Published as a conference paper at ICLR 2020

## MULTILINGUAL ALIGNMENT OF CONTEXTUAL WORD REPRESENTATIONS


**Steven Cao, Nikita Kitaev & Dan Klein**
Computer Science Division
University of California, Berkeley
_{_ stevencao,kitaev,klein _}_ @berkeley.edu


ABSTRACT


We propose procedures for evaluating and strengthening contextual embedding
alignment and show that they are useful in analyzing and improving multilingual
BERT. In particular, after our proposed alignment procedure, BERT exhibits significantly improved zero-shot performance on XNLI compared to the base model,
remarkably matching pseudo-fully-supervised translate-train models for Bulgarian and Greek. Further, to measure the degree of alignment, we introduce a contextual version of word retrieval and show that it correlates well with downstream
zero-shot transfer. Using this word retrieval task, we also analyze BERT and
find that it exhibits systematic deficiencies, e.g. worse alignment for open-class
parts-of-speech and word pairs written in different scripts, that are corrected by
the alignment procedure. These results support contextual alignment as a useful
concept for understanding large multilingual pre-trained models.


1 INTRODUCTION


Figure 1: t-SNE (Maaten & Hinton, 2008) visualization of the embedding space of multilingual
BERT for English-German word pairs (left: pre-alignment, right: post-alignment). Each point is a
different instance of the word in the Europarl corpus. This figure suggests that BERT begins already
somewhat aligned out-of-the-box but becomes much more aligned after our proposed procedure.


Embedding alignment was originally studied for word vectors with the goal of enabling cross-lingual
transfer, where the embeddings for two languages are in alignment if word translations, e.g. _cat_ and
_Katze_, have similar representations (Mikolov et al., 2013a; Smith et al., 2017). Recently, large pretrained models have largely subsumed word vectors based on their accuracy on downstream tasks,
partly due to the fact that their word representations are context-dependent, allowing them to more
richly capture the meaning of a word (Peters et al., 2018; Howard & Ruder, 2018; Radford et al.,
2018; Devlin et al., 2018). Therefore, with the same goal of cross-lingual transfer but for these more
complex models, we might consider contextual embedding alignment, where we observe whether
word pairs within parallel sentences, e.g. _cat_ in _“The cat sits”_ and _Katze_ in _“Die Katze sitzt,”_ have
similar representations.


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Published as a conference paper at ICLR 2020


One model relevant to these questions is multilingual BERT, a version of BERT pre-trained on 104
languages that achieves remarkable transfer on downstream tasks. For example, after the model is
fine-tuned on the English MultiNLI training set, it achieves 74.3% accuracy on the test set in Spanish, which is only 7.1% lower than the English accuracy (Devlin et al., 2018; Conneau et al., 2018b).
Furthermore, while the model transfers better to languages similar to English, it still achieves reasonable accuracies even on languages with different scripts.


However, given the way that multilingual BERT was pre-trained, it is unclear why we should expect
such high zero-shot performance. Compared to monolingual BERT which exhibits no zero-shot
transfer, multilingual BERT differs only in that (1) during pre-training (i.e. masked word prediction),
each batch contains sentences from all of the languages, and (2) it uses a single shared vocabulary,
formed by WordPiece on the concatenated monolingual corpora (Devlin et al., 2019). Therefore,
we might wonder: (1) How can we better understand BERT’s multilingualism? (2) Can we further
improve BERT’s cross-lingual transfer?


In this paper, we show that contextual embedding alignment is a useful concept for addressing
these questions. First, we propose a contextual version of word retrieval to evaluate the degree
of alignment, where a model is presented with two parallel corpora, and given a word within a
sentence in one corpus, it must find the correct word and sentence in the other. Using this metric
of alignment, we show that multilingual BERT achieves zero-shot transfer because its embeddings
are partially aligned, as depicted in Figure 1, with the degree of alignment predicting the degree of
downstream transfer.


Next, using between 10K and 250K sentences per language from the Europarl corpus as parallel
data (Koehn, 2005), we propose a fine-tuning-based alignment procedure and show that it significantly improves BERT as a multilingual model. Specifically, on zero-shot XNLI, where the model
is trained on English MultiNLI and tested on other languages (Conneau et al., 2018b), the aligned
model improves accuracies by 2.78% on average over the base model, and it remarkably matches
translate-train models for Bulgarian and Greek, which approximate the fully-supervised setting.


To put our results in the context of past work, we also use word retrieval to compare our finetuning procedure to two alternatives: (1) fastText augmented with sentence and aligned using rotations (Bojanowski et al., 2017; R¨uckl´e et al., 2018; Artetxe et al., 2018), and (2) BERT aligned using
rotations (Aldarmaki & Diab, 2019; Schuster et al., 2019; Wang et al., 2019). We find that when
there are multiple occurences per word, fine-tuned BERT outperforms fastText, which outperforms
rotation-aligned BERT. This result supports the intuition that contextual alignment is more difficult
than its non-contextual counterpart, given that a rotation, at least when applied naively, is no longer
sufficient to produce strong alignments. In addition, when there is only one occurrence per word,
fine-tuned BERT matches the performance of fastText. Given that context disambiguation is no
longer necessary, this result suggests that our fine-tuning procedure is able to align BERT at the type
level to a degree that matches non-contextual approaches.


