Introduction
Neural machine translation (NMT) has gained a lot of attention recently due to its substantial improvements in machine translation quality achieving state-of-the-art performance for several languages BIBREF0 , BIBREF1 , BIBREF2 . The core architecture of neural machine translation models is based on the general encoder-decoder approach BIBREF3 . Neural machine translation is an end-to-end approach that learns to encode source sentences into distributed representations and decode these representations into sentences in the target language. Among the different neural MT models, attentional NMT BIBREF4 , BIBREF5 has become popular due to its capability to use the most relevant parts of the source sentence at each translation step. This capability also makes the attentional model superior in translating longer sentences BIBREF4 , BIBREF5 .
Figure FIGREF1 shows an example of how attention uses the most relevant source words to generate a target word at each step of the translation. In this paper we focus on studying the relevance of the attended parts, especially cases where attention is `smeared out' over multiple source words where their relevance is not entirely obvious, see, e.g., “would" and “like" in Figure FIGREF1 . Here, we ask whether these are due to errors of the attention mechanism or are a desired behavior of the model.
Since the introduction of attention models in neural machine translation BIBREF4 various modifications have been proposed BIBREF5 , BIBREF6 , BIBREF7 . However, to the best of our knowledge there is no study that provides an analysis of what kind of phenomena is being captured by attention. There are some works that have looked to attention as being similar to traditional word alignment BIBREF8 , BIBREF6 , BIBREF7 , BIBREF9 . Some of these approaches also experimented with training the attention model using traditional alignments BIBREF8 , BIBREF7 , BIBREF9 . liu-EtAl:2016:COLING have shown that attention could be seen as a reordering model as well as an alignment model.
In this paper, we focus on investigating the differences between attention and alignment and what is being captured by the attention mechanism in general. The questions that we are aiming to answer include: Is the attention model only capable of modelling alignment? And how similar is attention to alignment in different syntactic phenomena?
Our analysis shows that attention models traditional alignment in some cases more closely while it captures information beyond alignment in others. For instance, attention agrees with traditional alignments to a high degree in the case of nouns. However, it captures other information rather than only the translational equivalent in the case of verbs.
This paper makes the following contributions: 1) We provide a detailed comparison of attention in NMT and word alignment. 2) We show that while different attention mechanisms can lead to different degrees of compliance with respect to word alignments, global compliance is not always helpful for word prediction. 3) We show that attention follows different patterns depending on the type of the word being generated. 4) We demonstrate that attention does not always comply with alignment. We provide evidence showing that the difference between attention and alignment is due to attention model capability to attend the context words influencing the current word translation.
Related Work
liu-EtAl:2016:COLING investigate how training the attention model in a supervised manner can benefit machine translation quality. To this end they use traditional alignments obtained by running automatic alignment tools (GIZA++ BIBREF10 and fast_align BIBREF11 ) on the training data and feed it as ground truth to the attention network. They report some improvements in translation quality arguing that the attention model has learned to better align source and target words. The approach of training attention using traditional alignments has also been proposed by others BIBREF9 , BIBREF8 . chen2016guided show that guided attention with traditional alignment helps in the domain of e-commerce data which includes lots of out of vocabulary (OOV) product names and placeholders, but not much in the other domains. alkhouli-EtAl:2016:WMT have separated the alignment model and translation model, reasoning that this avoids propagation of errors from one model to the other as well as providing more flexibility in the model types and training of the models. They use a feed-forward neural network as their alignment model that learns to model jumps in the source side using HMM/IBM alignments obtained by using GIZA++.
shi-padhi-knight:2016:EMNLP2016 show that various kinds of syntactic information are being learned and encoded in the output hidden states of the encoder. The neural system for their experimental analysis is not an attentional model and they argue that attention does not have any impact for learning syntactic information. However, performing the same analysis for morphological information, belinkov2017neural show that attention has also some effect on the information that the encoder of neural machine translation system encodes in its output hidden states. As part of their analysis they show that a neural machine translation system that has an attention model can learn the POS tags of the source side more efficiently than a system without attention.
Recently, koehn2017six carried out a brief analysis of how much attention and alignment match in different languages by measuring the probability mass that attention gives to alignments obtained from an automatic alignment tool. They also report differences based on the most attended words.
The mixed results reported by chen2016guided, alkhouli-EtAl:2016:WMT, liu-EtAl:2016:COLING on optimizing attention with respect to alignments motivates a more thorough analysis of attention models in NMT.
