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 are method improvements of F1 for paraphrase identification?
Context 1: Introduction
Data imbalance is a common issue in a variety of NLP tasks such as tagging and machine reading comprehension  Table TABREF3 gives concrete examples: for the Named Entity Recognition (NER) task BIBREF2, BIBREF3, most tokens are backgrounds with tagging class $O$  Specifically, the number of tokens tagging class $O$ is 5 times as many as those with entity labels for the CoNLL03 dataset and 8 times for the OntoNotes5 0 dataset; Data-imbalanced issue is more severe for MRC tasks BIBREF4, BIBREF5, BIBREF6, BIBREF7, BIBREF8 with the value of negative-positive ratio being 50-200 
Data imbalance results in the following two issues: (1) the training-test discrepancy: Without balancing the labels, the learning process tends to converge to a point that strongly biases towards class with the majority label  This actually creates a discrepancy between training and test: at training time, each training instance contributes equally to the objective function while at test time, F1 score concerns more about positive examples; (2) the overwhelming effect of easy-negative examples  As pointed out by meng2019dsreg, significantly large number of negative examples also means that the number of easy-negative example is large  The huge number of easy examples tends to overwhelm the training, making the model not sufficiently learned to distinguish between positive examples and hard-negative examples  The cross-entropy objective (CE for short) or maximum likelihood (MLE) objective, which is widely adopted as the training objective for data-imbalanced NLP tasks BIBREF9, BIBREF10, BIBREF11, BIBREF12, BIBREF13, BIBREF14, BIBREF15, handles neither of the issues 
To handle the first issue, we propose to replace CE or MLE with losses based on the Sørensen–Dice coefficient BIBREF0 or Tversky index BIBREF1  The Sørensen–Dice coefficient, dice loss for short, is the harmonic mean of precision and recall  It attaches equal importance to false positives (FPs) and false negatives (FNs) and is thus more immune to data-imbalanced datasets  Tversky index extends dice loss by using a weight that trades precision and recall, which can be thought as the approximation of the $F_{\beta }$ score, and thus comes with more flexibility  Therefore, We use dice loss or Tversky index to replace CE loss to address the first issue 
Only using dice loss or Tversky index is not enough since they are unable to address the dominating influence of easy-negative examples  This is intrinsically because dice loss is actually a hard version of the F1 score  Taking the binary classification task as an example, at test time, an example will be classified as negative as long as its probability is smaller than 0 5, but training will push the value to 0 as much as possible  This gap isn't a big issue for balanced datasets, but is extremely detrimental if a big proportion of training examples are easy-negative ones: easy-negative examples can easily dominate training since their probabilities can be pushed to 0 fairly easily  Meanwhile, the model can hardly distinguish between hard-negative examples and positive ones  Inspired by the idea of focal loss BIBREF16 in computer vision, we propose a dynamic weight adjusting strategy, which associates each training example with a weight in proportion to $(1-p)$, and this weight dynamically changes as training proceeds  This strategy helps to deemphasize confident examples during training as their $p$ approaches the value of 1, makes the model attentive to hard-negative examples, and thus alleviates the dominating effect of easy-negative examples 
Combing both strategies, we observe significant performance boosts on a wide range of data imbalanced NLP tasks  Notably, we are able to achieve SOTA results on CTB5 (97 92, +1 86), CTB6 (96 57, +1 80) and UD1 4 (96 98, +2 19) for the POS task; SOTA results on CoNLL03 (93 33, +0 29), OntoNotes5 0 (92 07, +0 96)), MSRA 96 72(+0 97) and OntoNotes4 0 (84 47,+2 36) for the NER task; along with competitive results on the tasks of machine reading comprehension and paraphrase identification 
The rest of this paper is organized as follows: related work is presented in Section 2  We describe different training objectives in Section 3  Experimental results are presented in Section 4  We perform ablation studies in Section 5, followed by a brief conclusion in Section 6 
Related Work ::: Data Resample
The idea of weighting training examples has a long history  Importance sampling BIBREF17 assigns weights to different samples and changes the data distribution  Boosting algorithms such as AdaBoost BIBREF18 select harder examples to train subsequent classifiers  Similarly, hard example mining BIBREF19 downsamples the majority class and exploits the most difficult examples  Oversampling BIBREF20, BIBREF21 is used to balance the data distribution  Another line of data resampling is to dynamically control the weights of examples as training proceeds  For example, focal loss BIBREF16 used a soft weighting scheme that emphasizes harder examples during training  In self-paced learning BIBREF22, example weights are obtained through optimizing the weighted training loss which encourages learning easier examples first  At each training step, self-paced learning algorithm optimizes model parameters and example weights jointly  Other works BIBREF23, BIBREF24 adjusted the weights of different training examples based on training loss  Besides, recent work BIBREF25, BIBREF26 proposed to learn a separate network to predict sample weights 
Related Work ::: Data Imbalance Issue in Object Detection