Finally, we use the contextual word retrieval task to conduct finer-grained analysis of multilingual
BERT, with the goal of better understanding its strengths and shortcomings. Specifically, we find
that base BERT has trouble aligning open-class compared to closed-class parts-of-speech, as well
as word pairs that have large differences in usage frequency, suggesting insight into the pre-training
procedure that we explore in Section 5. Together, these experiments support contextual alignment
as an important task that provides useful insight into large multilingual pre-trained models.


2 RELATED WORK


**Word vector alignment.** There has been a long line of works that learn aligned word vectors
from varying levels of supervision (Ruder et al., 2019). One popular family of methods starts with
word vectors learned independently for each language (using a method like skip-gram with negative
sampling (Mikolov et al., 2013b)), and it learns a mapping from source language vectors to target
language vectors with a bilingual dictionary as supervision (Mikolov et al., 2013a; Smith et al.,
2017; Artetxe et al., 2017). When the mapping is constrained to be an orthogonal linear transformation, the optimal mapping that minimizes distances between word pairs can be solved in closed
form (Artetxe et al., 2016; Schonemann, 1966). Alignment is evaluated using bilingual lexicon induction, so these papers also propose ways to mitigate the hubness problem in nearest neighbors,


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e.g. by using alternate similarity functions like CSLS (Conneau et al., 2018a). A recent set of works
has also shown that the mapping can be learned with minimal to no supervision by starting with
some minimal seed dictionary and alternating between learning the linear map and inducing the dictionary (Artetxe et al., 2018; Conneau et al., 2018a; Hoshen & Wolf, 2018; Xu et al., 2018; Chen &
Cardie, 2018).


**Incorporating context into alignment.** One key challenge in making alignment context aware is
that the embeddings are now different across multiple occurrences of the same word. Past papers
have handled this issue by removing context and aligning the “average sense” of a word. In one
such study, Schuster et al. (2019) learn a rotation to align contextual ELMo embeddings (Peters
et al., 2018) with the goal of improving zero-shot multilingual dependency parsing, and they handle
context by taking the average embedding for a word in all of its contexts. In another paper, Aldarmaki & Diab (2019) learn a rotation on sentence vectors, produced by taking the average word
vector over the sentence, and they show that the resulting alignment also works well for word-level
tasks. In a contemporaneous work, Wang et al. (2019) align not only the word but also the context
by learning a linear transformation using word-aligned parallel data to align multilingual BERT,
with the goal of improving zero-shot dependency parsing numbers. In this paper, we similarly align
not only the word but also the context, and we also depart from these past works by using more
expressive alignment methods than rotation.


**Incorporating parallel texts into pre-training.** Instead of performing alignment post-hoc, another line of works proposes contextual pre-training procedures that are more cross-lingually-aware.
Wieting et al. (2019) pre-train sentence embeddings using parallel texts by maximizing similarity between sentence pairs while minimizing similarity with negative examples. Lample & Conneau (2019) propose a cross-lingual pre-training objective that incorporates parallel data in addition to monolingual corpora, leading to improved downstream cross-lingual transfer. In contrast,
our method uses less parallel data and aligns existing pre-trained models rather than requiring pretraining from scratch.


**Analyzing multilingual BERT.** Pires et al. (2019) present a series of probing experiments to better
understand multilingual BERT, and they find that transfer is possible even between dissimilar languages, but that it works better between languages that are typologically similar. They conclude that
BERT is remarkably multilingual but falls short for certain language pairs.


3 METHODS


3.1 MULTILINGUAL PRE-TRAINING


We first briefly describe multilingual BERT (Devlin et al., 2018). Like monolingual BERT, multilingual BERT is pre-trained on sentences from Wikipedia to perform two tasks: masked word
prediction, where it must predict words that are masked within a sentence, and next sentence prediction, where it must predict whether the second sentence follows the first one. The model is trained
on 104 languages, with each batch containing training sentences from each language, and it uses a
shared vocabulary formed by WordPiece on the 104 Wikipedias concatenated (Wu et al., 2016).


3.2 DEFINING AND EVALUATING CONTEXTUAL ALIGNMENT


In the following sections, we describe how to define, evaluate, and improve contextual alignment. Given two languages, a model is in _contextual alignment_ if it has similar representations
for word pairs within parallel sentences. More precisely, suppose we have _N_ parallel sentences
_C_ = _{_ ( **s** [1] _,_ **t** [1] ) _, ...,_ ( **s** _[N]_ _,_ **t** _[N]_ ) _}_, where ( **s** _,_ **t** ) is a source-target sentence pair. Also, let each sentence
pair ( **s** _,_ **t** ) have word pairs, denoted _a_ ( **s** _,_ **t** ) = _{_ ( _i_ 1 _, j_ 1) _, ...,_ ( _im, jm_ ) _}_, containing position tuples
( _i, j_ ) such that the words **s** _i_ and **t** _j_ are translations of each other. [1] We will use _f_ to represent a
pre-trained model such that _f_ ( _i,_ **s** ) is the contextual embedding for the _i_ th word in **s** .


