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. Ngrams of which length are aligned using PARENT?
Context 1: Introduction
The task of generating natural language descriptions of structured data (such as tables) BIBREF2 , BIBREF3 , BIBREF4 has seen a growth in interest with the rise of sequence to sequence models that provide an easy way of encoding tables and generating text from them BIBREF0 , BIBREF1 , BIBREF5 , BIBREF6  
For text generation tasks, the only gold standard metric is to show the output to humans for judging its quality, but this is too expensive to apply repeatedly anytime small modifications are made to a system  Hence, automatic metrics that compare the generated text to one or more reference texts are routinely used to compare models BIBREF7   For table-to-text generation, automatic evaluation has largely relied on BLEU BIBREF8 and ROUGE BIBREF9   The underlying assumption behind these metrics is that the reference text is gold-standard, i e , it is the ideal target text that a system should generate  In practice, however, when datasets are collected automatically and heuristically, the reference texts are often not ideal  Figure FIGREF2 shows an example from the WikiBio dataset BIBREF0   Here the reference contains extra information which no system can be expected to produce given only the associated table  We call such reference texts divergent from the table 
We show that existing automatic metrics, including BLEU, correlate poorly with human judgments when the evaluation sets contain divergent references (§ SECREF36 )  For many table-to-text generation tasks, the tables themselves are in a pseudo-natural language format (e g , WikiBio, WebNLG BIBREF6 , and E2E-NLG BIBREF10 )  In such cases we propose to compare the generated text to the underlying table as well to improve evaluation  We develop a new metric, PARENT (Precision And Recall of Entailed N-grams from the Table) (§ SECREF3 )  When computing precision, PARENT effectively uses a union of the reference and the table, to reward correct information missing from the reference  When computing recall, it uses an intersection of the reference and the table, to ignore extra incorrect information in the reference  The union and intersection are computed with the help of an entailment model to decide if a text n-gram is entailed by the table  We show that this method is more effective than using the table as an additional reference  Our main contributions are:
Table-to-Text Generation
We briefly review the task of generating natural language descriptions of semi-structured data, which we refer to as tables henceforth BIBREF11 , BIBREF12   Tables can be expressed as set of records INLINEFORM0 , where each record is a tuple (entity, attribute, value)  When all the records are about the same entity, we can truncate the records to (attribute, value) pairs  For example, for the table in Figure FIGREF2 , the records are {(Birth Name, Michael Dahlquist), (Born, December 22 1965),    }  The task is to generate a text INLINEFORM1 which summarizes the records in a fluent and grammatical manner  For training and evaluation we further assume that we have a reference description INLINEFORM2 available for each table  We let INLINEFORM3 denote an evaluation set of tables, references and texts generated from a model INLINEFORM4 , and INLINEFORM5 , INLINEFORM6 denote the collection of n-grams of order INLINEFORM7 in INLINEFORM8 and INLINEFORM9 , respectively  We use INLINEFORM10 to denote the count of n-gram INLINEFORM11 in INLINEFORM12 , and INLINEFORM13 to denote the minimum of its counts in INLINEFORM14 and INLINEFORM15   Our goal is to assign a score to the model, which correlates highly with human judgments of the quality of that model 
PARENT
PARENT evaluates each instance INLINEFORM0 separately, by computing the precision and recall of INLINEFORM1 against both INLINEFORM2 and INLINEFORM3  
Evaluation via Information Extraction
BIBREF1 proposed to use an auxiliary model, trained to extract structured records from text, for evaluation  However, the extraction model presented in that work is limited to the closed-domain setting of basketball game tables and summaries  In particular, they assume that each table has exactly the same set of attributes for each entity, and that the entities can be identified in the text via string matching  These assumptions are not valid for the open-domain WikiBio dataset, and hence we train our own extraction model to replicate their evaluation scheme 
Our extraction system is a pointer-generator network BIBREF19 , which learns to produce a linearized version of the table from the text  The network learns which attributes need to be populated in the output table, along with their values  It is trained on the training set of WikiBio  At test time we parsed the output strings into a set of (attribute, value) tuples and compare it to the ground truth table  The F-score of this text-to-table system was INLINEFORM0 , which is comparable to other challenging open-domain settings BIBREF20   More details are included in the Appendix SECREF52  
Given this information extraction system, we consider the following metrics for evaluation, along the lines of BIBREF1   Content Selection (CS): F-score for the (attribute, value) pairs extracted from the generated text compared to those extracted from the reference  Relation Generation (RG): Precision for the (attribute, value) pairs extracted from the generated text compared to those in the ground truth table  RG-F: Since our task emphasizes the recall of information from the table as well, we consider another variant which computes the F-score of the extracted pairs to those in the table  We omit the content ordering metric, since our extraction system does not align records to the input text 
Experiments & Results
In this section we compare several automatic evaluation metrics by checking their correlation with the scores assigned by humans to table-to-text models  Specifically, given INLINEFORM0 models INLINEFORM1 , and their outputs on an evaluation set, we show these generated texts to humans to judge their quality, and obtain aggregated human evaluation scores for all the models, INLINEFORM2 (§ SECREF33 )  Next, to evaluate an automatic metric, we compute the scores it assigns to each model, INLINEFORM3 , and check the Pearson correlation between INLINEFORM4 and INLINEFORM5 BIBREF21  
Data & Models
Our main experiments are on the WikiBio dataset BIBREF0 , which is automatically constructed and contains many divergent references  In § SECREF47 we also present results on the data released as part of the WebNLG challenge 
We developed several models of varying quality for generating text from the tables in WikiBio  This gives us a diverse set of outputs to evaluate the automatic metrics on  Table TABREF32 lists the models along with their hyperparameter settings and their scores from the human evaluation (§ SECREF33 )  Our focus is primarily on neural sequence-to-sequence methods since these are most widely used, but we also include a template-based baseline  All neural models were trained on the WikiBio training set  Training details and sample outputs are included in Appendices SECREF56 & SECREF57  
We divide these models into two categories and measure correlation separately for both the categories  The first category, WikiBio-Systems, includes one model each from the four families listed in Table TABREF32   This category tests whether a metric can be used to compare different model families with a large variation in the quality of their outputs  The second category, WikiBio-Hyperparams, includes 13 different hyperparameter settings of PG-Net BIBREF19 , which was the best performing system overall  9 of these were obtained by varying the beam size and length normalization penalty of the decoder network BIBREF23 , and the remaining 4 were obtained by re-scoring beams of size 8 with the information extraction model described in § SECREF4   All the models in this category produce high quality fluent texts, and differ primarily on the quantity and accuracy of the information they express  Here we are testing whether a metric can be used to compare similar systems with a small variation in performance  This is an important use-case as metrics are often used to tune hyperparameters of a model 
