type of head, as noted by BIBREF9, is the positional head  These heads tend to focus their attention on either the previous or next token in the sequence, thus obtaining representations of the neighborhood of the current time step  In Figure FIGREF47, we show attention plots for such heads, found for each of the studied models  The sparsity of our models allows these heads to be more confident in their representations, by assigning the whole probability distribution to a single token in the sequence  Concretely, we may measure a positional head's confidence as the average attention weight assigned to the previous token  The softmax model has three heads for position $-1$, with median confidence $93 5\%$  The $1 5$-entmax model also has three heads for this position, with median confidence $94 4\%$  The adaptive model has four heads, with median confidences $95 9\%$, the lowest-confidence head being dense with $\alpha =1 18$, while the highest-confidence head being sparse ($\alpha =1 91$) 
For position $+1$, the models each dedicate one head, with confidence around $95\%$, slightly higher for entmax  The adaptive model sets $\alpha =1 96$ for this head 
Analysis ::: Identifying Head Specializations ::: BPE-merging head 
Due to the sparsity of our models, we are able to identify other head specializations, easily identifying which heads should be further analysed  In Figure FIGREF51 we show one such head where the $\alpha $ value is particularly high (in the encoder, layer 1, head 4 depicted in Figure FIGREF37)  We found that this head most often looks at the current time step with high confidence, making it a positional head with offset 0  However, this head often spreads weight sparsely over 2-3 neighboring tokens, when the tokens are part of the same BPE cluster or hyphenated words  As this head is in the first layer, it provides a useful service to the higher layers by combining information evenly within some BPE clusters 
For each BPE cluster or cluster of hyphenated words, we computed a score between 0 and 1 that corresponds to the maximum attention mass assigned by any token to the rest of the tokens inside the cluster in order to quantify the BPE-merging capabilities of these heads  There are not any attention heads in the softmax model that are able to obtain a score over $80\%$, while for $1 5$-entmax and $\alpha $-entmax there are two heads in each ($83 3\%$ and $85 6\%$ for $1 5$-entmax and $88 5\%$ and $89 8\%$ for $\alpha $-entmax) 
Analysis ::: Identifying Head Specializations ::: Interrogation head 
On the other hand, in Figure FIGREF52 we show a head for which our adaptively sparse model chose an $\alpha $ close to 1, making it closer to softmax (also shown in encoder, layer 1, head 3 depicted in Figure FIGREF37)  We observe that this head assigns a high probability to question marks at the end of the sentence in time steps where the current token is interrogative, thus making it an interrogation-detecting head  We also observe this type of heads in the other models, which we also depict in Figure FIGREF52  The average attention weight placed on the question mark when the current token is an interrogative word is $98 5\%$ for softmax, $97 0\%$ for $1 5$-entmax, and $99 5\%$ for $\alpha $-entmax 
Furthermore, we can examine sentences where some tendentially sparse heads become less so, thus identifying sources of ambiguity where the head is less confident in its prediction  An example is shown in Figure FIGREF55 where sparsity in the same head differs for sentences of similar length 
Related Work ::: Sparse attention 
Prior work has developed sparse attention mechanisms, including applications to NMT BIBREF19, BIBREF12, BIBREF20, BIBREF22, BIBREF34  BIBREF14 introduced the entmax function this work builds upon  In their work, there is a single attention mechanism which is controlled by a fixed $\alpha $  In contrast, this is the first work to allow such attention mappings to dynamically adapt their curvature and sparsity, by automatically adjusting the continuous $\alpha $ parameter  We also provide the first results using sparse attention in a Transformer model 
Related Work ::: Fixed sparsity patterns 