1These pairs are called word alignments in the machine translation community, but we use the term “word
pairs” to avoid confusion with embedding alignment. Also, because BERT operates on subwords while the
corpus is aligned at the word level, we keep only the BERT vector for the last subword of each word.


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Published as a conference paper at ICLR 2020


As an example, we might have the following sentence pair:


0 1 2 3 4 0 1 2 3 4 5
**s** = _{I_ _ate_ _the_ _apple_ _.}_ **t** = _{Ich_ _habe_ _den_ _Apfel_ _gegessen_ _.}_
_a_ ( **s** _,_ **t** ) = _{_ (0 _,_ 0) _,_ (1 _,_ 4) _,_ (2 _,_ 2) _,_ (3 _,_ 3) _,_ (4 _,_ 5) _}_


Then, using the parallel corpus _C_, we can measure the contextual alignment of the model _f_ using its
accuracy in _contextual word retrieval_ . In this task, the model is presented with two parallel corpora,
and given a word within a sentence in one corpus, it must find the correct word and sentence in the
other. Specifically, we can define a nearest neighbor retrieval function


neighbor( _i,_ **s** ; _f, C_ ) = argmax sim( _f_ ( _i,_ **s** ) _, f_ ( _j,_ **t** )) _,_
**t** _∈C,_ 0 _≤j≤_ len( **t** )


where _i_ and _j_ denote the position within a sentence and sim is a similarity function. The accuracy
is then given by the percentage of exact matches over the entire corpus, or



_A_ ( _f_ ; _C_ ) = [1]

_N_






( **s** _,_ **t** ) _∈C_




 
I(neighbor( _i,_ **s** ; _f, C_ ) = ( _j,_ **t** )) _,_

( _i,j_ ) _∈a_ ( **s** _,_ **t** )



where I represents the indicator function. We can perform the same procedure in the other direction,
where we pull target words given source words, so we report the average between the two directions.
As our similarity function, we use CSLS, a modified version of cosine similarity that mitigates
the hubness problem, with neighborhood size 10 (Conneau et al., 2018a). One additional point is
that this procedure can be made more or less contextual based on the corpus: a corpus with more
occurrences for each word type requires better representations of context. Therefore, we also test
non-contextual word retrieval by removing all but the first occurrence of each word type.


Given parallel data, these word pairs can be procured in an unsupervised fashion using standard
techniques developed by the machine translation community (Brown et al., 1993). While these
methods can be noisy, by running the algorithm in both the source-target and target-source directions
and only keeping word pairs in their intersection, we can trade-off coverage for accuracy, producing
a reasonably high-precision dataset (Och & Ney, 2003).


3.3 ALIGNING PRE-TRAINED CONTEXTUAL EMBEDDINGS


To improve the alignment of the model _f_ with respect to the corpus _C_, we can encapsulate alignment
in the loss function



_L_ ( _f_ ; _C_ ) = _−_ 

( **s** _,_ **t** ) _∈C_




 - sim( _f_ ( _i,_ **s** ) _, f_ ( _j,_ **t** )) _,_


( _i,j_ ) _∈a_ ( **s** _,_ **t** )



where we sum the similarities between word pairs. Because the CSLS metric is not easily optimized,
we instead use the squared error loss, or sim( _f_ ( _i,_ **s** ) _, f_ ( _j,_ **t** )) = _−||f_ ( _i,_ **s** ) _−_ _f_ ( _j,_ **t** ) _||_ [2] 2 [.]


However, note that this loss function does not account for the informativity of _f_ ; for example, it is
zero if _f_ is constant. Therefore, at a high level, we would like to minimize _L_ ( _f_ ; _C_ ) while maintaining some aspect of _f_ that makes it useful, e.g. its high accuracy when fine-tuned on downstream
tasks. Letting _f_ 0 denote the initial pre-trained model before alignment, we achieve this goal by
defining a regularization term



_R_ ( _f_ ; _C_ ) = 

**t** _∈C_



len( **t** )

- _||f_ ( _j,_ **t** ) _−_ _f_ 0( _j,_ **t** ) _||_ [2] 2 _[,]_


_i_ =1



which imposes a penalty if the target language embeddings stray from their initialization. Then,
we sample minibatches _B ⊂_ _C_ and take gradient steps of the function _L_ ( _f_ ; _B_ ) + _λR_ ( _f_ ; _B_ ) directly on the weights of _f_, which moves the source embeddings toward the target embeddings while
preventing the latter from drifting too far. In our experiments, we set _λ_ = 1.