Human Evaluation
We collected human judgments on the quality of the 16 models trained for WikiBio, plus the reference texts  Workers on a crowd-sourcing platform, proficient in English, were shown a table with pairs of generated texts, or a generated text and the reference, and asked to select the one they prefer  Figure FIGREF34 shows the instructions they were given  Paired comparisons have been shown to be superior to rating scales for comparing generated texts BIBREF24   However, for measuring correlation the comparisons need to be aggregated into real-valued scores, INLINEFORM0 , for each of the INLINEFORM1 models  For this, we use Thurstone's method BIBREF22 , which assigns a score to each model based on how many times it was preferred over an alternative 
The data collection was performed separately for models in the WikiBio-Systems and WikiBio-Hyperparams categories  1100 tables were sampled from the development set, and for each table we got 8 different sentence pairs annotated across the two categories, resulting in a total of 8800 pairwise comparisons  Each pair was judged by one worker only which means there may be noise at the instance-level, but the aggregated system-level scores had low variance (cf  Table TABREF32 )  In total around 500 different workers were involved in the annotation  References were also included in the evaluation, and they received a lower score than PG-Net, highlighting the divergence in WikiBio 
Compared Metrics
Text only: We compare BLEU BIBREF8 , ROUGE BIBREF9 , METEOR BIBREF18 , CIDEr and CIDEr-D BIBREF25 using their publicly available implementations 
Information Extraction based: We compare the CS, RG and RG-F metrics discussed in § SECREF4  
Text & Table: We compare a variant of BLEU, denoted as BLEU-T, where the values from the table are used as additional references  BLEU-T draws inspiration from iBLEU BIBREF26 but instead rewards n-grams which match the table rather than penalizing them  For PARENT, we compare both the word-overlap model (PARENT-W) and the co-occurrence model (PARENT-C) for determining entailment  We also compare versions where a single INLINEFORM0 is tuned on the entire dataset to maximize correlation with human judgments, denoted as PARENT*-W/C 
Correlation Comparison
We use bootstrap sampling (500 iterations) over the 1100 tables for which we collected human annotations to get an idea of how the correlation of each metric varies with the underlying data  In each iteration, we sample with replacement, tables along with their references and all the generated texts for that table  Then we compute aggregated human evaluation and metric scores for each of the models and compute the correlation between the two  We report the average correlation across all bootstrap samples for each metric in Table TABREF37   The distribution of correlations for the best performing metrics are shown in Figure FIGREF38  
Table TABREF37 also indicates whether PARENT is significantly better than a baseline metric  BIBREF21 suggest using the William's test for this purpose, but since we are computing correlations between only 4/13 systems at a time, this test has very weak power in our case  Hence, we use the bootstrap samples to obtain a INLINEFORM0 confidence interval of the difference in correlation between PARENT and any other metric and check whether this is above 0 BIBREF27  
Correlations are higher for the systems category than the hyperparams category  The latter is a more difficult setting since very similar models are compared, and hence the variance of the correlations is also high  Commonly used metrics which only rely on the reference (BLEU, ROUGE, METEOR, CIDEr) have only weak correlations with human judgments  In the hyperparams category, these are often negative, implying that tuning models based on these may lead to selecting worse models  BLEU performs the best among these, and adding n-grams from the table as references improves this further (BLEU-T) 
Among the extractive evaluation metrics, CS, which also only relies on the reference, has poor correlation in the hyperparams category  RG-F, and both variants of the PARENT metric achieve the highest correlation for both settings  There is no significant difference among these for the hyperparams category, but for systems, PARENT-W is significantly better than the other two  While RG-F needs a full information extraction pipeline in its implementation, PARENT-C only relies on co-occurrence counts, and PARENT-W can be used out-of-the-box for any dataset  To our knowledge, this is the first rigorous evaluation of using information extraction for generation evaluation 
On this dataset, the word-overlap model showed higher correlation than the co-occurrence model for entailment  In § SECREF47 we will show that for the WebNLG dataset, where more paraphrasing is involved between the table and text, the opposite is true  Lastly, we note that the heuristic for selecting INLINEFORM0 is sufficient to produce high correlations for PARENT, however, if human annotations are available, this can be tuned to produce significantly higher correlations (PARENT*-W/C) 
Analysis
In this section we further analyze the performance of PARENT-W under different conditions, and compare to the other best metrics from Table TABREF37  
To study the correlation as we vary the number of divergent references, we also collected binary labels from workers for whether a reference is entailed by the corresponding table  We define a reference as entailed when it mentions only information which can be inferred from the table  Each table and reference pair was judged by 3 independent workers, and we used the majority vote as the label for that pair  Overall, only INLINEFORM0 of the references were labeled as entailed by the table  Fleiss' INLINEFORM1 was INLINEFORM2 , which indicates a fair agreement  We found the workers sometimes disagreed on what information can be reasonably entailed by the table 
Figure FIGREF40 shows the correlations as we vary the percent of entailed examples in the evaluation set of WikiBio  Each point is obtained by fixing the desired proportion of entailed examples, and sampling subsets from the full set which satisfy this proportion  PARENT and RG-F remain stable and show a high correlation across the entire range, whereas BLEU and BLEU-T vary a lot  In the hyperparams category, the latter two have the worst correlation when the evaluation set contains only entailed examples, which may seem surprising  However, on closer examination we found that this subset tends to omit a lot of information from the tables  Systems which produce more information than these references are penalized by BLEU, but not in the human evaluation  PARENT overcomes this issue by measuring recall against the table in addition to the reference 
We check how different components in the computation of PARENT contribute to its correlation to human judgments  Specifically, we remove the probability INLINEFORM0 of an n-gram INLINEFORM1 being entailed by the table from Eqs  EQREF19 and EQREF23   The average correlation for PARENT-W drops to INLINEFORM5 in this case  We also try a variant of PARENT with INLINEFORM6 , which removes the contribution of Table Recall (Eq  EQREF22 )  The average correlation is INLINEFORM7 in this case  With these components, the correlation is INLINEFORM8 , showing that they are crucial to the performance of PARENT 
BIBREF28 point out that hill-climbing on an automatic metric is meaningless if that metric has a low instance-level correlation to human judgments  In Table TABREF46 we show the average accuracy of the metrics in making the same judgments as humans between pairs of generated texts  Both variants of PARENT are significantly better than the other metrics, however the best accuracy is only INLINEFORM0 for the binary task  This is a challenging task, since there are typically only subtle differences between the texts  Achieving higher instance-level accuracies will require more sophisticated language understanding models for evaluation 