Attention Models
This section provides a short background on attention and discusses two most popular attention models which are also used in this paper. The first model is a non-recurrent attention model which is equivalent to the “global attention" method proposed by DBLPjournalscorrLuongPM15. The second attention model that we use in our investigation is an input-feeding model similar to the attention model first proposed by bahdanau-EtAl:2015:ICLR and turned to a more general one and called input-feeding by DBLPjournalscorrLuongPM15. Below we describe the details of both models.
Both non-recurrent and input-feeding models compute a context vector INLINEFORM0 at each time step. Subsequently, they concatenate the context vector to the hidden state of decoder and pass it through a non-linearity before it is fed into the softmax output layer of the translation network. DISPLAYFORM0
The difference of the two models lays in the way they compute the context vector. In the non-recurrent model, the hidden state of the decoder is compared to each hidden state of the encoder. Often, this comparison is realized as the dot product of vectors. Then the comparison result is fed to a softmax layer to compute the attention weight. DISPLAYFORM0 DISPLAYFORM1
Here INLINEFORM0 is the hidden state of the decoder at time INLINEFORM1 , INLINEFORM2 is INLINEFORM3 th hidden state of the encoder and INLINEFORM4 is the length of the source sentence. Then the computed alignment weights are used to compute a weighted sum over the encoder hidden states which results in the context vector mentioned above: DISPLAYFORM0
The input-feeding model changes the context vector computation in a way that at each step INLINEFORM0 the context vector is aware of the previously computed context INLINEFORM1 . To this end, the input-feeding model feeds back its own INLINEFORM2 to the network and uses the resulting hidden state instead of the context-independent INLINEFORM3 , to compare to the hidden states of the encoder. This is defined in the following equations: DISPLAYFORM0 DISPLAYFORM1
Here, INLINEFORM0 is the function that the stacked LSTM applies to the input, INLINEFORM1 is the last generated target word, and INLINEFORM2 is the output of previous time step of the input-feeding network itself, meaning the output of Equation EQREF2 in the case that context vector has been computed using INLINEFORM3 from Equation EQREF7 .
Comparing Attention with Alignment
As mentioned above, it is a commonly held assumption that attention corresponds to word alignments. To verify this, we investigate whether higher consistency between attention and alignment leads to better translations.
Measuring Attention-Alignment Accuracy
In order to compare attentions of multiple systems as well as to measure the difference between attention and word alignment, we convert the hard word alignments into soft ones and use cross entropy between attention and soft alignment as a loss function. For this purpose, we use manual alignments provided by RWTH German-English dataset as the hard alignments. The statistics of the data are given in Table TABREF8 . We convert the hard alignments to soft alignments using Equation EQREF10 . For unaligned words, we first assume that they have been aligned to all the words in the source side and then do the conversion. DISPLAYFORM0
Here INLINEFORM0 is the set of source words aligned to target word INLINEFORM1 and INLINEFORM2 is the number of source words in the set.
After conversion of the hard alignments to soft ones, we compute the attention loss as follows: DISPLAYFORM0
Here INLINEFORM0 is the source sentence and INLINEFORM1 is the weight of the alignment link between source word INLINEFORM2 and the target word (see Equation EQREF10 ). INLINEFORM3 is the attention weight INLINEFORM4 (see Equation EQREF4 ) of the source word INLINEFORM5 , when generating the target word INLINEFORM6 .
In our analysis, we also look into the relation between translation quality and the quality of the attention with respect to the alignments. For measuring the quality of attention, we use the attention loss defined in Equation EQREF11 . As a measure of translation quality, we choose the loss between the output of our NMT system and the reference translation at each translation step, which we call word prediction loss. The word prediction loss for word INLINEFORM0 is logarithm of the probability given in Equation EQREF12 . DISPLAYFORM0
Here INLINEFORM0 is the source sentence, INLINEFORM1 is target word at time step INLINEFORM2 , INLINEFORM3 is the target history given by the reference translation and INLINEFORM4 is given by Equation EQREF2 for either non-recurrent or input-feeding attention models.
Spearman's rank correlation is used to compute the correlation between attention loss and word prediction loss: DISPLAYFORM0
where INLINEFORM0 and INLINEFORM1 are the ranks of the attention losses and word prediction losses, respectively, INLINEFORM2 is the covariance between two input variables, and INLINEFORM3 and INLINEFORM4 are the standard deviations of INLINEFORM5 and INLINEFORM6 .