In the multilingual case, suppose we have _k_ parallel corpora _C_ [1] _, ..., C_ _[k]_, where each corpus has a
different source language with the target language as English. Then, we sample equal-sized batches
_B_ _[i]_ _⊂_ _C_ _[i]_ from each corpus and take gradient steps on [�] _i_ _[k]_ =1 _[L]_ [(] _[f]_ [;] _[ B][i]_ [) +] _[ λR]_ [(] _[f]_ [;] _[ B][i]_ [)][, which moves]
all of the non-English embeddings toward English.


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Published as a conference paper at ICLR 2020


Note that this alignment method departs from prior work, in which each non-English language is
rotated to match the English embedding space through individual learned matrices. Specifically, the
most widely used post-hoc alignment method learns a rotation _W_ applied to the source vectors to
minimize the distance between parallel word pairs, or




 - _||Wf_ ( _i,_ **s** ) _−_ _f_ ( _j,_ **t** ) _||_ [2] 2 _s.t._ _W_ _[⊤]_ _W_ = _I._ (1)


( _i,j_ ) _∈a_ ( **s** _,_ **t** )



min
_W_






( **s** _,_ **t** ) _∈C_



This problem is known as the Procrustes problem and can be solved in closed form (Schonemann,
1966). This approach has the nice property that the vectors are only rotated, preserving distances
and therefore the semantic information captured by the embeddings (Artetxe et al., 2016). However,
rotation requires the strong assumption that the embedding spaces are roughly isometric (Søgaard
et al., 2018), an assumption that may not hold for contextual pre-trained models because they represent more aspects of a word than just its type, i.e. context and syntax, which are less likely to
be isomorphic between languages. Given that past work has also found independent alignment per
language pair to be inferior to joint training (Heyman et al., 2019), another advantage of our method
is that the alignment for all languages is done simultaneously.


As our dataset, we use the Europarl corpora for English paired with Bulgarian, German, Greek,
Spanish, and French, the languages represented in both Europarl and XNLI (Koehn, 2005). After
tokenization (Koehn et al., 2007), we produce word pairs using fastAlign and keep the one-to-one
pairs in the intersection (Dyer et al., 2013). We use the most recent 1024 sentences as the test set, the
previous 1024 sentences as the development set, and the following 250K sentences as the training
set. Furthermore, we modify the test set accuracy calculation to only include word pairs not seen in
the training set. We also remove any exact matches, e.g. punctuation and numbers, because BERT is
already aligned for these pairs due to its shared vocabulary. Given that parallel data may be limited
for low-resource language pairs, we also report numbers for 10K and 50K parallel sentences.


3.4 SENTENCE-AUGMENTED NON-CONTEXTUAL BASELINE


Given that there has been a long line of work on word vector alignment (Artetxe et al., 2018; Conneau et al., 2018a; Smith et al., 2017, _inter alia_ ), we also compare BERT to a sentence-augmented
fastText baseline (Bojanowski et al., 2017). Following Artetxe et al. (2018), we first normalize, then
mean-center, then normalize the word vectors, and we then learn a rotation with the same parallel
data as in the contextual case, as described in Equation 1. We also strengthen this baseline by including sentence information: specifically, during word retrieval, we concatenate each word vector
with a vector representing its sentence. Following R¨uckl´e et al. (2018), we compute the sentence
vector by concatenating the average, maximum, and minimum vector over all of the words in the
sentence, a method that was shown to be state-of-the-art for a suite of cross-lingual tasks. We also
experimented with other methods, such as first retrieving the sentence and then the word, but found
this method resulted in the highest accuracy. As a result, the fastText vectors are 1200-dimensional,
while the BERT vectors are 768-dimensional.


3.5 TESTING ZERO-SHOT TRANSFER


The next step is to determine whether better alignment improves cross-lingual transfer. As our
downstream task, we use the XNLI dataset, where the English MultiNLI development and test sets
are human-translated into multiple languages (Conneau et al., 2018b; Williams et al., 2018). Given
a pair of sentences, the task is to predict whether the first sentence implies the second, where there
are three labels: entailment, neutral, or contradiction. Starting from either the base or aligned multilingual BERT, we train on English and evaluate on Bulgarian, German, Greek, Spanish, and French,
the XNLI languages represented in Europarl.


As our architecture, following Devlin et al. (2018), we apply a linear layer followed by softmax
on the [CLS] embedding of the sentence pair, producing scores for each of the three labels. The
model is trained using cross-entropy loss and selected based on its development set accuracy averaged across all of the languages. As a fully-supervised ceiling, we also compare to models trained
and tested on the same language, where for the non-English training data, we use the machine translations of the English MultiNLI training data provided by Conneau et al. (2018b). While the quality
of the training data is affected by the quality of the MT system, this comparison nevertheless serves
as a good approximation for the fully-supervised setting.