WebNLG Dataset
To check how PARENT correlates with human judgments when the references are elicited from humans (and less likely to be divergent), we check its correlation with the human ratings provided for the systems competing in the WebNLG challenge BIBREF6   The task is to generate text describing 1-5 RDF triples (e g  John E Blaha, birthPlace, San Antonio), and human ratings were collected for the outputs of 9 participating systems on 223 instances  These systems include a mix of pipelined, statistical and neural methods  Each instance has upto 3 reference texts associated with the RDF triples, which we use for evaluation 
The human ratings were collected on 3 distinct aspects – grammaticality, fluency and semantics, where semantics corresponds to the degree to which a generated text agrees with the meaning of the underlying RDF triples  We report the correlation of several metrics with these ratings in Table TABREF48   Both variants of PARENT are either competitive or better than the other metrics in terms of the average correlation to all three aspects  This shows that PARENT is applicable for high quality references as well 
While BLEU has the highest correlation for the grammar and fluency aspects, PARENT does best for semantics  This suggests that the inclusion of source tables into the evaluation orients the metric more towards measuring the fidelity of the content of the generation  A similar trend is seen comparing BLEU and BLEU-T  As modern neural text generation systems are typically very fluent, measuring their fidelity is of increasing importance  Between the two entailment models, PARENT-C is better due to its higher correlation with the grammaticality and fluency aspects 
The INLINEFORM0 parameter in the calculation of PARENT decides whether to compute recall against the table or the reference (Eq  EQREF22 )  Figure FIGREF50 shows the distribution of the values taken by INLINEFORM1 using the heuristic described in § SECREF3 for instances in both WikiBio and WebNLG  For WikiBio, the recall of the references against the table is generally low, and hence the recall of the generated text relies more on the table  For WebNLG, where the references are elicited from humans, this recall is much higher (often INLINEFORM2 ), and hence the recall of the generated text relies more on the reference 
Related Work
Over the years several studies have evaluated automatic metrics for measuring text generation performance BIBREF29 , BIBREF30 , BIBREF31 , BIBREF32 , BIBREF33 , BIBREF34 , BIBREF35   The only consensus from these studies seems to be that no single metric is suitable across all tasks  A recurring theme is that metrics like BLEU and NIST BIBREF36 are not suitable for judging content quality in NLG  Recently, BIBREF37 did a comprehensive study of several metrics on the outputs of state-of-the-art NLG systems, and found that while they showed acceptable correlation with human judgments at the system level, they failed to show any correlation at the sentence level  Ours is the first study which checks the quality of metrics when table-to-text references are divergent  We show that in this case even system level correlations can be unreliable 
Hallucination BIBREF38 , BIBREF39 refers to when an NLG system generates text which mentions extra information than what is present in the source from which it is generated  Divergence can be viewed as hallucination in the reference text itself  PARENT deals with hallucination by discounting n-grams which do not overlap with either the reference or the table 
PARENT draws inspiration from iBLEU BIBREF26 , a metric for evaluating paraphrase generation, which compares the generated text to both the source text and the reference  While iBLEU penalizes texts which match the source, here we reward such texts since our task values accuracy of generated text more than the need for paraphrasing the tabular content BIBREF40   Similar to SARI for text simplification BIBREF41 and Q-BLEU for question generation BIBREF42 , PARENT falls under the category of task-specific metrics 
Conclusions
We study the automatic evaluation of table-to-text systems when the references diverge from the table  We propose a new metric, PARENT, which shows the highest correlation with humans across a range of settings with divergent references in WikiBio  We also perform the first empirical evaluation of information extraction based metrics BIBREF1 , and find RG-F to be effective  Lastly, we show that PARENT is comparable to the best existing metrics when references are elicited by humans on the WebNLG data 
Acknowledgements
Bhuwan Dhingra is supported by a fellowship from Siemens, and by grants from Google  We thank Maruan Al-Shedivat, Ian Tenney, Tom Kwiatkowski, Michael Collins, Slav Petrov, Jason Baldridge, David Reitter and other members of the Google AI Language team for helpful discussions and suggestions  We thank Sam Wiseman for sharing data for an earlier version of this paper  We also thank the anonymous reviewers for their feedback 
Information Extraction System
For evaluation via information extraction BIBREF1 we train a model for WikiBio which accepts text as input and generates a table as the output  Tables in WikiBio are open-domain, without any fixed schema for which attributes may be present or absent in an instance  Hence we employ the Pointer-Generator Network (PG-Net) BIBREF19 for this purpose  Specifically, we use a sequence-to-sequence model, whose encoder and decoder are both single-layer bi-directional LSTMs  The decoder is augmented with an attention mechanism over the states of the encoder  Further, it also uses a copy mechanism to optionally copy tokens directly from the source text  We do not use the coverage mechanism of BIBREF19 since that is specific to the task of summarization they study  The decoder is trained to produce a linearized version of the table where the rows and columns are flattened into a sequence, and separate by special tokens  Figure FIGREF53 shows an example 
Clearly, since the references are divergent, the model cannot be expected to produce the entire table, and we see some false information being hallucinated after training  Nevertheless, as we show in § SECREF36 , this system can be used for evaluating generated texts  After training, we can parse the output sequence along the special tokens INLINEFORM0 R INLINEFORM1 and INLINEFORM2 C INLINEFORM3 to get a set of (attribute, value) pairs  Table TABREF54 shows the precision, recall and F-score of these extracted pairs against the ground truth tables, where the attributes and values are compared using an exact string match 
Hyperparameters
After tuning we found the same set of hyperparameters to work well for both the table-to-text PG-Net, and the inverse information extraction PG-Net  The hidden state size of the biLSTMs was set to 200  The input and output vocabularies were set to 50000 most common words in the corpus, with additional special symbols for table attribute names (such as “birth-date”)  The embeddings of the tokens in the vocabulary were initialized with Glove BIBREF43   Learning rate of INLINEFORM0 was used during training, with the Adam optimizer, and a dropout of INLINEFORM1 was also applied to the outputs of the biLSTM  Models were trained till the loss on the dev set stopped dropping  Maximum length of a decoded text was set to 40 tokens, and that of the tables was set to 120 tokens  Various beam sizes and length normalization penalties were applied for the table-to-text system, which are listed in the main paper  For the information extraction system, we found a beam size of 8 and no length penalty to produce the highest F-score on the dev set 
Sample Outputs
Table TABREF55 shows some sample references and the corresponding predictions from the best performing model, PG-Net for WikiBio 
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: Unanswerable

Answer with content missing: (Parent subsections) combine precisions for n-gram orders 1-4

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 4: Introduction
