Original: C ROSS -L INGUAL A BILITY OF M ULTILINGUAL BERT: A N E MPIRICAL S TUDY
Revised: C ROSS -L INGUAL A BILITY OF M ULTILINGUAL BERT: A N E MPIRICAL S TUDY

Original: A BSTRACT
Revised: A BSTRACT

Original: Recent work has exhibited the surprising cross-lingual abilities of multilingual
Revised: Recent work has exhibited the surprising cross-lingual abilities of multilingual

Original: BERT ( M-BERT ) – surprising since it is trained without any cross-lingual objective and with no aligned data.
Revised: BERT ( M-BERT ) – surprising since it is trained without any cross-lingual objective and with no aligned data.

Original: In this work, we provide a comprehensive study of the contribution of different components in M-BERT to its cross-lingual ability.
Revised: In this work, we provide a comprehensive study of the contribution of different components in M-BERT to its cross-lingual ability.

Original: We study the impact of linguistic properties of the languages, the architecture of the model, and the learning objectives.
Revised: We study the impact of linguistic properties of the languages, the architecture of the model and the learning objectives.

Original: The experimental study is done in the context of three typologically different languages – Spanish, Hindi, and Russian – and using two conceptually different NLP tasks, textual entailment and named entity recognition.
Revised: The experimental study is done in the context of three typologically different languages – Spanish, Hindi and Russian – and using two conceptually different NLP tasks, textual entailment and named entity recognition.

Original: Among our key conclusions is the fact that the lexical overlap between languages plays a negligible role in the cross-lingual success, while the depth of the network is an integral part of it.
Revised: Among our key conclusions is the fact that the lexical overlap between languages plays a negligible role in the cross-lingual success, while the depth of the network is an integral part of it.

Original: All our models and implementations can be found at our project page1 .
Revised: All our models and implementations can be found on our project page

Original:  I NTRODUCTION
Revised:  I NTRODUCTION

Original: Embeddings of natural language text via unsupervised learning, coupled with sufﬁcient supervised training data, have been ubiquitous in NLP in recent years and have shown success in a wide range of monolingual NLP tasks, mostly in English.
Revised: Embeddings of natural language text via unsupervised learning, coupled with sufﬁcient supervised training data, have been ubiquitous in NLP in recent years and have shown success in a wide range of monolingual NLP tasks, mostly in English.

Original: Training models for other languages have been shown more difﬁcult, and recent approaches relied on bilingual embeddings that allowed the transfer of supervision in high resource languages like English to models in lower resource languages; however, inducing these bilingual embeddings required some level of supervision (Upadhyay et al., 2016).
Revised: Training models for other languages has been shown more difﬁcult, and recent approaches relied on bilingual embeddings that allowed the transfer of supervision in high resource languages like English to models in lower resource languages; however, inducing these bilingual embeddings required some level of supervision (Upadhyay et al., 2016).

Original: Multilingual BERT 2 ( M-BERT ), a Transformer-based (Vaswani et al., 2017) language model trained on raw Wikipedia text of 104 languages suggests an entirely different approach.
Revised: Multilingual BERT 2 ( M-BERT ), a Transformer-based (Vaswani et al., 2017) language model trained on raw Wikipedia text of 104 languages suggests an entirely different approach.

Original: Not only  the modelis contextual, but its training also requires no supervision – no alignment between the languages is done.
Revised: Not only is the model contextual, but its training also requires no supervision – no alignment between the languages is done.

Original: Nevertheless, and despite being trained with no explicit cross-lingual objective, M-BERT produces a representation that seems to generalize well across languages for a variety of downstream tasks (Wu & Dredze, 2019).
Revised: Nevertheless, and despite being trained with no explicit cross-lingual objective, M-BERT produces a representation that seems to generalize well across languages for a variety of downstream tasks (Wu & Dredze, 2019).

Original: In this work, we attempt to develop an understanding of the success of M-BERT .
Revised: In this work, we attempt to develop an understanding of the success of M-BERT .

Original: We study a range of aspects on two different NLP tasks, in order to identify the key components in the success of the model.
Revised: We study a range of aspects on two different NLP tasks, in order to identify the key components in the success of the model.