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English Bulgarian German Greek Spanish French Average


Translate-Train


Base BERT 81.9 73.6 75.9 71.6 77.8 76.8 76.3


Zero-Shot _[a]_


Base BERT 80.4 68.7 70.4 67.0 74.5 73.4 72.4
Sentence-aligned BERT (rotation) **81.1** 68.9 71.2 66.7 74.9 73.5 72.7
Word-aligned BERT (rotation) 78.8 69.0 71.3 67.1 74.3 73.0 72.2
Word-aligned BERT (fine-tuned) 80.1 **73.4** **73.1** **71.4** **75.5** **74.5** **74.7**


XLM (MLM + TLM) 85.0 77.4 77.8 76.6 78.9 78.7 79.1


Table 1: Accuracy on the XNLI test set, where we compare to base BERT (Devlin et al., 2018)
and two rotation-based methods, sentence alignment (Aldarmaki & Diab, 2019) and word alignment (Wang et al., 2019). We also include the current state-of-the-art zero-shot achieved by
XLM (Lample & Conneau, 2019). Rotation-based methods provide small gains on some languages
but not others. On the other hand, after fine-tuning-based alignment, Bulgarian and Greek match the
translate-train ceiling, while German, Spanish, and French close roughly one-third of the gap.


_a_ Note that the zero-shot Base BERT numbers are slightly different from those reported in Devlin et al.
(2019) because we select a single model using the average accuracy across the six languages. This selection
method also accounts for the varying English accuracies across the zero-shot methods.


Sentences English Bulgarian German Greek Spanish French Average


None 80.4 68.7 70.4 67.0 74.5 73.4 72.4
10K 79.2 71.0 71.8 67.5 75.3 74.1 73.2
50K **81.1** 73 72.6 69.6 75 **74.5** 74.3
250K 80.1 **73.4** **73.1** **71.4** **75.5** **74.5** **74.7**


Table 2: Zero-shot accuracy on the XNLI test set, where we align BERT with varying amounts of
parallel data. The method scales with the amount of data but achieves a large fraction of the gains
with 50K sentences per language pair.


4 RESULTS


4.1 ZERO-SHOT XNLI TRANSFER


First, we test whether alignment improves multilingual BERT by applying the models to zero-shot
XNLI, as displayed in Table 1. We see that our alignment procedure greatly improves accuracies,
with all languages seeing a gain of at least 1%. In particular, the Bulgarian and Greek zero-shot
numbers are boosted by almost 5% each and match the translate-train numbers, suggesting that the
alignment procedure is especially effective for languages that are initially difficult for BERT. We
also run alignment for more distant language pairs (Chinese, Arabic, Urdu) and find similar results,
which we report in the appendix.


Comparing to rotation-based methods (Aldarmaki & Diab, 2019; Wang et al., 2019), we find that a
rotation produces small gains for some languages, namely Bulgarian, German, and Spanish, but is
sub-optimal overall, providing evidence that the increased expressivity of our proposed procedure is
beneficial for contextual alignment. We explore this comparison more in Section 5.1.


4.2 ALIGNMENT WITH LESS DATA


Given that our goal is zero-shot transfer, we cannot expect to always have large amounts of parallel data. Therefore, we also characterize the performance of our alignment method with varying
amounts of data, as displayed in Table 2. We find that it improves transfer with as little as 10K
sentences per language, making it a promising approach for low-resource languages.


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bg-en de-en el-en es-en fr-en Average


Contextual


Aligned fastText + sentence 44.0 46.4 42.0 48.6 44.5 45.1
Base BERT 19.5 26.1 13.9 32.5 28.3 24.1
Word-aligned BERT (rotation) 29.8 31.6 20.8 36.8 31.0 30.0
Word-aligned BERT (fine-tuned) **50.7** **51.3** **49.8** **51.0** **48.6** **50.3**


Non-Contextual


Aligned fastText + sentence 61.3 **65.4** 61.6 **71.1** 64.8 64.8
Base BERT 29.1 37.0 22.3 46.5 41.8 35.3
Word-aligned BERT (rotation) 39.6 43.6 32.4 51.4 46.1 42.6
Word-aligned BERT (fine-tuned) **62.8** 64.3 **67.5** 68.4 **66.3** **65.9**


Table 3: Word retrieval accuracy for the aligned sentence-augmented fastText baseline and BERT
pre- and post-alignment. Across languages, base BERT has variable accuracy while fine-tuningaligned BERT is consistently effective. Fine-tuned BERT also matches fastText in a version of the
task where context is not necessary, suggesting that our method matches the type-level alignment of
fastText while also aligning context.


5 ANALYSIS


5.1 WORD RETRIEVAL


In the following sections, we present word retrieval results to both compare our method to past work
and better understand the strengths and weaknesses of multilingual BERT. Table 3 displays the word
retrieval accuracies for the aligned sentence-augmented fastText baseline and BERT pre- and postalignment. First, we find that in contextual retrieval, fine-tuned BERT outperforms fastText, which
outperforms rotation-aligned BERT. This result supports the intuition that aligning large pre-trained
models is more difficult than aligning word vectors, given that a rotation, at least when applied
naively, produces sub-par alignments. In addition, fine-tuned BERT matches the performance of
fastText in non-contextual retrieval, suggesting that our alignment procedure overcomes these challenges and achieves type-level alignment that matches non-contextual approaches. In the appendix,
we also provide examples of aligned BERT disambiguating between different meanings of a word,
giving qualitative evidence of the benefit of context alignment.