Deep Learning approaches have achieved impressive results on various NLP tasks BIBREF0 , BIBREF1 , BIBREF2 and have become the de facto approach for any NLP task  However, these deep learning techniques have found to be less effective for low-resource languages when the available training data is very less BIBREF3   Recently, several approaches like Multi-task learning BIBREF4 , multilingual learning BIBREF5 , semi-supervised learning BIBREF2 , BIBREF6 and transfer learning BIBREF7 , BIBREF3 have been explored by the deep learning community to overcome data sparsity in low-resource languages  Transfer learning trains a model for a parent task and fine-tunes the learned parent model weights (features) for a related child task BIBREF7 , BIBREF8   This effectively reduces the requirement on training data for the child task as the model would have learned relevant features from the parent task data thereby, improving the performance on the child task 
Transfer learning has also been explored in the multilingual Neural Machine Translation BIBREF3 , BIBREF9 , BIBREF10   The goal is to improve the NMT performance on the source to target language pair (child task) using an assisting source language (assisting to target translation is the parent task)  Here, the parent model is trained on the assisting and target language parallel corpus and the trained weights are used to initialize the child model  The child model can now be fine-tuned on the source-target language pairs, if parallel corpus is available  The divergence between the source and the assisting language can adversely impact the benefits obtained from transfer learning  Multiple studies have shown that transfer learning works best when the languages are related BIBREF3 , BIBREF10 , BIBREF9   Several studies have tried to address lexical divergence between the source and the target languages BIBREF10 , BIBREF11 , BIBREF12   However, the effect of word order divergence and its mitigation has not been explored  In a practical setting, it is not uncommon to have source and assisting languages with different word order  For instance, it is possible to find parallel corpora between English and some Indian languages, but very little parallel corpora between Indian languages  Hence, it is natural to use English as an assisting language for inter-Indian language translation 
To see how word order divergence can be detrimental, let us consider the case of the standard RNN (Bi-LSTM) encoder-attention-decoder architecture BIBREF13   The encoder generates contextual representations (annotation vectors) for each source word, which are used by the attention network to match the source words to the current decoder state  The contextual representation is word-order dependent  Hence, if the assisting and the source languages do not have similar word order the generated contextual representations will not be consistent  The attention network (and hence the decoder) sees different contextual representations for similar words in parallel sentences across different languages  This makes it difficult to transfer knowledge learned from the assisting language to the source language 
We illustrate this by visualizing the contextual representations generated by the encoder of an English to Hindi NMT system for two versions of the English input: (a) original word order (SVO) (b) word order of the source language (SOV, for Bengali)  Figure FIGREF1 shows that the encoder representations obtained are very different  The attention network and the decoder now have to work with very different representations  Note that the plot below does not take into account further lexical and other divergences between source and assisting languages, since we demonstrated word order divergence with the same language on the source side 
To address this word order divergence, we propose to pre-order the assisting language sentences to match the word order of the source language  We consider an extremely resource constrained scenario, where we do not have any parallel corpus for the child task  We are limited to a bilingual dictionary for transfer information from the assisting to the source language  From our experiments, we show that there is a significant increase in the translation accuracy for the unseen source-target language pair 
Addressing Lexical Divergence
BIBREF3 explored transfer learning for NMT on low-resource languages  They studied the influence of language divergence between languages chosen for training the parent and child model, and showed that choosing similar languages for training the parent and child model leads to better improvements from transfer learning  A limitation of BIBREF3 approach is that they ignore the lexical similarity between languages and also the source language embeddings are randomly initialized  BIBREF10 , BIBREF11 , BIBREF12 take advantage of lexical similarity between languages in their work  BIBREF10 proposed to use Byte-Pair Encoding (BPE) to represent the sentences in both the parent and the child language to overcome the above limitation  They show using BPE benefits transfer learning especially when the involved languages are closely-related agglutinative languages  Similarly, BIBREF11 utilize lexical similarity between the source and assisting languages by training a character-level NMT system  BIBREF12 address lexical divergence by using bilingual embeddings and mixture of universal token embeddings  One of the languages' vocabulary, usually English vocabulary is considered as universal tokens and every word in the other languages is represented as a mixture of universal tokens  They show results on extremely low-resource languages 
Addressing Word Order Divergence
To the best of our knowledge, no work has addressed word order divergence in transfer learning for multilingual NMT  However, some work exists for other NLP tasks that could potentially address word order  For Named Entity Recognition (NER), BIBREF14 use a self-attention layer after the Bi-LSTM layer to address word-order divergence for Named Entity Recognition (NER) task  The approach does not show any significant improvements over multiple languages  A possible reason is that the divergence has to be addressed before/during construction of the contextual embeddings in the Bi-LSTM layer, and the subsequent self-attention layer does not address word-order divergence  BIBREF15 use adversarial training for cross-lingual question-question similarity ranking in community question answering  The adversarial training tries to force the encoder representations of similar sentences from different input languages to have similar representations 
Use of Pre-ordering
Pre-ordering the source language sentences to match the target language word order has been useful in addressing word-order divergence for Phrase-Based SMT BIBREF16 , BIBREF17 , BIBREF18 , BIBREF19   Recently, BIBREF20 proposed a way to measure and reduce the divergence between the source and target languages based on morphological and syntactic properties, also termed as anisomorphism  They demonstrated that by reducing the anisomorphism between the source and target languages, consistent improvements in NMT performance were obtained  The NMT system used additional features like word forms, POS tags and dependency relations in addition to parallel corpora  On the other hand, BIBREF21 observed a drop in performance due to pre-ordering for NMT  Unlike BIBREF20 , the NMT system was trained on pre-ordered sentences and no additional features were provided to the system  Note that all these works address source-target divergence, not divergence between source languages in multilingual NMT 
Proposed Solution
Consider the task of translating from an extremely low-resource language (source) to a target language  The parallel corpus between the two languages if available may be too small to train a NMT model  Similar to existing works BIBREF3 , BIBREF10 , BIBREF12 , we use transfer learning to overcome data sparsity and train a NMT model between the source and the target languages

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 are the existing approaches?