If there is a close relationship between word prediction quality and consistency of attention versus alignment, then there should be high correlation between word prediction loss and attention loss. Figure FIGREF13 shows an example with different levels of consistency between attention and word alignments. For the target words “will" and “come" the attention is not focused on the manually aligned word but distributed between the aligned word and other words. The focus of this paper is examining cases where attention does not follow alignment, answering the questions whether those cases represent errors or desirable behavior of the attention model.
Measuring Attention Concentration
As another informative variable in our analysis, we look into the attention concentration. While most word alignments only involve one or a few words, attention can be distributed more freely. We measure the concentration of attention by computing the entropy of the attention distribution: DISPLAYFORM0
Empirical Analysis of Attention Behaviour
We conduct our analysis using the two different attention models described in Section SECREF3 . Our first attention model is the global model without input-feeding as introduced by DBLPjournalscorrLuongPM15. The second model is the input-feeding model BIBREF5 , which uses recurrent attention. Our NMT system is a unidirectional encoder-decoder system as described in BIBREF5 , using 4 recurrent layers.
We trained the systems with dimension size of 1,000 and batch size of 80 for 20 epochs. The vocabulary for both source and target side is set to be the 30K most common words. The learning rate is set to be 1 and a maximum gradient norm of 5 has been used. We also use a dropout rate of 0.3 to avoid overfitting.
Impact of Attention Mechanism
We train both of the systems on the WMT15 German-to-English training data, see Table TABREF18 for some statistics. Table TABREF17 shows the BLEU scores BIBREF12 for both systems on different test sets.
Since we use POS tags and dependency roles in our analysis, both of which are based on words, we chose not to use BPE BIBREF13 which operates at the sub-word level.
We report alignment error rate (AER) BIBREF14 , which is commonly used to measure alignment quality, in Table TABREF20 to show the difference between attentions and human alignments provided by RWTH German-English dataset. To compute AER over attentions, we follow DBLPjournalscorrLuongPM15 to produce hard alignments from attentions by choosing the most attended source word for each target word. We also use GIZA++ BIBREF10 to produce automatic alignments over the data set to allow for a comparison between automatically generated alignments and the attentions generated by our systems. GIZA++ is run in both directions and alignments are symmetrized using the grow-diag-final-and refined alignment heuristic.
As shown in Table TABREF20 , the input-feeding system not only achieves a higher BLEU score, but also uses attentions that are closer to the human alignments.
Table TABREF21 compares input-feeding and non-recurrent attention in terms of attention loss computed using Equation EQREF11 . Here the losses between the attention produced by each system and the human alignments is reported. As expected, the difference in attention losses are in line with AER.
The difference between these comparisons is that AER only takes the most attended word into account while attention loss considers the entire attention distribution.
Alignment Quality Impact on Translation
Based on the results in Section SECREF19 , one might be inclined to conclude that the closer the attention is to the word alignments the better the translation. However, chen2016guided, liu-EtAl:2016:COLING, alkhouli-EtAl:2016:WMT report mixed results by optimizing their NMT system with respect to word prediction and alignment quality. These findings warrant a more fine-grained analysis of attention. To this end, we include POS tags in our analysis and study the patterns of attention based on POS tags of the target words. We choose POS tags because they exhibit some simple syntactic characteristics. We use the coarse grained universal POS tags BIBREF15 given in Table TABREF25 .
To better understand how attention accuracy affects translation quality, we analyse the relationship between attention loss and word prediction loss for individual part-of-speech classes. Figure FIGREF22 shows how attention loss differs when generating different POS tags. One can see that attention loss varies substantially across different POS tags. In particular, we focus on the cases of NOUN and VERB which are the most frequent POS tags in the dataset. As shown, the attention of NOUN is the closest to alignments on average. But the average attention loss for VERB is almost two times larger than the loss for NOUN.
Considering this difference and the observations in Section SECREF19 , a natural follow-up would be to focus on getting the attention of verbs to be closer to alignments. However, Figure FIGREF22 shows that the average word prediction loss for verbs is actually smaller compared to the loss for nouns. In other words, although the attention for verbs is substantially more inconsistent with the word alignments than for nouns, the NMT system translates verbs more accurately than nouns on average.