Recent research improves the scalability of Transformer-like networks through static, fixed sparsity patterns BIBREF10, BIBREF35  Our adaptively-sparse Transformer can dynamically select a sparsity pattern that finds relevant words regardless of their position (e g , Figure FIGREF52)  Moreover, the two strategies could be combined  In a concurrent line of research, BIBREF11 propose an adaptive attention span for Transformer language models  While their work has each head learn a different contiguous span of context tokens to attend to, our work finds different sparsity patterns in the same span  Interestingly, some of their findings mirror ours – we found that attention heads in the last layers tend to be denser on average when compared to the ones in the first layers, while their work has found that lower layers tend to have a shorter attention span compared to higher layers 
Related Work ::: Transformer interpretability 
The original Transformer paper BIBREF0 shows attention visualizations, from which some speculation can be made of the roles the several attention heads have  BIBREF7 study the syntactic abilities of the Transformer self-attention, while BIBREF6 extract dependency relations from the attention weights  BIBREF8 find that the self-attentions in BERT BIBREF3 follow a sequence of processes that resembles a classical NLP pipeline  Regarding redundancy of heads, BIBREF9 develop a method that is able to prune heads of the multi-head attention module and make an empirical study of the role that each head has in self-attention (positional, syntactic and rare words)  BIBREF36 also aim to reduce head redundancy by adding a regularization term to the loss that maximizes head disagreement and obtain improved results  While not considering Transformer attentions, BIBREF18 show that traditional attention mechanisms do not necessarily improve interpretability since softmax attention is vulnerable to an adversarial attack leading to wildly different model predictions for the same attention weights  Sparse attention may mitigate these issues; however, our work focuses mostly on a more mechanical aspect of interpretation by analyzing head behavior, rather than on explanations for predictions 
Conclusion and Future Work
We contribute a novel strategy for adaptively sparse attention, and, in particular, for adaptively sparse Transformers  We present the first empirical analysis of Transformers with sparse attention mappings (i e , entmax), showing potential in both translation accuracy as well as in model interpretability 
In particular, we analyzed how the attention heads in the proposed adaptively sparse Transformer can specialize more and with higher confidence  Our adaptivity strategy relies only on gradient-based optimization, side-stepping costly per-head hyper-parameter searches  Further speed-ups are possible by leveraging more parallelism in the bisection algorithm for computing $\alpha $-entmax 
Finally, some of the automatically-learned behaviors of our adaptively sparse Transformers – for instance, the near-deterministic positional heads or the subword joining head – may provide new ideas for designing static variations of the Transformer 
Acknowledgments
This work was supported by the European Research Council (ERC StG DeepSPIN 758969), and by the Fundação para a Ciência e Tecnologia through contracts UID/EEA/50008/2019 and CMUPERI/TIC/0046/2014 (GoLocal)  We are grateful to Ben Peters for the $\alpha $-entmax code and Erick Fonseca, Marcos Treviso, Pedro Martins, and Tsvetomila Mihaylova for insightful group discussion  We thank Mathieu Blondel for the idea to learn $\alpha $  We would also like to thank the anonymous reviewers for their helpful feedback 
Supplementary Material
Background ::: Regularized Fenchel-Young prediction functions
Definition 1 (BIBREF23)
Let $\Omega \colon \triangle ^d \rightarrow {\mathbb {R}}\cup \lbrace \infty \rbrace $ be a strictly convex regularization function  We define the prediction function $\mathbf {\pi }_{\Omega }$ as
Background ::: Characterizing the @!START@$\alpha $@!END@-entmax mapping
Lemma 1 (BIBREF14) For any $\mathbf {z}$, there exists a unique $\tau ^\star $ such that
Proof: From the definition of $\mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}$,
we may easily identify it with a regularized prediction function (Def  UNKREF81):