Context 3: Introduction
Users of photo-sharing websites such as Flickr often provide short textual descriptions in the form of tags to help others find the images  With the availability of GPS systems in current electronic devices such as smartphones, latitude and longitude coordinates are nowadays commonly made available as well  The tags associated with such georeferenced photos often describe the location where these photos were taken, and Flickr can thus be regarded as a source of environmental information  The use of Flickr for modelling urban environments has already received considerable attention  For instance, various approaches have been proposed for modelling urban regions BIBREF0 , and for identifying points-of-interest BIBREF1 and itineraries BIBREF2 , BIBREF3   However, the usefulness of Flickr for characterizing the natural environment, which is the focus of this paper, is less well-understood 
Many recent studies have highlighted that Flickr tags capture valuable ecological information, which can be used as a complementary source to more traditional sources  To date, however, ecologists have mostly used social media to conduct manual evaluations of image content with little automated exploitation of the associated tags BIBREF4 , BIBREF5 , BIBREF6   One recent exception is BIBREF7 , where bag-of-words representations derived from Flickr tags were found to give promising result for predicting a range of different environemental phenomena 
Our main hypothesis in this paper is that by using vector space embeddings instead of bag-of-words representations, the ecological information which is implicitly captured by Flickr tags can be utilized in a more effective way  Vector space embeddings are representations in which the objects from a given domain are encoded using relatively low-dimensional vectors  They have proven useful in natural language processing, especially for encoding word meaning BIBREF8 , BIBREF9 , and in machine learning more generally  In this paper, we are interested in the use of such representations for modelling geographic locations  Our main motivation for using vector space embeddings is that they allow us to integrate the textual information we get from Flickr with available structured information in a very natural way  To this end, we rely on an adaptation of the GloVe word embedding model BIBREF9 , but rather than learning word vectors, we learn vectors representing locations  Similar to how the representation of a word in GloVe is determined by the context words surrounding it, the representation of a location in our model is determined by the tags of the photos that have been taken near that location  To incorporate numerical features from structured environmental datasets (e g  average temperature), we associate with each such feature a linear mapping that can be used to predict that feature from a given location vector  This is inspired by the fact that salient properties of a given domain can often be modelled as directions in vector space embeddings BIBREF10 , BIBREF11 , BIBREF12   Finally, evidence from categorical datasets (e g  land cover types) is taken into account by requiring that locations belonging to the same category are represented using similar vectors, similar to how semantic types are sometimes modelled in the context of knowledge graph embedding BIBREF13  
While our point-of-departure is a standard word embedding model, we found that the off-the-shelf GloVe model performed surprisingly poorly, meaning that a number of modifications are needed to achieve good results  Our main findings are as follows  First, given that the number of tags associated with a given location can be quite small, it is important to apply some kind of spatial smoothing, i e  the importance of a given tag for a given location should not only depend on the occurrences of the tag at that location, but also on its occurrences at nearby locations  To this end, we use a formulation which is based on spatially smoothed version of pointwise mutual information  Second, given the wide diversity in the kind of information that is covered by Flickr tags, we find that term selection is in some cases critical to obtain vector spaces that capture the relevant aspects of geographic locations  For instance, many tags on Flickr refer to photography related terms, which we would normally not want to affect the vector representation of a given location  Finally, even with these modifications, vector space embeddings learned from Flickr tags alone are sometimes outperformed by bag-of-words representations  However, our vector space embeddings lead to substantially better predictions in cases where structured (scientific) information is also taken into account  In this sense, the main value of using vector space embeddings in this context is not so much about abstracting away from specific tag usages, but rather about the fact that such representations allow us to integrate numerical and categorical features in a much more natural way than is possible with bag-of-words representations 
The remainder of this paper is organized as follows  In the next section, we provide a discussion of existing work  Section SECREF3 then presents our model for embedding geographic locations from Flickr tags and structured data  Next, in Section SECREF4 we provide a detailed discussion about the experimental results  Finally, Section SECREF5 summarizes our conclusions 
Vector space embeddings
The use of low-dimensional vector space embeddings for representing objects has already proven effective in a large number of applications, including natural language processing (NLP), image processing, and pattern recognition  In the context of NLP, the most prominent example is that of word embeddings, which represent word meaning using vectors of typically around 300 dimensions  A large number of different methods for learning such word embeddings have already been proposed, including Skip-gram and the Continuous Bag-of-Words (CBOW) model BIBREF8 , GloVe BIBREF9 , and fastText BIBREF14   They have been applied effectively in many downstream NLP tasks such as sentiment analysis BIBREF15 , part of speech tagging BIBREF16 , BIBREF17 , and text classification BIBREF18 , BIBREF19   The model we consider in this paper builds on GloVe, which was designed to capture linear regularities of word-word co-occurrence  In GloVe, there are two word vectors INLINEFORM0 and INLINEFORM1 for each word in the vocabulary, which are learned by minimizing the following objective: DISPLAYFORM0
where INLINEFORM0 is the number of times that word INLINEFORM1 appears in the context of word INLINEFORM2 , INLINEFORM3 is the vocabulary size, INLINEFORM4 is the target word bias, INLINEFORM5 is the context word bias  The weighting function INLINEFORM6 is used to limit the impact of rare terms  It is defined as 1 if INLINEFORM7 and as INLINEFORM8 otherwise, where INLINEFORM9 is usually fixed to 100 and INLINEFORM10 to 0 75  Intuitively, the target word vectors INLINEFORM11 correspond to the actual word representations which we would like to find, while the context word vectors INLINEFORM12 model how occurrences of INLINEFORM13 in the context of a given word INLINEFORM14 affect the representation of this latter word  In this paper we will use a similar model, which will however be aimed at learning location vectors instead of the target word vectors 