The background-object label imbalance issue is severe and thus well studied in the field of object detection BIBREF27, BIBREF28, BIBREF29, BIBREF30, BIBREF31  The idea of hard negative mining (HNM) BIBREF30 has gained much attention recently  shrivastava2016ohem proposed the online hard example mining (OHEM) algorithm in an iterative manner that makes training progressively more difficult, and pushes the model to learn better  ssd2016liu sorted all of the negative samples based on the confidence loss and picking the training examples with the negative-positive ratio at 3:1  pang2019rcnn proposed a novel method called IoU-balanced sampling and aploss2019chen designed a ranking model to replace the conventional classification task with a average-precision loss to alleviate the class imbalance issue  The efforts made on object detection have greatly inspired us to solve the data imbalance issue in NLP 
Losses ::: Notation
For illustration purposes, we use the binary classification task to demonstrate how different losses work  The mechanism can be easily extended to multi-class classification 
Let $\lbrace x_i\rbrace $ denote a set of instances  Each $x_i$ is associated with a golden label vector $y_i = [y_{i0},y_{i1} ]$, where $y_{i1}\in \lbrace 0,1\rbrace $ and $y_{i0}\in \lbrace 0,1\rbrace $ respectively denote the positive and negative classes, and thus $y_i$ can be either $[0,1]$ or $[0,1]$  Let $p_i = [p_{i0},p_{i1} ]$ denote the probability vector, and $p_{i1}$ and $p_{i0}$ respectively denote the probability that a model assigns the positive and negative label to $x_i$ 
Losses ::: Cross Entropy Loss
The vanilla cross entropy (CE) loss is given by:
As can be seen from Eq DISPLAY_FORM8, each $x_i$ contributes equally to the final objective  Two strategies are normally used to address the the case where we wish that not all $x_i$ are treated equal: associating different classes with different weighting factor $\alpha $ or resampling the datasets  For the former, Eq DISPLAY_FORM8 is adjusted as follows:
where $\alpha _i\in [0,1]$ may be set by the inverse class frequency or treated as a hyperparameter to set by cross validation  In this work, we use $\lg (\frac{n-n_t}{n_t}+K)$ to calculate the coefficient $\alpha $, where $n_t$ is the number of samples with class $t$ and $n$ is the total number of samples in the training set  $K$ is a hyperparameter to tune  The data resampling strategy constructs a new dataset by sampling training examples from the original dataset based on human-designed criteria, e g , extract equal training samples from each class  Both strategies are equivalent to changing the data distribution and thus are of the same nature  Empirically, these two methods are not widely used due to the trickiness of selecting $\alpha $ especially for multi-class classification tasks and that inappropriate selection can easily bias towards rare classes BIBREF32 
Losses ::: Dice coefficient and Tversky index
Sørensen–Dice coefficient BIBREF0, BIBREF33, dice coefficient (DSC) for short, is a F1-oriented statistic used to gauge the similarity of two sets  Given two sets $A$ and $B$, the dice coefficient between them is given as follows:
In our case, $A$ is the set that contains of all positive examples predicted by a specific model, and $B$ is the set of all golden positive examples in the dataset  When applied to boolean data with the definition of true positive (TP), false positive (FP), and false negative (FN), it can be then written as follows:
For an individual example $x_i$, its corresponding DSC loss is given as follows:
As can be seen, for a negative example with $y_{i1}=0$, it does not contribute to the objective  For smoothing purposes, it is common to add a $\gamma $ factor to both the nominator and the denominator, making the form to be as follows:
As can be seen, negative examples, with $y_{i1}$ being 0 and DSC being $\frac{\gamma }{ p_{i1}+\gamma }$, also contribute to the training  Additionally, milletari2016v proposed to change the denominator to the square form for faster convergence, which leads to the following dice loss (DL):
Another version of DL is to directly compute set-level dice coefficient instead of the sum of individual dice coefficient  We choose the latter due to ease of optimization 
Tversky index (TI), which can be thought as the approximation of the $F_{\beta }$ score, extends dice coefficient to a more general case  Given two sets $A$ and $B$, tversky index is computed as follows:
Tversky index offers the flexibility in controlling the tradeoff between false-negatives and false-positives  It degenerates to DSC if $\alpha =\beta =0 5$  The Tversky loss (TL) for the training set $\lbrace x_i,y_i\rbrace $ is thus as follows:
Losses ::: Self-adusting Dice Loss
Consider a simple case where the dataset consists of only one example $x_i$, which is classified as positive as long as $p_{i1}$ is larger than 0 5  The computation of $F1$ score is actually as follows:
Comparing Eq DISPLAY_FORM14 with Eq DISPLAY_FORM22, we can see that Eq DISPLAY_FORM14 is actually a soft form of $F1$, using a continuous $p$ rather than the binary $\mathbb {I}( p_{i1}>0 5)$  This gap isn't a big issue for balanced datasets, but is extremely detrimental if a big proportion of training examples are easy-negative ones: easy-negative examples can easily dominate training since their probabilities can be pushed to 0 fairly easily  Meanwhile, the model can hardly distinguish between hard-negative examples and positive ones, which has a huge negative effect on the final F1 performance 
To address this issue, we propose to multiply the soft probability $p$ with a decaying factor $(1-p)$, changing Eq DISPLAY_FORM22 to the following form:
One can think $(1-p_{i1})$ as a weight associated with each example, which changes as training proceeds  The intuition of changing $p_{i1}$ to $(1-p_{i1}) p_{i1}$ is to push down the weight of easy examples  For easy examples whose probability are approaching 0 or 1, $(1-p_{i1}) p_{i1}$ makes the model attach significantly less focus to them  Figure FIGREF23 gives gives an explanation from the perspective in derivative: the derivative of $\frac{(1-p)p}{1+(1-p)p}$ with respect to $p$ approaches 0 immediately after $p$ approaches 0, which means the model attends less to examples once they are correctly classified 
A close look at Eq DISPLAY_FORM14 reveals that it actually mimics the idea of focal loss (FL for short) BIBREF16 for object detection in vision  Focal loss was proposed for one-stage object detector to handle foreground-background tradeoff encountered during training  It down-weights the loss assigned to well-classified examples by adding a $(1-p)^{\beta }$ factor, leading the final loss to be $(1-p)^{\beta }\log p$ 
In Table TABREF18, we show the losses used in our experiments, which is described in the next section 
Experiments
We evaluate the proposed method on four NLP tasks: part-of-speech tagging, named entity recognition, machine reading comprehension and paraphrase identification  Baselines in our experiments are optimized by using the standard cross-entropy training objective 
Experiments ::: Part-of-Speech Tagging
Part-of-speech tagging (POS) is the task of assigning a label (e g , noun, verb, adjective) to each word in a given text  In this paper, we choose BERT as the backbone and conduct experiments on three Chinese POS datasets  We report the span-level micro-averaged precision, recall and F1 for evaluation  Hyperparameters are tuned on the corresponding development set of each dataset 
Experiments ::: Part-of-Speech Tagging ::: Datasets
We conduct experiments on the widely used Chinese Treebank 5 0, 6 0 as well as UD1 4 
CTB5 is a Chinese dataset for tagging and parsing, which contains 507,222 words, 824,983 characters and 18,782 sentences extracted from newswire sources 
CTB6 is an extension of CTB5, containing 781,351 words, 1,285,149 characters and 28,295 sentences 
UD is the abbreviation of Universal Dependencies, which is a framework for consistent annotation of grammar (parts of speech, morphological features, and syntactic dependencies) across different human languages  In this work, we use UD1 4 for Chinese POS tagging 
Experiments ::: Part-of-Speech Tagging ::: Baselines
We use the following baselines:
Joint-POS: shao2017character jointly learns Chinese word segmentation and POS 
Lattice-LSTM: lattice2018zhang constructs a word-character lattice 
Bert-Tagger: devlin2018bert treats part-of-speech as a tagging task 
Experiments ::: Part-of-Speech Tagging ::: Results
Table presents the experimental results on the POS task  As can be seen, the proposed DSC loss outperforms the best baseline results by a large margin, i e , outperforming BERT-tagger by +1 86 in terms of F1 score on CTB5, +1 80 on CTB6 and +2 19 on UD1 4  As far as we are concerned, we are achieving SOTA performances on the three datasets  Weighted cross entropy and focal loss only gain a little performance improvement on CTB5 and CTB6, and the dice loss obtains huge gain on CTB5 but not on CTB6, which indicates the three losses are not consistently robust in resolving the data imbalance issue  The proposed DSC loss performs robustly on all the three datasets 
Experiments ::: Named Entity Recognition
Named entity recognition (NER) refers to the task of detecting the span and semantic category of entities from a chunk of text  Our implementation uses the current state-of-the-art BERT-MRC model proposed by xiaoya2019ner as a backbone  For English datasets, we use BERT$_\text{Large}$ English checkpoints, while for Chinese we use the official Chinese checkpoints  We report span-level micro-averaged precision, recall and F1-score  Hyperparameters are tuned on the development set of each dataset 
Experiments ::: Named Entity Recognition ::: Datasets
For the NER task, we consider both Chinese datasets, i e , OntoNotes4 0 BIBREF34 and MSRA BIBREF35, and English datasets, i e , CoNLL2003 BIBREF36 and OntoNotes5 0 BIBREF37 
CoNLL2003 is an English dataset with 4 entity types: Location, Organization, Person and Miscellaneous  We followed data processing protocols in BIBREF14 
English OntoNotes5 0 consists of texts from a wide variety of sources and contains 18 entity types  We use the standard train/dev/test split of CoNLL2012 shared task 
Chinese MSRA performs as a Chinese benchmark dataset containing 3 entity types  Data in MSRA is collected from news domain  Since the development set is not provided in the original MSRA dataset, we randomly split the training set into training and development splits by 9:1  We use the official test set for evaluation 
Chinese OntoNotes4 0 is a Chinese dataset and consists of texts from news domain, which has 18 entity types  In this paper, we take the same data split as wu2019glyce did 
Experiments ::: Named Entity Recognition ::: Baselines
We use the following baselines:
ELMo: a tagging model from peters2018deep 
Lattice-LSTM: lattice2018zhang constructs a word-character lattice, only used in Chinese datasets 
CVT: from kevin2018cross, which uses Cross-View Training(CVT) to improve the representations of a Bi-LSTM encoder 
Bert-Tagger: devlin2018bert treats NER as a tagging task 
Glyce-BERT: wu2019glyce combines glyph information with BERT pretraining 
BERT-MRC: The current SOTA model for both Chinese and English NER datasets proposed by xiaoya2019ner, which formulate NER as machine reading comprehension task 
Experiments ::: Named Entity Recognition ::: Results
Table shows experimental results on NER datasets  For English datasets including CoNLL2003 and OntoNotes5 0, our proposed method outperforms BERT-MRCBIBREF38 by +0 29 and +0 96 respectively  We observe huge performance boosts on Chinese datasets, achieving F1 improvements by +0 97 and +2 36 on MSRA and OntoNotes4 0, respectively  As far as we are concerned, we are setting new SOTA performances on all of the four NER datasets 