We first note that for all $\mathbf {p}\in \triangle ^d$,
From the constant invariance and scaling properties of $\mathbf {\pi }_{\Omega }$ BIBREF23,
Using BIBREF23, noting that $g^{\prime }(t) = t^{\alpha - 1}$ and $(g^{\prime })^{-1}(u) = u^{{1}{\alpha -1}}$, yields
Since $\mathsf {H}^{\textsc {T}}_\alpha $ is strictly convex on the simplex, $\mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}$ has a unique solution $\mathbf {p}^\star $  Equation DISPLAY_FORM88 implicitly defines a one-to-one mapping between $\mathbf {p}^\star $ and $\tau ^\star $ as long as $\mathbf {p}^\star \in \triangle $, therefore $\tau ^\star $ is also unique 
Background ::: Connections to softmax and sparsemax
The Euclidean projection onto the simplex, sometimes referred to, in the context of neural attention, as sparsemax BIBREF19, is defined as
The solution can be characterized through the unique threshold $\tau $ such that $\sum _i \operatornamewithlimits{\mathsf {sparsemax}}(\mathbf {z})_i = 1$ and BIBREF38
Thus, each coordinate of the sparsemax solution is a piecewise-linear function  Visibly, this expression is recovered when setting $\alpha =2$ in the $\alpha $-entmax expression (Equation DISPLAY_FORM85); for other values of $\alpha $, the exponent induces curvature 
On the other hand, the well-known softmax is usually defined through the expression
which can be shown to be the unique solution of the optimization problem
where $\mathsf {H}^\textsc {S}(\mathbf {p}) -\sum _i p_i \log p_i$ is the Shannon entropy  Indeed, setting the gradient to 0 yields the condition $\log p_i = z_j - \nu _i - \tau - 1$, where $\tau $ and $\nu > 0$ are Lagrange multipliers for the simplex constraints $\sum _i p_i = 1$ and $p_i \ge 0$, respectively  Since the l h s  is only finite for $p_i>0$, we must have $\nu _i=0$ for all $i$, by complementary slackness  Thus, the solution must have the form $p_i = {\exp (z_i)}{Z}$, yielding Equation DISPLAY_FORM92 
Jacobian of @!START@$\alpha $@!END@-entmax w r t  the shape parameter @!START@$\alpha $@!END@: Proof of Proposition @!START@UID22@!END@
Recall that the entmax transformation is defined as:
where $\alpha \ge 1$ and $\mathsf {H}^{\textsc {T}}_{\alpha }$ is the Tsallis entropy,
and $\mathsf {H}^\textsc {S}(\mathbf {p}):= -\sum _j p_j \log p_j$ is the Shannon entropy 
In this section, we derive the Jacobian of $\operatornamewithlimits{\mathsf {entmax }}$ with respect to the scalar parameter $\alpha $ 
Jacobian of @!START@$\alpha $@!END@-entmax w r t  the shape parameter @!START@$\alpha $@!END@: Proof of Proposition @!START@UID22@!END@ ::: General case of @!START@$\alpha >1$@!END@
From the KKT conditions associated with the optimization problem in Eq  DISPLAY_FORM85, we have that the solution $\mathbf {p}^{\star }$ has the following form, coordinate-wise:
where $\tau ^{\star }$ is a scalar Lagrange multiplier that ensures that $\mathbf {p}^{\star }$ normalizes to 1, i e , it is defined implicitly by the condition:
For general values of $\alpha $, Eq  DISPLAY_FORM98 lacks a closed form solution  This makes the computation of the Jacobian
non-trivial  Fortunately, we can use the technique of implicit differentiation to obtain this Jacobian 
The Jacobian exists almost everywhere, and the expressions we derive expressions yield a generalized Jacobian BIBREF37 at any non-differentiable points that may occur for certain ($\alpha $, $\mathbf {z}$) pairs  We begin by noting that $\frac{\partial p_i^{\star }}{\partial \alpha } = 0$ if $p_i^{\star } = 0$, because increasing $\alpha $ keeps sparse coordinates sparse  Therefore we need to worry only about coordinates that are in the support of $\mathbf {p}^\star $  We will assume hereafter that the $i$th coordinate of $\mathbf {p}^\star $ is non-zero  We have:
We can see that this Jacobian depends on $\frac{\partial \tau ^{\star }}{\partial \alpha }$, which we now compute using implicit differentiation 
Let $\mathcal {S} = \lbrace i: p^\star _i > 0 \rbrace $)  By differentiating both sides of Eq  DISPLAY_FORM98, re-using some of the steps in Eq  DISPLAY_FORM101, and recalling Eq  DISPLAY_FORM97, we get
from which we obtain:
Finally, plugging Eq  DISPLAY_FORM103 into Eq  DISPLAY_FORM101, we get:
where we denote by