Beyond word embeddings, various methods have been proposed for learning vector space representations from structured data such as knowledge graphs BIBREF20 , BIBREF21 , BIBREF22 , social networks BIBREF23 , BIBREF24 and taxonomies BIBREF25 , BIBREF26   The idea of combining a word embedding model with structured information has also been explored by several authors, for example to improve the word embeddings based on information coming from knowledge graphs BIBREF27 , BIBREF28   Along similar lines, various lexicons have been used to obtain word embeddings that are better suited at modelling sentiment BIBREF15 and antonymy BIBREF29 , among others  The method proposed by BIBREF30 imposes the condition that words that belong to the same semantic category are closer together than words from different categories, which is somewhat similar in spirit to how we will model categorical datasets in our model 
Embeddings for geographic information
The problem of representing geographic locations using embeddings has also attracted some attention  An early example is BIBREF31 , which used principal component analysis and stacked autoencoders to learn low-dimensional vector representations of city neighbourhoods based on census data  They use these representations to predict attributes such as crime, which is not included in the given census data, and find that in most of the considered evaluation tasks, the low-dimensional vector representations lead to more faithful predictions than the original high-dimensional census data 
Some existing works combine word embedding models with geographic coordinates  For example, in BIBREF32 an approach is proposed to learn word embeddings based on the assumption that words which tend to be used in the same geographic locations are likely to be similar  Note that their aim is dual to our aim in this paper: while they use geographic location to learn word vectors, we use textual descriptions to learn vectors representing geographic locations 
Several methods also use word embedding models to learn representations of Points-of-Interest (POIs) that can be used for predicting user visits BIBREF33 , BIBREF34 , BIBREF35   These works use the machinery of existing word embedding models to learn POI representations, intuitively by letting sequences of POI visits by a user play the role of sequences of words in a sentence  In other words, despite the use of word embedding models, many of these approaches do not actually consider any textual information  For example, in BIBREF34 the Skip-gram model is utilized to create a global pattern of users' POIs  Each location was treated as a word and the other locations visited before or after were treated as context words  They then use a pair-wise ranking loss BIBREF36 which takes into account the user's location visit frequency to personalize the location recommendations  The methods of BIBREF34 were extended in BIBREF35 to use a temporal embedding and to take more account of geographic context, in particular the distances between preferred and non-preferred neighboring POIs, to create a “geographically hierarchical pairwise preference ranking model”  Similarly, in BIBREF37 the CBOW model was trained with POI data  They ordered POIs spatially within the traffic-based zones of urban areas  The ordering was used to generate characteristic vectors of POI types  Zone vectors represented by averaging the vectors of the POIs contained in them, were then used as features to predict land use types  In the CrossMap method BIBREF38 they learned embeddings for spatio-temporal hotspots obtained from social media data of locations, times and text  In one form of embedding, intended to enable reconstruction of records, neighbourhood relations in space and time were encoded by averaging hotspots in a target location's spatial and temporal neighborhoods  They also proposed a graph-based embedding method with nodes of location, time and text  The concatenation of the location, time and text vectors were then used as features to predict peoples' activities in urban environments  Finally, in BIBREF39 , a method is proposed that uses the Skip-gram model to represent POI types, based on the intuition that the vector representing a given POI type should be predictive of the POI types that found near places of that type 
Our work is different from these studies, as our focus is on representing locations based on a given text description of that location (in the form of Flickr tags), along with numerical and categorical features from scientific datasets 
Analyzing Flickr tags
Many studies have focused on analyzing Flickr tags to extract useful information in domains such as linguistics BIBREF40 , geography BIBREF0 , BIBREF41 , and ecology BIBREF42 , BIBREF7 , BIBREF43   Most closely related to our work, BIBREF7 found that the tags of georeferenced Flickr photos can effectively supplement traditional scientific environmental data in tasks such as predicting climate features, land cover, species occurrence, and human assessments of scenicness  To encode locations, they simply combine a bag-of-words representation of geographically nearby tags with a feature vector that encodes associated structured scientific data  They found that the predictive value of Flickr tags is roughly on a par with that of the scientific datasets, and that combining both types of information leads to significantly better results than using either of them alone  As we show in this paper, however, their straightforward way of combining both information sources, by concatenating the two types of feature vectors, is far from optimal 
Despite the proven importance of Flickr tags, the problem of embedding Flickr tags has so far received very limited attention  To the best of our knowledge, BIBREF44 is the only work that generated embeddings for Flickr tags  However, their focus was on learning embeddings that capture word meaning (being evaluated on word similarity tasks), whereas we use such embeddings as part of our method for representing locations 
Model Description
In this section, we introduce our embedding model, which combines Flickr tags and structured scientific information to represent a set of locations INLINEFORM0   The proposed model has the following form: DISPLAYFORM0
where INLINEFORM0 and INLINEFORM1 are parameters to control the importance of each component in the model  Component INLINEFORM2 will be used to constrain the representation of the locations based on their textual description (i e  Flickr tags), INLINEFORM3 will be used to constrain the representation of the locations based on their numerical features, and INLINEFORM4 will impose the constraint that locations belonging to the same category should be close together in the space  We will discuss each of these components in more detail in the following sections 
Tag Based Location Embedding
Many of the tags associated with Flickr photos describe characteristics of the places where these photos were taken BIBREF45 , BIBREF46 , BIBREF47   For example, tags may correspond to place names (e g  Brussels, England, Scandinavia), landmarks (e g  Eiffel Tower, Empire State Building) or land cover types (e g  mountain, forest, beach)  To allow us to build location models using such tags, we collected the tags and meta-data of 70 million Flickr photos with coordinates in Europe (which is the region our experiments will focus on), all of which were uploaded to Flickr before the end of September 2015  In this section we first explain how tags can be weighted to obtain bag-of-words representations of locations from Flickr  Subsequently we describe a tag selection method, which will allow us to specialize the embedding depending on which aspects of the considered locations are of interest, after which we discuss the actual embedding model 