To formalize this relationship we compute Spearman's rank correlation between word prediction loss and attention loss, based on the POS tags of the target side, for the input-feeding model, see Figure FIGREF27 .
The low correlation for verbs confirms that attention to other parts of source sentence rather than the aligned word is necessary for translating verbs and that attention does not necessarily have to follow alignments. However, the higher correlation for nouns means that consistency of attention with alignments is more desirable. This could, in a way, explain the mixed result reported for training attention using alignments BIBREF9 , BIBREF7 , BIBREF8 . Especially the results by chen2016guided in which large improvements are achieved for the e-commerce domain which contains many OOV product names and placeholders, but no or very weak improvements were achieved over common domains.
Attention Concentration
In word alignment, most target words are aligned to one source word. The average number of source words aligned to nouns and verbs is 1.1 and 1.2 respectively. To investigate to what extent this also holds for attention we measure the attention concentration by computing the entropy of the attention distribution, see Equation EQREF16 .
Figure FIGREF28 shows the average entropy of attention based on POS tags. As shown, nouns have one of the lowest entropies meaning that on average the attention for nouns tends to be concentrated. This also explains the closeness of the attention to alignments for nouns. In addition, the correlation between attention entropy and attention loss in case of nouns is high as shown in Figure FIGREF28 . This means that attention entropy can be used as a measure of closeness of attention to alignment in the case of nouns.
The higher attention entropy for verbs, in Figure FIGREF28 , shows that the attention is more distributed compared to nouns. The low correlation between attention entropy and word prediction loss (see Figure FIGREF32 ) shows that attention concentration is not required when translating into verbs. This also confirms that the correct translation of verbs requires the systems to pay attention to different parts of the source sentence.
Another interesting observation here is the low correlation for pronouns (PRON) and particles (PRT), see Figure FIGREF32 . As can be seen in Figure FIGREF28 , these tags have more distributed attention comparing to nouns, for example. This could either mean that the attention model does not know where to focus or it deliberately pays attention to multiple, somehow relevant, places to be able to produce a better translation. The latter is supported by the relatively low word prediction losses, shown in the Figure FIGREF22 .
Attention Distribution
To further understand under which conditions attention is paid to words other than the aligned words, we study the distribution of attention over the source words. First, we measure how much attention is paid to the aligned words for each POS tag, on average. To this end, we compute the percentage of the probability mass that the attention model has assigned to aligned words for each POS tag, see Table TABREF35 .
One can notice that less than half of the attention is paid to alignment points for most of the POS tags. To examine how the rest of attention in each case has been distributed over the source sentence we measure the attention distribution over dependency roles in the source side. We first parse the source side of RWTH data using the ParZu parser BIBREF16 . Then we compute how the attention probability mass given to the words other than the alignment points, is distributed over dependency roles. Table TABREF33 gives the most attended roles for each POS tag. Here, we focus on POS tags discussed earlier. One can see that the most attended roles when translating to nouns include adjectives and determiners and in the case of translating to verbs, it includes auxiliary verbs, adverbs (including negation), subjects, and objects.
Conclusion
In this paper, we have studied attention in neural machine translation and provided an analysis of the relation between attention and word alignment. We have shown that attention agrees with traditional alignment to a certain extent. However, this differs substantially by attention mechanism and the type of the word being generated. We have shown that attention has different patterns based on the POS tag of the target word. The concentrated pattern of attention and the relatively high correlations for nouns show that training the attention with explicit alignment labels is useful for generating nouns. However, this is not the case for verbs, since the large portion of attention being paid to words other than alignment points, is already capturing other relevant information. Training attention with alignments in this case will force the attention model to forget these useful information. This explains the mixed results reported when guiding attention to comply with alignments BIBREF9 , BIBREF7 , BIBREF8 .
Acknowledgments
This research was funded in part by the Netherlands Organization for Scientific Research (NWO) under project numbers 639.022.213 and 612.001.218.

Question: What useful information does attention capture?
Answer: it captures other information rather than only the translational equivalent in the case of verbs

Alignment points of the POS tags.

Question: What datasets are used?
Answer: WMT15 German-to-English, RWTH German-English dataset

RWTH German-English dataset

Question: In what cases is attention different from alignment?
Answer: For certain POS tags, e.g. VERB, PRON.

most word alignments only involve one or a few words, attention can be distributed more freely