The distribution $\tilde{\mathbf {p}}(\alpha )$ can be interpreted as a “skewed” distribution obtained from $\mathbf {p}^{\star }$, which appears in the Jacobian of $\mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}(\mathbf {z})$ w r t  $\mathbf {z}$ as well BIBREF14 
Jacobian of @!START@$\alpha $@!END@-entmax w r t  the shape parameter @!START@$\alpha $@!END@: Proof of Proposition @!START@UID22@!END@ ::: Solving the indetermination for @!START@$\alpha =1$@!END@
We can write Eq  DISPLAY_FORM104 as
When $\alpha \rightarrow 1^+$, we have $\tilde{\mathbf {p}}(\alpha ) \rightarrow \mathbf {p}^{\star }$, which leads to a $\frac{0}{0}$ indetermination 
To solve this indetermination, we will need to apply L'Hôpital's rule twice  Let us first compute the derivative of $\tilde{p}_i(\alpha )$ with respect to $\alpha $  We have
therefore
Differentiating the numerator and denominator in Eq  DISPLAY_FORM107, we get:
with
and
When $\alpha \rightarrow 1^+$, $B$ becomes again a $\frac{0}{0}$ indetermination, which we can solve by applying again L'Hôpital's rule  Differentiating the numerator and denominator in Eq  DISPLAY_FORM112:
Finally, summing Eq  DISPLAY_FORM111 and Eq  DISPLAY_FORM113, we get
Jacobian of @!START@$\alpha $@!END@-entmax w r t  the shape parameter @!START@$\alpha $@!END@: Proof of Proposition @!START@UID22@!END@ ::: Summary
To sum up, we have the following expression for the Jacobian of $\mathop {\mathsf {\alpha }\textnormal {-}\mathsf {entmax }}$ with respect to $\alpha $:

ground_truth: the attention heads in the proposed adaptively sparse Transformer can specialize more and with higher confidence

We introduce sparse attention into the Transformer architecture

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

Please answer the questions based on the text provided below. Why masking words in the decoder is helpful?
Context 4: 
Refined Memory Layer  This layer maps the coarse memories to the refined memories  First we use knowledge aided self attention (introduced later) to fuse INLINEFORM0 into themselves, the outputs of which are represented as INLINEFORM1   Then we process INLINEFORM2 with a BiLSTM, whose hidden state dimensionality is INLINEFORM3   By concatenating the forward LSTM outputs and the backward LSTM outputs, we obtain the refined memories INLINEFORM4 , which are the final passage representations 
Answer Span Prediction Layer  This layer predicts the answer start position and the answer end position based on the above layers  First we obtain the answer start position distribution INLINEFORM0 : INLINEFORM1 INLINEFORM2
where INLINEFORM0 , INLINEFORM1 , and INLINEFORM2 are trainable parameters; INLINEFORM3 represents the refined memory of each passage word INLINEFORM4 (i e  the INLINEFORM5 -th column in INLINEFORM6 ); INLINEFORM7 represents the question summary obtained by performing an attention pooling over INLINEFORM8   Then we obtain the answer end position distribution INLINEFORM9 : INLINEFORM10 INLINEFORM11
where INLINEFORM0 , INLINEFORM1 , and INLINEFORM2 are trainable parameters; INLINEFORM3 represents vector concatenation  Finally we construct an answer span prediction matrix INLINEFORM4 , where INLINEFORM5 represents the upper triangular matrix of a matrix INLINEFORM6   Therefore, for the training, we minimize INLINEFORM7 on each training example whose labeled answer span is INLINEFORM8 ; for the inference, we separately take the row index and column index of the maximum element in INLINEFORM9 as INLINEFORM10 and INLINEFORM11  
Knowledge Aided Mutual Attention
As a part of the coarse memory layer, knowledge aided mutual attention is aimed at fusing the question context embeddings INLINEFORM0 into the passage context embeddings INLINEFORM1 , where the key problem is to calculate the similarity between each passage context embedding INLINEFORM2 (i e  the INLINEFORM3 -th column in INLINEFORM4 ) and each question context embedding INLINEFORM5 (i e  the INLINEFORM6 -th column in INLINEFORM7 )  To solve this problem, BIBREF3 proposed a similarity function: INLINEFORM8
where INLINEFORM0 is a trainable parameter; INLINEFORM1 represents element-wise multiplication  This similarity function has also been adopted by several other works BIBREF17 , BIBREF5   However, since context embeddings contain high-level information, we believe that introducing the pre-extracted general knowledge into the calculation of such similarities will make the results more reasonable  Therefore we modify the above similarity function to the following form: INLINEFORM2