Tag weighting  Let INLINEFORM0 be a set of geographic locations, each characterized by latitude and longitude coordinates  To generate a bag-of-words representation of a given location, we have to weight the relevance of each tag to that location  To this end, we have followed the weighting scheme from BIBREF7 , which combines a Gaussian kernel (to model spatial proximity) with Positive Pointwise Mutual Information (PPMI) BIBREF48 , BIBREF49  
Let us write INLINEFORM0 for the set of users who have assigned tag INLINEFORM1 to a photo with coordinates near INLINEFORM2   To assess how relevant INLINEFORM3 is to the location INLINEFORM4 , the number of times INLINEFORM5 occurs in photos near INLINEFORM6 is clearly an important criterion  However, rather than simply counting the number of occurrences within some fixed radius, we use a Gaussian kernel to weight the tag occurrences according to their distance from that location: INLINEFORM7
where the threshold INLINEFORM0 is assumed to be fixed, INLINEFORM1 is the location of a Flickr photo, INLINEFORM2 is the Haversine distance, and we will assume that the bandwidth parameter INLINEFORM3 is set to INLINEFORM4   A tag occurrence is counted only once for all photos by the same user at the same location, which is important to reduce the impact of bulk uploading  The value INLINEFORM5 reflects how frequent tag INLINEFORM6 is near location INLINEFORM7 , but it does not yet take into account the total number of tag occurrences near INLINEFORM8 , nor how popular the tag INLINEFORM9 is overall  To measure how strongly tag INLINEFORM10 is associated with location INLINEFORM11 , we use PPMI, which is a commonly used measure of association in natural language processing  However, rather than estimating PPMI scores from term frequencies, we will use the INLINEFORM12 values instead: INLINEFORM13
where: INLINEFORM0
with INLINEFORM0 the set of all tags, and INLINEFORM1 the set of locations 
Tag selection  Inspired by BIBREF50 , we use a term selection method in order to focus on the tags that are most important for the tasks that we want to consider and reduce the impact of tags that might relate only to a given individual or a group of users  In particular, we obtained good results with a method based on Kullback-Leibler (KL) divergence, which is based on BIBREF51   Let INLINEFORM0 be a set of (mutually exclusive) properties of locations in which we are interested (e g  land cover categories)  For the ease of presentation, we will identify INLINEFORM1 with the set of locations that have the corresponding property  Then, we select tags from INLINEFORM2 that maximize the following score: INLINEFORM3
where INLINEFORM0 is the probability that a photo with tag INLINEFORM1 has a location near INLINEFORM2 and INLINEFORM3 is the probability that an arbitrary tag occurrence is assigned to a photo near a location in INLINEFORM4   Since INLINEFORM5 often has to be estimated from a small number of tag occurrences, it is estimated using Bayesian smoothing: INLINEFORM6
where INLINEFORM0 is a parameter controlling the amount of smoothing, which will be tuned in the experiments  On the other hand, for INLINEFORM1 we can simply use a maximum likelihood estimation: INLINEFORM2
Location embedding  We now want to find a vector INLINEFORM0 for each location INLINEFORM1 such that similar locations are represented using similar vectors  To achieve this, we use a close variant of the GloVe model, where tag occurrences are treated as context words of geographic locations  In particular, with each location INLINEFORM2 we associate a vector INLINEFORM3 and with each tag INLINEFORM4 we associate a vector INLINEFORM5 and a bias term INLINEFORM6 , and consider the following objective (which in our full model ( EQREF7 ) will be combined with components that are derived from the structured information): INLINEFORM7
Note how tags play the role of the context words in the GloVe model, while instead of learning target word vectors we now learn location vectors  In contrast to GloVe, our objective does not directly refer to co-occurrence statistics, but instead uses the INLINEFORM0 scores  One important consequence of this is that we can also consider pairs INLINEFORM1 for which INLINEFORM2 does not occur in INLINEFORM3 at all; such pairs are usually called negative examples  While they cannot be used in the standard GloVe model, some authors have already reported that introducing negative examples in variants of GloVe can lead to an improvement BIBREF52   In practice, evaluating the full objective above would not be computationally feasible, as we may need to consider millions of locations and millions of tags  Therefore, rather than considering all tags in INLINEFORM4 for the inner summation, we only consider those tags that appear at least once near location INLINEFORM5 together with a sample of negative examples 
Structured Environmental Data
There is a wide variety of structured data that can be used to describe locations  In this work, we have restricted ourselves to the same datasets as BIBREF7   These include nine (real-valued) numerical features, which are latitude, longitude, elevation, population, and five climate related features (avg  temperature, avg  precipitation, avg  solar radiation, avg  wind speed, and avg  water vapor pressure)  In addition, 180 categorical features were used, which are CORINE land cover classes at level 1 (5 classes), level 2 (15 classes) and level 3 (44 classes) and 116 soil types (SoilGrids)  Note that each location should belong to exactly 4 categories: one CORINE class at each of the three levels and a soil type 
Numerical features  Numerical features can be treated similarly to the tag occurrences, i e  we will assume that the value of a given numerical feature can be predicted from the location vectors using a linear mapping  In particular, for each numerical feature INLINEFORM0 we consider a vector INLINEFORM1 and a bias term INLINEFORM2 , and the following objective: INLINEFORM3
where we write INLINEFORM0 for set of all numerical features and INLINEFORM1 is the value of feature INLINEFORM2 for location INLINEFORM3 , after z-score normalization 
Categorical features  To take into account the categorical features, we impose the constraint that locations belonging to the same category should be close together in the space  To formalize this, we represent each category type INLINEFORM0 as a vector INLINEFORM1 , and consider the following objective: INLINEFORM2
Evaluation Tasks
We will use the method from BIBREF7 as our main baseline  This will allow us to directly evaluate the effectiveness of embeddings for the considered problem, since we have used the same structured datasets and same tag weighting scheme  For this reason, we will also follow their evaluation methodology  In particular, we will consider three evaluation tasks:
Predicting the distribution of 100 species across Europe, using the European network of nature protected sites Natura 2000 dataset as ground truth  For each of these species, a binary classification problem is considered  The set of locations INLINEFORM0 is defined as the 26,425 distinct sites occurring in the dataset 
Predicting soil type, again each time treating the task as a binary classification problem, using the same set of locations INLINEFORM0 as in the species distribution experiments  For these experiments, none of the soil type features are used for generating the embeddings 