Experiments ::: Machine Reading Comprehension
Machine reading comprehension (MRC) BIBREF39, BIBREF40, BIBREF41, BIBREF40, BIBREF42, BIBREF15 has become a central task in natural language understanding  MRC in the SQuAD-style is to predict the answer span in the passage given a question and the passage  In this paper, we choose the SQuAD-style MRC task and report Extract Match (EM) in addition to F1 score on validation set  All hyperparameters are tuned on the development set of each dataset 
Experiments ::: Machine Reading Comprehension ::: Datasets
The following five datasets are used for MRC task: SQuAD v1 1, SQuAD v2 0 BIBREF4, BIBREF6 and Quoref BIBREF8 
SQuAD v1 1 and SQuAD v2 0 are the most widely used QA benchmarks  SQuAD1 1 is a collection of 100K crowdsourced question-answer pairs, and SQuAD2 0 extends SQuAD1 1 allowing no short answer exists in the provided passage 
Quoref is a QA dataset which tests the coreferential reasoning capability of reading comprehension systems, containing 24K questions over 4 7K paragraphs from Wikipedia 
Experiments ::: Machine Reading Comprehension ::: Baselines
We use the following baselines:
QANet: qanet2018 builds a model based on convolutions and self-attention  Convolution to model local interactions and self-attention to model global interactions 
BERT: devlin2018bert treats NER as a tagging task 
XLNet: xlnet2019 proposes a generalized autoregressive pretraining method that enables learning bidirectional contexts 
Experiments ::: Machine Reading Comprehension ::: Results
Table shows the experimental results for MRC tasks  With either BERT or XLNet, our proposed DSC loss obtains significant performance boost on both EM and F1  For SQuADv1 1, our proposed method outperforms XLNet by +1 25 in terms of F1 score and +0 84 in terms of EM and achieves 87 65 on EM and 89 51 on F1 for SQuAD v2 0  Moreover, on QuoRef, the proposed method surpasses XLNet results by +1 46 on EM and +1 41 on F1  Another observation is that, XLNet outperforms BERT by a huge margin, and the proposed DSC loss can obtain further performance improvement by an average score above 1 0 in terms of both EM and F1, which indicates the DSC loss is complementary to the model structures 
Experiments ::: Paraphrase Identification
Paraphrases are textual expressions that have the same semantic meaning using different surface words  Paraphrase identification (PI) is the task of identifying whether two sentences have the same meaning or not  We use BERT BIBREF11 and XLNet BIBREF43 as backbones and report F1 score for comparison  Hyperparameters are tuned on the development set of each dataset 
Experiments ::: Paraphrase Identification ::: Datasets
We conduct experiments on two widely used datasets for PI task: MRPC BIBREF44 and QQP 
MRPC is a corpus of sentence pairs automatically extracted from online news sources, with human annotations of whether the sentence pairs are semantically equivalent  The MRPC dataset has imbalanced classes (68% positive, 32% for negative) 
QQP is a collection of question pairs from the community question-answering website Quora  The class distribution in QQP is also unbalanced (37% positive, 63% negative) 
Experiments ::: Paraphrase Identification ::: Results
Table shows the results for PI task  We find that replacing the training objective with DSC introduces performance boost for both BERT and XLNet  Using DSC loss improves the F1 score by +0 58 for MRPC and +0 73 for QQP 
Ablation Studies ::: The Effect of Dice Loss on Accuracy-oriented Tasks
We argue that the most commonly used cross-entropy objective is actually accuracy-oriented, whereas the proposed dice loss (DL) performs as a hard version of F1-score  To explore the effect of the dice loss on accuracy-oriented tasks such as text classification, we conduct experiments on the Stanford Sentiment Treebank sentiment classification datasets including SST-2 and SST-5  We fine-tune BERT$_\text{Large}$ with different training objectives  Experiment results for SST are shown in   For SST-5, BERT with CE achieves 55 57 in terms of accuracy, with DL and DSC losses slightly degrade the accuracy performance and achieve 54 63 and 55 19, respectively  For SST-2, BERT with CE achieves 94 9 in terms of accuracy  The same as SST-5, we observe a slight performance drop with DL and DSC, which means that the dice loss actually works well for F1 but not for accuracy 
Ablation Studies ::: The Effect of Hyperparameters in Tversky index
As mentioned in Section SECREF10, Tversky index (TI) offers the flexibility in controlling the tradeoff between false-negatives and false-positives  In this subsection, we explore the effect of hyperparameters (i e , $\alpha $ and $\beta $) in TI to test how they manipulate the tradeoff  We conduct experiments on the Chinese OntoNotes4 0 NER dataset and English QuoRef MRC dataset to examine the influence of tradeoff between precision and recall  Experiment results are shown in Table   The highest F1 for Chinese OntoNotes4 0 is 84 67 when $\alpha $ is set to 0 6 while for QuoRef, the highest F1 is 68 44 when $\alpha $ is set to 0 4  In addition, we can observe that the performance varies a lot as $\alpha $ changes in distinct datasets, which shows that the hyperparameters $\alpha ,\beta $ play an important role in the proposed method 
Conclusion
In this paper, we alleviate the severe data imbalance issue in NLP tasks  We propose to use dice loss in replacement of the standard cross-entropy loss, which performs as a soft version of F1 score  Using dice loss can help narrow the gap between training objectives and evaluation metrics  Empirically, we show that the proposed training objective leads to significant performance boost for part-of-speech, named entity recognition, machine reading comprehension and paraphrase identification tasks 