where INLINEFORM0 represents the enhanced context embedding of a word INLINEFORM1   We use the pre-extracted general knowledge to construct the enhanced context embeddings  Specifically, for each word INLINEFORM2 , whose context embedding is INLINEFORM3 , to construct its enhanced context embedding INLINEFORM4 , first recall that we have extracted a set INLINEFORM5 , which includes the positions of the passage words that INLINEFORM6 is semantically connected to, thus by gathering the columns in INLINEFORM7 whose indexes are given by INLINEFORM8 , we obtain the matching context embeddings INLINEFORM9   Then by constructing a INLINEFORM10 -attended summary of INLINEFORM11 , we obtain the matching vector INLINEFORM12 (if INLINEFORM13 , which makes INLINEFORM14 , we will set INLINEFORM15 ): INLINEFORM16 INLINEFORM17
where INLINEFORM0 , INLINEFORM1 , and INLINEFORM2 are trainable parameters; INLINEFORM3 represents the INLINEFORM4 -th column in INLINEFORM5   Finally we pass the concatenation of INLINEFORM6 and INLINEFORM7 through a dense layer with ReLU activation, whose output dimensionality is INLINEFORM8   Therefore we obtain the enhanced context embedding INLINEFORM9  
Based on the modified similarity function and the enhanced context embeddings, to perform knowledge aided mutual attention, first we construct a knowledge aided similarity matrix INLINEFORM0 , where each element INLINEFORM1   Then following BIBREF5 , we construct the passage-attended question summaries INLINEFORM2 and the question-attended passage summaries INLINEFORM3 : INLINEFORM4 INLINEFORM5
where INLINEFORM0 represents softmax along the row dimension and INLINEFORM1 along the column dimension  Finally following BIBREF17 , we pass the concatenation of INLINEFORM2 , INLINEFORM3 , INLINEFORM4 , and INLINEFORM5 through a dense layer with ReLU activation, whose output dimensionality is INLINEFORM6   Therefore we obtain the outputs INLINEFORM7  
Knowledge Aided Self Attention
As a part of the refined memory layer, knowledge aided self attention is aimed at fusing the coarse memories INLINEFORM0 into themselves  If we simply follow the self attentions of other works BIBREF4 , BIBREF18 , BIBREF19 , BIBREF17 , then for each passage word INLINEFORM1 , we should fuse its coarse memory INLINEFORM2 (i e  the INLINEFORM3 -th column in INLINEFORM4 ) with the coarse memories of all the other passage words  However, we believe that this is both unnecessary and distracting, since each passage word has nothing to do with many of the other passage words  Thus we use the pre-extracted general knowledge to guarantee that the fusion of coarse memories for each passage word will only involve a precise subset of the other passage words  Specifically, for each passage word INLINEFORM5 , whose coarse memory is INLINEFORM6 , to perform the fusion of coarse memories, first recall that we have extracted a set INLINEFORM7 , which includes the positions of the other passage words that INLINEFORM8 is semantically connected to, thus by gathering the columns in INLINEFORM9 whose indexes are given by INLINEFORM10 , we obtain the matching coarse memories INLINEFORM11   Then by constructing a INLINEFORM12 -attended summary of INLINEFORM13 , we obtain the matching vector INLINEFORM14 (if INLINEFORM15 , which makes INLINEFORM16 , we will set INLINEFORM17 ): INLINEFORM18 INLINEFORM19
where INLINEFORM0 , INLINEFORM1 , and INLINEFORM2 are trainable parameters  Finally we pass the concatenation of INLINEFORM3 and INLINEFORM4 through a dense layer with ReLU activation, whose output dimensionality is INLINEFORM5   Therefore we obtain the fusion result INLINEFORM6 , and further the outputs INLINEFORM7  
Related Works
Attention Mechanisms  Besides those mentioned above, other interesting attention mechanisms include performing multi-round alignment to avoid the problems of attention redundancy and attention deficiency BIBREF20 , and using mutual attention as a skip-connector to densely connect pairwise layers BIBREF21  