We also find that before alignment, BERT’s performance varies greatly between languages, while
after alignment it is consistently effective. In particular, Bulgarian and Greek initially have very
low accuracies. This phenomenon is also reflected in the XNLI numbers (Table 1), where Bulgarian
and Greek receive the largest boosts from alignment. Examining the connection between alignment
and zero-shot more closely, we find that the word retrieval accuracies are highly correlated with
downstream zero-shot performance (Figure 2), supporting our evaluation measure as predictive of
cross-lingual transfer.


The language discrepancies are also consistent with a hypothesis by Pires et al. (2019) to explain
BERT’s multilingualism. They posit that due to the shared vocabulary, shared words between languages, e.g. numbers and names, are forced to have the same representation. Then, due to the
masked word prediction task, other words that co-occur with these shared words also receive similar
representations. If this hypothesis is true, then languages with higher lexical overlap with English are
likely to experience higher transfer. As an extreme form of this phenomenon, Bulgarian and Greek
have completely different scripts and should experience worse transfer than the common-script languages, an intuition that is confirmed by the word retrieval and XNLI accuracies. The fact that all
languages are equally aligned with English post-alignment suggests that the pre-training procedure
is suboptimal for these languages.


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Lexical Overlap Numeral Punctuation Proper Noun Average


Base BERT 0.90 0.88 0.80 0.86
Aligned BERT 0.97 0.96 0.95 0.96


Closed-Class Determiner Preposition Conjunction Pronoun Auxiliary Average


Base BERT 0.76 0.72 0.71 0.70 0.61 0.70
Aligned BERT 0.91 0.86 0.89 0.89 0.84 0.88


Open-Class Noun Adverb Adjective Verb Average


Base BERT 0.61 0.57 0.50 0.49 0.54
Aligned BERT 0.90 0.88 0.90 0.89 0.89


Table 4: Accuracy by part-of-speech tag for non-contextual word retrieval. To achieve better
word type coverage, we do not remove word pairs seen in the training set. The tags are grouped into
lexically overlapping, closed-class, and open-class groups. The “Particle,” “Symbol,” “Interjection,”
and “Other” tags are omitted.







74


72


70


68







66
15 20 25 30


Contextual word retrieval accuracy


Figure 2: XNLI zero-shot versus word retrieval accuracy for base BERT, where each
point is a language paired with English.
This plot suggests that alignment correlates
well with cross-lingual transfer.


|1.00<br>0.95<br>0.90<br>0.85<br>0.80<br>0.75<br>0.70<br>0.65<br>0.60|Aligned BERT<br>Base BERT|
|---|---|
|0.60<br>0.65<br>0.70<br>0.75<br>0.80<br>0.85<br>0.90<br>0.95<br>1.00|100<br>101<br>102<br>103<br>104|



Figure 3: Contextual word retrieval accuracy plotted
against difference in frequency rank between source
and target. The accuracy of base BERT plummets for
larger differences, suggesting that its alignment depends on word pairs having similar usage statistics.





5.2 WORD RETRIEVAL PART-OF-SPEECH ANALYSIS


Next, to gain insight into the multilingual pre-training procedure, we analyze the accuracy broken
down by part-of-speech using the Universal Part-of-Speech Tagset (Petrov et al., 2012), annotated
using polyglot (Al-Rfou et al., 2013) for Bulgarian and spaCy (Honnibal & Montani, 2017) for the
other languages, as displayed in Table 4. Unsurprisingly, multilingual BERT has high alignment
out-of-the-box for groups with high lexical overlap, e.g. numerals, punctuation, and proper nouns,
due to its shared vocabulary. We further divide the remaining tags into closed-class and open-class,
where closed-class parts-of-speech correspond to fixed sets of words serving grammatical functions
(e.g. determiner, preposition, conjunction, pronoun, and auxiliary), while open-class parts-of-speech
correspond to lexical words (e.g. noun, adverb, adjective, verb). Interestingly, we see that base BERT
has consistently lower accuracy for closed-class versus open-class categories (0 _._ 70 vs 0 _._ 54), but that
this discrepancy disappears after alignment (0 _._ 88 vs 0 _._ 89).