Context 3: Introduction
Pre-trained models BIBREF0, BIBREF1 have received much of attention recently thanks to their impressive results in many down stream NLP tasks  Additionally, multilingual pre-trained models enable many NLP applications for other languages via zero-short cross-lingual transfer  Zero-shot cross-lingual transfer has shown promising results for rapidly building applications for low resource languages  BIBREF2 show the potential of multilingual-BERT BIBREF0 in zero-shot transfer for a large number of languages from different language families on five NLP tasks, namely, natural language inference, document classification, named entity recognition, part-of-speech tagging, and dependency parsing 
Although multilingual models are an important ingredient for enhancing language technology in many languages, recent research on improving pre-trained models puts much emphasis on English BIBREF3, BIBREF4, BIBREF5  The current state of affairs makes it difficult to translate advancements in pre-training from English to non-English languages  To our best knowledge, there are only three available multilingual pre-trained models to date: (1) the multilingual-BERT (mBERT) that supports 104 languages, (2) cross-lingual language model BIBREF6 that supports 100 languages, and (3) Language Agnostic SEntence Representations BIBREF7 that supports 93 languages  Among the three models, LASER is based on neural machine translation approach and strictly requires parallel data to train 
Do multilingual models always need to be trained from scratch? Can we transfer linguistic knowledge learned by English pre-trained models to other languages? In this work, we develop a technique to rapidly transfer an existing pre-trained model from English to other languages in an energy efficient way BIBREF8  As the first step, we focus on building a bilingual language model (LM) of English and a target language  Starting from a pre-trained English LM, we learn the target language specific parameters (i e , word embeddings), while keeping the encoder layers of the pre-trained English LM fixed  We then fine-tune both English and target model to obtain the bilingual LM  We apply our approach to autoencoding language models with masked language model objective and show the advantage of the proposed approach in zero-shot transfer  Our main contributions in this work are:
We propose a fast adaptation method for obtaining a bilingual BERT$_{\textsc {base}}$ of English and a target language within a day using one Tesla V100 16GB GPU 
We evaluate our bilingual LMs for six languages on two zero-shot cross-lingual transfer tasks, namely natural language inference BIBREF9 and universal dependency parsing  We show that our models offer competitive performance or even better that mBERT 
We illustrate that our bilingual LMs can serve as an excellent feature extractor in supervised dependency parsing task 
Bilingual Pre-trained LMs
We first provide some background of pre-trained language models  Let $_e$ be English word-embeddings and $\Psi ()$ be the Transformer BIBREF10 encoder with parameters $$  Let $_{w_i}$ denote the embedding of word $w_i$ (i e , $_{w_i} = _e[w_1]$)  We omit positional embeddings and bias for clarity  A pre-trained LM typically performs the following computations: (i) transform a sequence of input tokens to contextualized representations $[_{w_1},\dots ,_{w_n}] = \Psi (_{w_1}, \dots , _{w_n}; )$, and (ii) predict an output word $y_i$ at $i^{\text{th}}$ position $p(y_i | _{w_i}) \propto \exp (_{w_i}^\top _{y_i})$ 
Autoencoding LM BIBREF0 corrupts some input tokens $w_i$ by replacing them with a special token [MASK]  It then predicts the original tokens $y_i = w_i$ from the corrupted tokens  Autoregressive LM BIBREF3 predicts the next token ($y_i = w_{i+1}$) given all the previous tokens  The recently proposed XLNet model BIBREF5 is an autoregressive LM that factorizes output with all possible permutations, which shows empirical performance improvement over GPT-2 due to the ability to capture bidirectional context  Here we assume that the encoder performs necessary masking with respect to each training objective 
Given an English pre-trained LM, we wish to learn a bilingual LM for English and a given target language $f$ under a limited computational resource budget  To quickly build a bilingual LM, we directly adapt the English pre-traind model to the target model  Our approach consists of three steps  First, we initialize target language word-embeddings $_f$ in the English embedding space such that embeddings of a target word and its English equivalents are close together (§SECREF8)  Next, we create a target LM from the target embeddings and the English encoder $\Psi ()$  We then fine-tune target embeddings while keeping $\Psi ()$ fixed (§SECREF14)  Finally, we construct a bilingual LM of $_e$, $_f$, and $\Psi ()$ and fine-tune all the parameters (§SECREF15)  Figure FIGREF7 illustrates the last two steps in our approach 
Bilingual Pre-trained LMs ::: Initializing Target Embeddings
Our approach to learn the initial foreign word embeddings $_f \in ^{|V_f| \times d}$ is based on the idea of mapping the trained English word embeddings $_e \in ^{|V_e| \times d}$ to $_f$ such that if a foreign word and an English word are similar in meaning then their embeddings are similar  Borrowing the idea of universal lexical sharing from BIBREF11, we represent each foreign word embedding $_f[i] \in ^d$ as a linear combination of English word embeddings $_e[j] \in ^d$
where $_i\in ^{|V_e|}$ is a sparse vector and $\sum _j^{|V_e|} \alpha _{ij} = 1$ 