Data Augmentation  It is proved that properly augmenting training examples can improve the performance of MRC models  For example, BIBREF22 trained a generative model to generate questions based on unlabeled text, which substantially boosted their performance; BIBREF5 trained a back-and-forth translation model to paraphrase training examples, which brought them a significant performance gain 
Multi-step Reasoning  Inspired by the fact that human beings are capable of understanding complex documents by reading them over and over again, multi-step reasoning was proposed to better deal with difficult MRC tasks  For example, BIBREF23 used reinforcement learning to dynamically determine the number of reasoning steps; BIBREF19 fixed the number of reasoning steps, but used stochastic dropout in the output layer to avoid step bias 
Linguistic Embeddings  It is both easy and effective to incorporate linguistic embeddings into the input layer of MRC models  For example, BIBREF24 and BIBREF19 used POS embeddings and NER embeddings to construct their input embeddings; BIBREF25 used structural embeddings based on parsing trees to constructed their input embeddings 
Transfer Learning  Several recent breakthroughs in MRC benefit from feature-based transfer learning BIBREF26 , BIBREF27 and fine-tuning-based transfer learning BIBREF28 , BIBREF29 , which are based on certain word-level or sentence-level models pre-trained on large external corpora in certain supervised or unsupervised manners 
Experimental Settings
MRC Dataset  The MRC dataset used in this paper is SQuAD 1 1, which contains over INLINEFORM0 passage-question pairs and has been randomly partitioned into three parts: a training set ( INLINEFORM1 ), a development set ( INLINEFORM2 ), and a test set ( INLINEFORM3 )  Besides, we also use two of its adversarial sets, namely AddSent and AddOneSent BIBREF6 , to evaluate the robustness to noise of MRC models  The passages in the adversarial sets contain misleading sentences, which are aimed at distracting MRC models  Specifically, each passage in AddSent contains several sentences that are similar to the question but not contradictory to the answer, while each passage in AddOneSent contains a human-approved random sentence that may be unrelated to the passage 
Implementation Details  We tokenize the MRC dataset with spaCy 2 0 13 BIBREF30 , manipulate WordNet 3 0 with NLTK 3 3, and implement KAR with TensorFlow 1 11 0 BIBREF31   For the data enrichment method, we set the hyper-parameter INLINEFORM0 to 3  For the dense layers and the BiLSTMs, we set the dimensionality unit INLINEFORM1 to 600  For model optimization, we apply the Adam BIBREF32 optimizer with a learning rate of INLINEFORM2 and a mini-batch size of 32  For model evaluation, we use Exact Match (EM) and F1 score as evaluation metrics  To avoid overfitting, we apply dropout BIBREF33 to the dense layers and the BiLSTMs with a dropout rate of INLINEFORM3   To boost the performance, we apply exponential moving average with a decay rate of INLINEFORM4  
Model Comparison in both Performance and the Robustness to Noise
We compare KAR with other MRC models in both performance and the robustness to noise  Specifically, we not only evaluate the performance of KAR on the development set and the test set, but also do this on the adversarial sets  As for the comparative objects, we only consider the single MRC models that rank in the top 20 on the SQuAD 1 1 leader board and have reported their performance on the adversarial sets  There are totally five such comparative objects, which can be considered as representatives of the state-of-the-art MRC models  As shown in Table TABREF12 , on the development set and the test set, the performance of KAR is on par with that of the state-of-the-art MRC models; on the adversarial sets, KAR outperforms the state-of-the-art MRC models by a large margin  That is to say, KAR is comparable in performance with the state-of-the-art MRC models, and significantly more robust to noise than them 