Original: Our study is done in the context of only two languages, source (typically English) and target (multiple, quite different languages).
Revised: Our study is done in the context of only two languages, source (typically English) and target (multiple, quite different languages).

Original: By involving only a pair of languages, we can study the performance on a given target language, ensuring that it is inﬂuenced only by the cross-lingual transfer from the source language, without having to worry about a third language interfering.
Revised: By involving only a pair of languages, we can study the performance on a given target language, ensuring that it is inﬂuenced only by the cross-lingual transfer from the source language, without having to worry about a third language interfering.

Original: We analyze the two-languages version of M-BERT ( B-BERT , from now on) in three orthogonal dimensions: (i) Linguistics properties and similarities of target and source languages; (ii) Network Architecture, and (iii) Input and Learning Objective.
Revised: We analyze the two-languages version of M-BERT ( B-BERT , from now on) in three orthogonal dimensions: (i) linguistic properties and similarities of target and source languages; (ii) network architecture, and (iii) input and learning objective.

Original: One hypothesis that came up when people think the success of M-BERT is due to  some level of language similarity.
Revised: One hypothesis that has been discussed as a way to explain the success of M-BERT has to do with some level of language similarity.

Original: This could be lexical similarity (shared words or word-parts) or structural similarities (word-ordering or word-frequency), or both.
Revised: This could be lexical similarity (shared words or wordparts) or structural similarities (word-ordering or word-frequency), or both.

Original: We, therefore, investigate the contribution of word-piece overlap – the extent to which the same word-pieces appear in both source and target languages – and distinguish it from other similarities, which we call structural similarity between the source and target languages.
Revised: Therefore, we begin by investigating the contribution of word-piece overlap – the extent to which the same word-pieces appear in both source and target languages – and distinguish it from other similarities, which we group into a structural similarity between the source and target languages.

Original: Surprisingly, as we show, B-BERT is cross-lingual even when there is absolutely no word-piece overlap.
Revised: Surprisingly, as we show, B-BERT is cross-lingual even when there is absolutely no word-piece overlap.

Original: That is, other aspects of language similarity must be contributing to the cross-lingual capabilities of the model.
Revised: That is, other aspects of language similarity must be contributing to the cross-lingual capabilities of the model.

Original: This is contrary to  Pires et al.
Revised: This is contrary to the Pires et al.

Original: (2019) hypothesis that M-BERT gains its power from shared word-pieces.
Revised: (2019) hypothesis that M-BERT gains its power from shared word-pieces.

Original: Furthermore, we show that the amount of word-piece overlap in B-BERT ’s training data contributes little to performance improvements.
Revised: Furthermore, we show that the amount of word-piece overlap in B-BERT ’s training data contributes little to performance improvements.

Original: Our study of the model architecture addresses the importance of (i) The network depth, (ii) the number of attention heads, and (iii) the total number of model parameters in B-BERT .
Revised: Our study of the model architecture addresses the importance of (i) the network depth, (ii) the number of attention heads, and (iii) the total number of model parameters in B-BERT .

Original: Our results suggest that depth and the total number of parameters of B-BERT are crucial for both monolingual and cross-lingual performance, whereas multi-head attention is not a signiﬁcant factor – a single attention head B-BERT can already give satisfactory results.
Revised: Our results suggest that depth and the total number of parameters of B-BERT are crucial for both monolingual and cross-lingual performance, whereas multi-head attention is not a signiﬁcant factor – a single attention head B-BERT can already give satisfactory results.

Original: To understand the role of the learning objective and the input representation, we study the effect of (i) the next sentence prediction objective, (ii) the language identiﬁer in the training data, and (iii) the level of tokenization in the input representation (character, word-piece, or word tokenization).
Revised: To understand the role of the learning objective and the input representation, we study the effect of (i) the next sentence prediction objective, (ii) the language identiﬁer in the training data, and (iii) the level of tokenization in the input representation (character, word-piece, or word tokenization).

Original: Our results indicate that the next sentence prediction objective actually hurts the performance of the model while identifying the language in the input does not affect B-BERT ’s performance crosslingually.
Revised: Our results indicate that the next sentence prediction objective actually hurts the performance of the model while identifying the language in the input does not affect B-BERT ’s performance crosslingually.