Predicting CORINE land cover classes at levels 1, 2 and level 3, each time treating the task as a binary classification problem, using the same set of locations INLINEFORM0 as in the species distribution experiments  For these experiments, none of the CORINE features are used for generating the embeddings 
In addition, we will also consider the following regression tasks:
Predicting 5 climate related features: the average precipitation, temperature, solar radiation, water vapor pressure, and wind speed  We again use the same set of locations INLINEFORM0 as for species distribution in this experiment  None of the climate features is used for constructing the embeddings for this experiment 
Predicting people's subjective opinions of landscape beauty in Britain, using the crowdsourced dataset from the ScenicOrNot website as ground truth  The set INLINEFORM0 is chosen as the set of locations of 191 605 rated locations from the ScenicOrNot dataset for which at least one georeferenced Flickr photo exists within a 1 km radius 
Experimental Setup
In all experiments, we use Support Vector Machines (SVMs) for classification problems and Support Vector Regression (SVR) for regression problems to make predictions from our representations of geographic locations  In both cases, we used the SVM INLINEFORM0 implementation BIBREF53   For each experiment, the set of locations INLINEFORM1 was split into two-thirds for training, one-sixth for testing, and one-sixth for tuning the parameters  All embedding models are learned with Adagrad using 30 iterations  The number of dimensions is chosen for each experiment from INLINEFORM2 based on the tuning data  For the parameters of our model in Equation EQREF7 , we considered values of INLINEFORM3 from {0 1, 0 01, 0 001, 0 0001} and values of INLINEFORM4 from {1, 10, 100, 1000, 10 000, 100 000}  To compute KL divergence, we need to determine a set of classes INLINEFORM5 for each experiment  For classification problems, we can simply consider the given categories, but for the regression problems we need to define such classes by discretizing the numerical values  For the scenicness experiments, we considered scores 3 and 7 as cut-off points, leading to three classes (i e  less than 3, between 3 and 7, and above 7)  Similarly, for each climate related features, we consider two cut-off values for discretization: 5 and 15 for average temperature, 50 and 100 for average precipitation, 10 000 and 17 000 for average solar radiation, 0 7 and 1 for average water vapor pressure, and 3 and 5 for wind speed  The smoothing parameter INLINEFORM6 was selected among INLINEFORM7 based on the tuning data  In all experiments where term selection is used, we select the top 100 000 tags  We fixed the radius INLINEFORM8 at 1km when counting the number of tag occurrences  Finally, we set the number of negative examples as 10 times the number of positive examples for each location, but with a cap at 1000 negative examples in each region for computational reasons  We tune all parameters with respect to the F1 score for the classification tasks, and Spearman INLINEFORM9 for the regression tasks 
Variants and Baseline Methods
We will refer to our model as EGEL (Embedding GEographic Locations), and will consider the following variants  EGEL-Tags only uses the information from the Flickr tags (i e  component INLINEFORM0 ), without using any negative examples and without feature selection  EGEL-Tags+NS is similar to EGEL-Tags but with the addition of negative examples  EGEL-KL(Tags+NS) additionally considers term selection  EGEL-All is our full method, i e  it additionally uses the structured information  We also consider the following baselines  BOW-Tags represents locations using a bag-of-words representation, using the same tag weighting as the embedding model  BOW-KL(Tags) uses the same representation but after term selection, using the same KL-based method as the embedding model  BOW-All combines the bag-of-words representation with the structured information, encoded as proposed in BIBREF7   GloVe uses the objective from the original GloVe model for learning location vectors, i e  this variant differs from EGEL-Tags in that instead of INLINEFORM1 we use the number of co-occurrences of tag INLINEFORM2 near location INLINEFORM3 , measured as INLINEFORM4  
Results and Discussion
We present our results for the binary classification tasks in Tables TABREF23 – TABREF24 in terms of average precision, average recall and macro average F1 score  The results of the regression tasks are reported in Tables TABREF25 and TABREF29 in terms of the mean absolute error between the predicted and actual scores, as well as the Spearman INLINEFORM0 correlation between the rankings induced by both sets of scores  It can be clearly seen from the results that our proposed method (EGEL-All) can effectively integrate Flickr tags with the available structured information  It outperforms the baselines for all the considered tasks  Furthermore, note that the PPMI-based weighting in EGEL-Tags consistently outperforms GloVe and that both the addition of negative examples and term selection lead to further improvements  The use of term selection leads to particularly substantial improvements for the regression problems 
While our experimental results confirm the usefulness of embeddings for predicting environmental features, this is only consistently the case for the variants that use both the tags and the structured datasets  In particular, comparing BOW-Tags with EGEL-Tags, we sometimes see that the former achieves the best results  While this might seem surprising, it is in accordance with the findings in BIBREF54 , BIBREF38 , among others, where it was also found that bag-of-words representations can sometimes lead to surprisingly effective baselines  Interestingly, we note that in all cases where EGEL-KL(Tags+NS) performs worse than BOW-Tags, we also find that BOW-KL(Tags) performs worse than BOW-Tags  This suggests that for these tasks there is a very large variation in the kind of tags that can inform the prediction model, possibly including e g  user-specific tags  Some of the information captured by such highly specific but rare tags is likely to be lost in the embedding 
To further analyze the difference in performance between BoW representations and embeddings, Figure TABREF29 compares the performance of the GloVe model with the bag-of-words model for predicting place scenicness, as a function of the number of tag occurrences at the considered locations  What is clearly noticeable in Figure TABREF29 is that GloVe performs better than the bag-of-words model for large corpora and worse for smaller corpora  This issue has been alleviated in our embedding method by the addition of negative examples 
 Conclusions
In this paper, we have proposed a model to learn geographic location embeddings using Flickr tags, numerical environmental features, and categorical information  The experimental results show that our model can integrate Flickr tags with structured information in a more effective way than existing methods, leading to substantial improvements over baseline methods on various prediction tasks about the natural environment 
Acknowledgments
Shelan Jeawak has been sponsored by HCED Iraq  Steven Schockaert has been supported by ERC Starting Grant 637277 

ground_truth: BOW-Tags, BOW-KL(Tags), BOW-All, GloVe