In this step of initializing foreign embeddings, having a good estimation of $$ could speed of the convergence when tuning the foreign model and enable zero-shot transfer (§SECREF5)  In the following, we discuss how to estimate $_i\;\forall i\in \lbrace 1,2, \dots , |V_f|\rbrace $ under two scenarios: (i) we have parallel data of English-foreign, and (ii) we only rely on English and foreign monolingual data 
Bilingual Pre-trained LMs ::: Initializing Target Embeddings ::: Learning from Parallel Corpus
Given an English-foreign parallel corpus, we can estimate word translation probability $p(e\,|\,f)$ for any (English-foreign) pair $(e, f)$ using popular word-alignment BIBREF12 toolkits such as fast-align BIBREF13  We then assign:
Since $_i$ is estimated from word alignment, it is a sparse vector 
Bilingual Pre-trained LMs ::: Initializing Target Embeddings ::: Learning from Monolingual Corpus
For low resource languages, parallel data may not be available  In this case, we rely only on monolingual data (e g , Wikipedias)  We estimate word translation probabilities from word embeddings of the two languages  Word vectors of these languages can be learned using fastText BIBREF14 and then are aligned into a shared space with English BIBREF15, BIBREF16  Unlike learning contextualized representations, learning word vectors is fast and computationally cheap  Given the aligned vectors $\bar{}_f$ of foreign and $\bar{}_e$ of English, we calculate the word translation matrix $\in ^{|V_f|\times |V_e|}$ as
Here, we use $\mathrm {sparsemax}$ BIBREF17 instead of softmax  Sparsemax is a sparse version of softmax and it puts zero probabilities on most of the word in the English vocabulary except few English words that are similar to a given foreign word  This property is desirable in our approach since it leads to a better initialization of the foreign embeddings 
Bilingual Pre-trained LMs ::: Fine-tuning Target Embeddings
After initializing foreign word-embeddings, we replace English word-embeddings in the English pre-trained LM with foreign word-embeddings to obtain the foreign LM  We then fine-tune only foreign word-embeddings on monolingual data  The training objective is the same as the training objective of the English pre-trained LM (i e , masked LM for BERT)  Since the trained encoder $\Psi ()$ is good at capturing association, the purpose of this step is to further optimize target embeddings such that the target LM can utilized the trained encoder for association task  For example, if the words Albert Camus presented in a French input sequence, the self-attention in the encoder more likely attends to words absurde and existentialisme once their embeddings are tuned 
Bilingual Pre-trained LMs ::: Fine-tuning Bilingual LM
We create a bilingual LM by plugging foreign language specific parameters to the pre-trained English LM (Figure FIGREF7)  The new model has two separate embedding layers and output layers, one for English and one for foreign language  The encoder layer in between is shared  We then fine-tune this model using English and foreign monolingual data  Here, we keep tuning the model on English to ensure that it does not forget what it has learned in English and that we can use the resulting model for zero-shot transfer (§SECREF3)

ground_truth: Using DSC loss improves the F1 score by +0.58 for MRPC and +0.73 for QQP

+0.58

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 tasks are used for evaluation?
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 $:
Context 3:  In this step, the encoder parameters are also updated so that in can learn syntactic aspects (i e , word order, morphological agreement) of the target languages 
Zero-shot Experiments
We build our bilingual LMs, named RAMEN, starting from BERT$_{\textsc {base}}$, BERT$_{\textsc {large}}$, RoBERTa$_{\textsc {base}}$, and RoBERTa$_{\textsc {large}}$ pre-trained models  Using BERT$_{\textsc {base}}$ allows us to compare the results with mBERT model  Using BERT$_{\textsc {large}}$ and RoBERTa allows us to investigate whether the performance of the target LM correlates with the performance of the source LM  We evaluate our models on two cross-lingual zero-shot tasks: (1) Cross-lingual Natural Language Inference (XNLI) and (2) dependency parsing 
Zero-shot Experiments ::: Data
We evaluate our approach for six target languages: French (fr), Russian (ru), Arabic (ar), Chinese (zh), Hindi (hi), and Vietnamese (vi)  These languages belong to four different language families  French, Russian, and Hindi are Indo-European languages, similar to English  Arabic, Chinese, and Vietnamese belong to Afro-Asiatic, Sino-Tibetan, and Austro-Asiatic family respectively  The choice of the six languages also reflects different training conditions depending on the amount of monolingual data  French and Russian, and Arabic can be regarded as high resource languages whereas Hindi has far less data and can be considered as low resource 
For experiments that use parallel data to initialize foreign specific parameters, we use the same datasets in the work of BIBREF6  Specifically, we use United Nations Parallel Corpus BIBREF18 for en-ru, en-ar, en-zh, and en-fr  We collect en-hi parallel data from IIT Bombay corpus BIBREF19 and en-vi data from OpenSubtitles 2018  For experiments that use only monolingual data to initialize foreign parameters, instead of training word-vectors from the scratch, we use the pre-trained word vectors from fastText BIBREF14 to estimate word translation probabilities (Eq  DISPLAY_FORM13)  We align these vectors into a common space using orthogonal Procrustes BIBREF20, BIBREF15, BIBREF16  We only use identical words between the two languages as the supervised signal  We use WikiExtractor to extract extract raw sentences from Wikipedias as monolingual data for fine-tuning target embeddings and bilingual LMs (§SECREF15)  We do not lowercase or remove accents in our data preprocessing pipeline 