5.3 USAGE HYPOTHESIS FOR ALIGNMENT


From this closed-class vs open-class difference, we hypothesize that BERT’s alignment of a particular word pair is influenced by the similarity of their usage statistics. Specifically, given that
BERT is trained through masked word prediction, its embeddings are in large part determined by


8


Published as a conference paper at ICLR 2020


the co-occurrences between words. Therefore, two words that are used in similar contexts should be
better aligned. This hypothesis provides an explanation of the closed-class vs open-class difference:
closed-class words are typically grammatical, so they are used in similar ways across typologically
similar languages. Furthermore, these words cannot be substituted for one another due to their
grammatical function. Therefore, their usage statistics are a strong signature that can be used for
alignment. On the other hand, open-class words can be substituted for one another: for example, in
most sentences, the noun tokens could be replaced by a wide range of semantically dissimilar nouns
with the sentence remaining syntactically well-formed. By this effect, many nouns have similar
co-occurrences, making them difficult to align through masked word prediction alone.


To further test this hypothesis, we plot the word retrieval accuracy versus the difference between the
frequency rank of the target and source word, where this difference measures discrepancies in usage,
as depicted in Figure 3. We see that accuracy drops off significantly as the source-target difference
increases, supporting our hypothesis. Furthermore, this shortcoming is remedied by alignment,
revealing another systematic deficiency of multilingual pre-training.


6 CONCLUSION


Given that the degree of alignment is causally predictive of downstream cross-lingual transfer, contextual alignment proves to be a useful concept for understanding and improving multilingual pretrained models. Given small amounts of parallel data, our alignment procedure improves multilingual BERT and corrects many of its systematic deficiencies. Contextual word retrieval also provides
useful new insights into the pre-training procedure, opening up new avenues for analysis.


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English Bulgarian German Greek Spanish French Arabic Chinese Urdu Average


Translate-Train


Base BERT 81.9 73.6 75.9 71.6 77.8 76.8 70.7 76.6 61.6 74.1


Zero-Shot


Base BERT 80.4 68.7 70.4 67.0 74.5 73.4 65.6 70.6 60.3 70.1
Aligned BERT (20K sent) **80.8** **71.6** **72.5** **68.1** **74.7** **73.6** **66.3** **71.5** **61.1** **71.1**


Table 5: Zero-shot accuracy on the XNLI test set with more languages, where we use 20K parallel
sentences for each language paired with English. This result confirms that the alignment method
works for distant languages and a variety of parallel corpora, including Europarl, MultiUN, and
Tanzil, which contains sentences from the Quran (Koehn, 2005; Eisele & Chen, 2010; Tiedemann,
2012).


A APPENDIX


A.1 OPTIMIZATION HYPERPARAMETERS


For both alignment and XNLI optimization, we use a learning rate of 5 _×_ 10 _[−]_ [5] with Adam hyperparameters _β_ = (0 _._ 9 _,_ 0 _._ 98), _ϵ_ = 10 _[−]_ [9] and linear learning rate warmup for the first 10% of the training
data. For alignment, the model is trained for one epoch, with each batch containing 2 sentence pairs
per language. For XNLI, each model is trained for 3 epochs with 32 examples per batch, and 10%
dropout is applied to the BERT embeddings.


A.2 ALIGNMENT OF CHINESE, ARABIC, AND URDU


In Table 5, we report numbers for additional languages, where we align a single BERT model for all
eight languages and then fine-tune on XNLI. We use 20K sentences per language, where we use the
MultiUN corpus for Arabic and Chinese (Eisele & Chen, 2010), the Tanzil corpus for Urdu (Tiedemann, 2012), and the Europarl corpus for the other five languages (Koehn, 2005). This result confirms that the alignment method works for a variety of languages and corpora. Furthermore, the
Tanzil corpus consists of sentences from the Quran, suggesting that the method works even when
the parallel corpus and downstream task contain sentences from entirely different domains.


A.3 EXAMPLES OF CONTEXT-AWARE RETRIEVAL


In this section, we qualitatively show that aligned BERT is able to disambiguate between different
occurences of a word.


First, we find two meanings of the word “like” occurring in the English-German Europarl test set.
Note also that in the second and third example, the two senses of “like” occur in the same sentence.


_•_ This empire did not look for colonies far from home or overseas, **like** most Western European States, but close by.
Dieses Reich suchte seine Kolonien nicht weit von zu Hause und in bersee **wie** die meisten
westeurop¨aischen Staaten, sondern in der unmittelbaren Umgebung.


_•_ **Like** other speakers, I would like to support the call for the arms embargo to remain.
**Wie** andere Sprecher, so m¨ochte auch ich den Aufruf zur Aufrechterhaltung des Waffenembargos untersttzen.


_•_ Like other speakers, I would **like** to support the call for the arms embargo to remain.
Wie andere Sprecher, so **m¨ochte** auch ich den Aufruf zur Aufrechterhaltung des Waffenembargos untersttzen.


_•_ I would also **like**, although they are absent, to mention the Commission and the Council.
Ich **m¨ochte** mir sogar erlauben, die Kommission und den Rat zu nennen, auch wenn sie
nicht anwesend sind.