To verify the effectiveness of general knowledge, we first study the relationship between the amount of general knowledge and the performance of KAR  As shown in Table TABREF13 , by increasing INLINEFORM0 from 0 to 5 in the data enrichment method, the amount of general knowledge rises monotonically, but the performance of KAR first rises until INLINEFORM1 reaches 3 and then drops down  Then we conduct an ablation study by replacing the knowledge aided attention mechanisms with the mutual attention proposed by BIBREF3 and the self attention proposed by BIBREF4 separately, and find that the F1 score of KAR drops by INLINEFORM2 on the development set, INLINEFORM3 on AddSent, and INLINEFORM4 on AddOneSent  Finally we find that after only one epoch of training, KAR already achieves an EM of INLINEFORM5 and an F1 score of INLINEFORM6 on the development set, which is even better than the final performance of several strong baselines, such as DCN (EM / F1: INLINEFORM7 / INLINEFORM8 ) BIBREF36 and BiDAF (EM / F1: INLINEFORM9 / INLINEFORM10 ) BIBREF3   The above empirical findings imply that general knowledge indeed plays an effective role in KAR 
To demonstrate the advantage of our explicit way to utilize general knowledge over the existing implicit way, we compare the performance of KAR with that reported by BIBREF10 , which used an encoding-based method to utilize the general knowledge dynamically retrieved from Wikipedia and ConceptNet  Since their best model only achieved an EM of INLINEFORM0 and an F1 score of INLINEFORM1 on the development set, which is much lower than the performance of KAR, we have good reason to believe that our explicit way works better than the existing implicit way 
Model Comparison in the Hunger for Data
We compare KAR with other MRC models in the hunger for data  Specifically, instead of using all the training examples, we produce several training subsets (i e  subsets of the training examples) so as to study the relationship between the proportion of the available training examples and the performance  We produce each training subset by sampling a specific number of questions from all the questions relevant to each passage  By separately sampling 1, 2, 3, and 4 questions on each passage, we obtain four training subsets, which separately contain INLINEFORM0 , INLINEFORM1 , INLINEFORM2 , and INLINEFORM3 of the training examples  As shown in Figure FIGREF15 , with KAR, SAN (re-implemented), and QANet (re-implemented without data augmentation) trained on these training subsets, we evaluate their performance on the development set, and find that KAR performs much better than SAN and QANet  As shown in Figure FIGREF16 and Figure FIGREF17 , with the above KAR, SAN, and QANet trained on the same training subsets, we also evaluate their performance on the adversarial sets, and still find that KAR performs much better than SAN and QANet  That is to say, when only a subset of the training examples are available, KAR outperforms the state-of-the-art MRC models by a large margin, and is still reasonably robust to noise 
Analysis
According to the experimental results, KAR is not only comparable in performance with the state-of-the-art MRC models, but also superior to them in terms of both the hunger for data and the robustness to noise  The reasons for these achievements, we believe, are as follows:
Conclusion
In this paper, we innovatively integrate the neural networks of MRC models with the general knowledge of human beings  Specifically, inter-word semantic connections are first extracted from each given passage-question pair by a WordNet-based data enrichment method, and then provided as general knowledge to an end-to-end MRC model named as Knowledge Aided Reader (KAR), which explicitly uses the general knowledge to assist its attention mechanisms  Experimental results show that KAR is not only comparable in performance with the state-of-the-art MRC models, but also superior to them in terms of both the hunger for data and the robustness to noise  In the future, we plan to use some larger knowledge bases, such as ConceptNet and Freebase, to improve the quality and scope of the general knowledge 
Acknowledgments
This work is partially supported by a research donation from iFLYTEK Co , Ltd , Hefei, China, and a discovery grant from Natural Sciences and Engineering Research Council (NSERC) of Canada 

ground_truth: ecause this process is similar to the cloze task in BERT's pre-train process, therefore by using the ability of the contextual language model the decoder can generate more fluent and natural sequences.