We tokenize English using the provided tokenizer from pre-trained models  For target languages, we use fastBPE to learn 30,000 BPE codes and 50,000 codes when transferring from BERT and RoBERTa respectively  We truncate the BPE vocabulary of foreign languages to match the size of the English vocabulary in the source models  Precisely, the size of foreign vocabulary is set to 32,000 when transferring from BERT and 50,000 when transferring from RoBERTa 
We use XNLI dataset BIBREF9 for classification task and Universal Dependencies v2 4 BIBREF21 for parsing task  Since a language might have more than one treebank in Universal Dependencies, we use the following treebanks: en_ewt (English), fr_gsd (French), ru_syntagrus (Russian) ar_padt (Arabic), vi_vtb (Vietnamese), hi_hdtb (Hindi), and zh_gsd (Chinese) 
Zero-shot Experiments ::: Data ::: Remark on BPE
BIBREF22 show that sharing subwords between languages improves alignments between embedding spaces  BIBREF2 observe a strong correlation between the percentage of overlapping subwords and mBERT's performances for cross-lingual zero-shot transfer  However, in our current approach, subwords between source and target are not shared  A subword that is in both English and foreign vocabulary has two different embeddings 
Zero-shot Experiments ::: Estimating translation probabilities
Since pre-trained models operate on subword level, we need to estimate subword translation probabilities  Therefore, we subsample 2M sentence pairs from each parallel corpus and tokenize the data into subwords before running fast-align BIBREF13 
Estimating subword translation probabilities from aligned word vectors requires an additional processing step since the provided vectors from fastText are not at subword level  We use the following approximation to obtain subword vectors: the vector $_s$ of subword $s$ is the weighted average of all the aligned word vectors $_{w_i}$ that have $s$ as an subword
where $p(w_j)$ is the unigram probability of word $w_j$ and $n_s = \sum _{w_j:\, s\in w_j} p(w_j)$  We take the top 50,000 words in each aligned word-vectors to compute subword vectors 
In both cases, not all the words in the foreign vocabulary can be initialized from the English word-embeddings  Those words are initialized randomly from a Gaussian $\mathcal {N}(0, {1}{d^2})$ 
Zero-shot Experiments ::: Hyper-parameters
In all the experiments, we tune RAMEN$_{\textsc {base}}$ for 175,000 updates and RAMEN$_{\textsc {large}}$ for 275,000 updates where the first 25,000 updates are for language specific parameters  The sequence length is set to 256  The mini-batch size are 64 and 24 when tuning language specific parameters using RAMEN$_{\textsc {base}}$ and RAMEN$_{\textsc {large}}$ respectively  For tuning bilingual LMs, we use a mini-batch size of 64 for RAMEN$_{\textsc {base}}$ and 24 for RAMEN$_{\textsc {large}}$ where half of the batch are English sequences and the other half are foreign sequences  This strategy of balancing mini-batch has been used in multilingual neural machine translation BIBREF23, BIBREF24 
We optimize RAMEN$_{\textsc {base}}$ using Lookahead optimizer BIBREF25 wrapped around Adam with the learning rate of $10^{-4}$, the number of fast weight updates $k=5$, and interpolation parameter $\alpha =0 5$  We choose Lookahead optimizer because it has been shown to be robust to the initial parameters of the based optimizer (Adam)  For Adam optimizer, we linearly increase the learning rate from $10^{-7}$ to $10^{-4}$ in the first 4000 updates and then follow an inverse square root decay  All RAMEN$_{\textsc {large}}$ models are optimized with Adam due to memory limit 
When fine-tuning RAMEN on XNLI and UD, we use a mini-batch size of 32, Adam's learning rate of $10^{-5}$  The number of epochs are set to 4 and 50 for XNLI and UD tasks respectively  All experiments are carried out on a single Tesla V100 16GB GPU  Each RAMEN$_{\textsc {base}}$ model is trained within a day and each RAMEN$_{\textsc {large}}$ is trained within two days 
Results
In this section, we present the results of out models for two zero-shot cross lingual transfer tasks: XNLI and dependency parsing 
Results ::: Cross-lingual Natural Language Inference
Table TABREF32 shows the XNLI test accuracy  For reference, we also include the scores from the previous work, notably the state-of-the-art system XLM BIBREF6  Before discussing the results, we spell out that the fairest comparison in this experiment is the comparison between mBERT and RAMEN$_{\textsc {base}}$+BERT trained with monolingual only 
We first discuss the transfer results from BERT  Initialized from fastText vectors, RAMEN$_{\textsc {base}}$ slightly outperforms mBERT by 1 9 points on average and widen the gap of 3 3 points on Arabic  RAMEN$_{\textsc {base}}$ gains extra 0 8 points on average when initialized from parallel data  With triple number of parameters, RAMEN$_{\textsc {large}}$ offers an additional boost in term of accuracy and initialization with parallel data consistently improves the performance  It has been shown that BERT$_{\textsc {large}}$ significantly outperforms BERT$_{\textsc {base}}$ on 11 English NLP tasks BIBREF0, the strength of BERT$_{\textsc {large}}$ also shows up when adapted to foreign languages 
Transferring from RoBERTa leads to better zero-shot accuracies

ground_truth: four machine translation tasks: German -> English, Japanese -> English, Romanian -> English, English -> German

 four machine translation tasks, IWSLT 2017 German $\rightarrow $ English BIBREF27, KFTT Japanese $\rightarrow $ English BIBREF28, WMT 2016 Romanian $\rightarrow $ English BIBREF29, WMT 2014 English $\rightarrow $ German BIBREF30

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 metrics are used for evaluation?