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Multiple meanings of “order”:


_•_ Moreover, the national political elite had to make a detour in Ambon in **order** to reach the
civil governor’s residence by warship.
In Ambon mußte die politische Spitze des Landes auch noch einen Umweg machen, **um**
mit einem Kriegsschiff die Residenz des Provinzgouverneurs zu erreichen.


_•_ Although the European Union has an interest in being surrounded by large, stable regions,
the tools it has available in **order** to achieve this are still very limited.

Der Europ¨aischen Union ist zwar an großen stabilen Regionen in ihrer Umgebung gelegen,
aber sie verfgt nach wie vor nur ber recht begrenzte Instrumente, **um** das zu erreichen.


_•_ We could reasonably expect the new Indonesian government to take action in three fundamental areas: restoring public **order**, prosecuting and punishing those who have blood on
their hands and entering into a political dialogue with the opposition.

Von der neuen indonesischen Regierung darf man mit Fug und Recht drei elementare Maßnahmen erwarten: die Wiederherstellung der ¨offentlichen **Ordnung**, die Verfolgung und
Bestrafung derjenigen, an deren H¨anden Blut klebt, und die Aufnahme des politischen Dialogs mit den Gegnern.


_•_ Firstly, I might mention the fact that the army needs to be reformed, secondly that a stable
system of law and **order** needs to be introduced.

Ich nenne hier an erster Stelle die notwendige Reform der Armee, ferner die Einfhrung
eines stabilen Systems rechtsstaatlicher **Ordnung** .


Multiple meanings of “support”:


_•_ Financial **support** is needed to enable poor countries to take part in these court activities.
Arme L¨ander m¨ussen finanziell **unterst¨utzt** werden, damit auch sie sich an der Arbeit des
Gerichtshofs beteiligen k¨onnen.


_•_ We must help them and ensure that a proper action plan is implemented to **support** their
work.

Es gilt einen wirklichen Aktionsplan auf den Weg zu bringen, um die Arbeit dieser Organisationen zu **unterst¨utzen** .


_•_ So I hope that you will all **support** this resolution condemning the abominable conditions
of prisoners and civilians in Djibouti.
Ich hoffe daher, daß Sie alle diese Entschließung **bef¨urworten**, die die entsetzlichen Bedingungen von Inhaftierten und Zivilpersonen in Dschibuti verurteilt.


_•_ It would be difficult to **support** a subsidy scheme that channelled most of the aid to the
large farms in the best agricultural regions.
Es w¨are auch problematisch, ein Beihilfesystem zu **bef¨urworten**, das die meisten Beihilfen
in die großen Betriebe in den besten landwirtschaftlichen Gebieten lenkt.


Multiple meanings of “close”:


_•_ This empire did not look for colonies far from home or overseas, like most Western European States, but **close** by.

Dieses Reich suchte seine Kolonien nicht weit von zu Hause und in bersee wie die meisten
westeurop¨aischen Staaten, sondern in der unmittelbaren **Umgebung** .


_•_ In addition, if we are to shut down or refuse investment from every company which may
have an association with the arms industry, then we would have to **close** virtually every
American and Japanese software company on the island of Ireland with catastrophic consequences.

Wenn wir zudem jedes Unternehmen, das auf irgendeine Weise mit der Rstungsindustrie
verbunden ist, schließen oder Investitionen dieser Unternehmen unterbinden, dann mßten
wir so ziemlich alle amerikanischen und japanischen Softwareunternehmen auf der irischen
Insel **schließen**, was katastrophale Auswirkungen h¨atte.


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Published as a conference paper at ICLR 2020


_•_ On the other hand, the deployment of resources left over in the Structural Funds from the
programme planning period 1994 to 1999 is hardly worth considering as the available funds
have already been allocated to specific measures, in this case in **close** collaboration with
the relevant French authorities.
Die Verwendung verbliebener Mittel der Strukturfonds aus dem Programmplanungszeitraum 1994 bis 1999 ist dagegen kaum in Erw¨agung zu ziehen, da die verfgbaren
Mittel bereits bestimmten Maßnahmen zugewiesen sind, und zwar im konkreten Fall im
**engen** Zusammenwirken mit den zust¨andigen franz¨osischen Beh¨orden.


_•_ This is particularly justified given that, as already stated, many Member States have very
**close** relations with Djibouti.
Zumal, wie erw¨ahnt, viele Mitgliedstaaten sehr **enge** Beziehungen zu Dschibuti unterhalten.


_•_ Mr President, it is regrettable that, at the **close** of the 20th century, a century symbolised so
positively by the peaceful women’s revolution, there are still countries, such as Kuwait and
Afghanistan, where half the population, women that is, is still denied fundamental human
rights.
Herr Pr¨asident! Es ist wirklich bedauerlich, daß es am **Ende** des 20. Jahrhunderts, eines
so positiv von der friedlichen Revolution der Frauen gepr¨agten Jahrhunderts, noch immer
L¨ander wie Kuwait und Afghanistan gibt, in denen der H¨alfte der Bev¨olkerung, den Frauen,
die elementaren Menschenrechte verweigert werden.


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