Context 3:  With the same initializing condition, RAMEN$_{\textsc {base}}$+RoBERTa outperforms RAMEN$_{\textsc {base}}$+BERT on average by 2 9 and 2 3 points when initializing from monolingual and parallel data respectively  This result show that with similar number of parameters, our approach benefits from a better English pre-trained model  When transferring from RoBERTa$_{\textsc {large}}$, we obtain state-of-the-art results for five languages 
Currently, RAMEN only uses parallel data to initialize foreign embeddings  RAMEN can also exploit parallel data through translation objective proposed in XLM  We believe that by utilizing parallel data during the fine-tuning of RAMEN would bring additional benefits for zero-shot tasks  We leave this exploration to future work  In summary, starting from BERT$_{\textsc {base}}$, our approach obtains competitive bilingual LMs with mBERT for zero-shot XNLI  Our approach shows the accuracy gains when adapting from a better pre-trained model 
Results ::: Universal Dependency Parsing
We build on top of RAMEN a graph-based dependency parser BIBREF27  For the purpose of evaluating the contextual representations learned by our model, we do not use part-of-speech tags  Contextualized representations are directly fed into Deep-Biaffine layers to predict arc and label scores  Table TABREF34 presents the Labeled Attachment Scores (LAS) for zero-shot dependency parsing 
We first look at the fairest comparison between mBERT and monolingually initialized RAMEN$_{\textsc {base}}$+BERT  The latter outperforms the former on five languages except Arabic  We observe the largest gain of +5 2 LAS for French  Chinese enjoys +3 1 LAS from our approach  With similar architecture (12 or 24 layers) and initialization (using monolingual or parallel data), RAMEN+RoBERTa performs better than RAMEN+BERT for most of the languages  Arabic and Hindi benefit the most from bigger models  For the other four languages, RAMEN$_{\textsc {large}}$ renders a modest improvement over RAMEN$_{\textsc {base}}$ 
Analysis ::: Impact of initialization
Initializing foreign embeddings is the backbone of our approach  A good initialization leads to better zero-shot transfer results and enables fast adaptation  To verify the importance of a good initialization, we train a RAMEN$_{\textsc {base}}$+RoBERTa with foreign word-embeddings are initialized randomly from $\mathcal {N}(0, {1}{d^2})$  For a fair comparison, we use the same hyper-parameters in §SECREF27  Table TABREF36 shows the results of XNLI and UD parsing of random initialization  In comparison to the initialization using aligned fastText vectors, random initialization decreases the zero-shot performance of RAMEN$_{\textsc {base}}$ by 15 9% for XNLI and 27 8 points for UD parsing on average  We also see that zero-shot parsing of SOV languages (Arabic and Hindi) suffers random initialization 
Analysis ::: Are contextual representations from RAMEN also good for supervised parsing?
All the RAMEN models are built from English and tuned on English for zero-shot cross-lingual tasks  It is reasonable to expect RAMENs do well in those tasks as we have shown in our experiments  But are they also a good feature extractor for supervised tasks? We offer a partial answer to this question by evaluating our model for supervised dependency parsing on UD datasets 
We used train/dev/test splits provided in UD to train and evaluate our RAMEN-based parser  Table TABREF38 summarizes the results (LAS) of our supervised parser  For a fair comparison, we choose mBERT as the baseline and all the RAMEN models are initialized from aligned fastText vectors  With the same architecture of 12 Transformer layers, RAMEN$_{\textsc {base}}$+BERT performs competitive to mBERT and outshines mBERT by +1 2 points for Vietnamese  The best LAS results are obtained by RAMEN$_{\textsc {large}}$+RoBERTa with 24 Transformer layers  Overall, our results indicate the potential of using contextual representations from RAMEN for supervised tasks 
Analysis ::: How does linguistic knowledge transfer happen through each training stages?
We evaluate the performance of RAMEN+RoBERTa$_{\textsc {base}}$ (initialized from monolingual data) at each training steps: initialization of word embeddings (0K update), fine-tuning target embeddings (25K), and fine-tuning the model on both English and target language (at each 25K updates)  The results are presented in Figure FIGREF40 
Without fine-tuning, the average accuracy of XLNI is 39 7% for a three-ways classification task, and the average LAS score is 3 6 for dependency parsing  We see the biggest leap in the performance after 50K updates  While semantic similarity task profits significantly at 25K updates of the target embeddings, syntactic task benefits with further fine-tuning the encoder  This is expected since the target languages might exhibit different syntactic structures than English and fine-tuning encoder helps to capture language specific structures  We observe a substantial gain of 19-30 LAS for all languages except French after 50K updates 
Language similarities have more impact on transferring syntax than semantics  Without tuning the English encoder, French enjoys 50 3 LAS for being closely related to English, whereas Arabic and Hindi, SOV languages, modestly reach 4 2 and 6 4 points using the SVO encoder  Although Chinese has SVO order, it is often seen as head-final while English is strong head-initial  Perhaps, this explains the poor performance for Chinese 
Limitations
While we have successfully adapted autoencoding pre-trained LMs from English to other languages, the question whether our approach can also be applied for autoregressive LM such as XLNet still remains  We leave the investigation to future work 
Conclusions
In this work, we have presented a simple and effective approach for rapidly building a bilingual LM under a limited computational budget  Using BERT as the starting point, we demonstrate that our approach produces better than mBERT on two cross-lingual zero-shot sentence classification and dependency parsing  We find that the performance of our bilingual LM, RAMEN, correlates with the performance of the original pre-trained English models  We also find that RAMEN is also a powerful feature extractor in supervised dependency parsing  Finally, we hope that our work sparks of interest in developing fast and effective methods for transferring pre-trained English models to other languages 

ground_truth: translation probabilities, Labeled Attachment Scores (LAS)

accuracy, Labeled Attachment Scores (LAS)