Original: Our experiments also show that character-level and word-level tokenization of the input results in signiﬁcantly worse performance than word-piece level tokenization.
Revised: Our experiments also show that character-level and word-level tokenization of the input results in signiﬁcantly worse performance than word-piece level tokenization.

Original: Overall, we provide an extensive set of experiments on three source-target language pairs, English–
Revised: Overall, we provide an extensive set of experiments on three source-target language pairs, English–

Original: Spanish, English–Russian, and English–Hindi. We chose these target languages since they vary in scripts and typological features.
Revised: Spanish, English–Russian, and English–Hindi, selected for variance of script and typological features.

Original: We evaluate the performance of B-BERT on two very different downstream tasks: cross-lingual Named Entity Recognition – a sequence prediction task the requires only local context – and cross-lingual Textual Entailment Dagan et al.
Revised: We evaluate the performance of B-BERT on two very different downstream tasks: crosslingual Named Entity Recognition – a sequence prediction task that requires only local context – and cross-lingual Textual Entailment Dagan et al.

Original: (2013) that requires more global representation of the text.
Revised: (2013) that requires more global representation of the text.

Original: Ours is not the ﬁrst study of M-BERT .
Revised: Ours is not the ﬁrst study of M-BERT .

Original: (Wu & Dredze, 2019) and (Pires et al., 2019) identiﬁed the cross-lingual success of the model and tried to understand it.
Revised: Wu & Dredze (2019) and Pires et al. identiﬁed the cross-lingual success of the model and tried to understand it.

Original: The former by considering M-BERT layer-wise, relating cross-lingual performance with the amount of shared word-pieces and the latter by considering the model’s ability to transfer between languages as a function of word order similarity in languages.
Revised: The former by considering M-BERT layer-wise, relating cross-lingual performance with the amount of shared word-pieces and the latter by considering the model’s ability to transfer between languages as a function of word order similarity in languages.

Original: However, both works treated M-BERT as a black box and compared M-BERT ’s performance on different languages.
Revised: However, both works treated M-BERT as a black box, comparing performance on different languages.

Original: This work, on the other hand, examines how B-BERT performs cross-lingually by probing its components, along multiple aspects.
Revised: This work, on the other hand, examines how B-BERT performs cross-lingually by probing its components along multiple aspects.

Original: We also note that some of the architectural conclusions have been observed earlier, if not investigated, in other contexts.
Revised: We also note that some of the architectural conclusions have been observed earlier, if not investigated, in other contexts.

Original: Liu et al.
Revised: Liu et al.

Original: ; Yang et al.
Revised: (2019) and Yang et al.

Original: (2019) argued that the next Sentence prediction objective of BERT (the monolingual model) is not very useful; we show that this is the case in the cross-lingual setting.
Revised: (2019) argued that the next Sentence prediction objective of BERT (the monolingual model) is not very useful; we show that this is the case in the cross-lingual setting.

Original: Voita et al.
Revised: Voita et al.

Original: (2019) prunes attention heads for a transformer based machine translation model and argues that most attention heads are not important; in this work, we show that the number of attention heads is not important in the cross-lingual setting.
Revised: (2019) prunes attention heads for a transformer based machine translation model and argues that most attention heads are not important; in this work, we show that the number of attention heads is not important in the cross-lingual setting.

Original: Our contributions are threefold: (i) we provide the ﬁrst extensive study of the aspects of the multilingual BERT that give rise to its cross-lingual ability. (ii) We develop a methodology that facilitates the analysis of similarities between languages and their impact on cross-lingual models; we do this by mapping English to a Fake-English language, that is identical in all aspects to English but shares no word-pieces with any target language. Finally, (iii) we develop a set of insights into B-BERT , along linguistics, architectural, and learning dimensions, that would contribute to further understanding and to the development of more advanced cross-lingual neural models.
Revised: Our contributions are threefold: (i) we provide the ﬁrst extensive study of the aspects of M-BERT that give rise to its cross-lingual ability; (ii) we develop a methodology that facilitates the analysis of similarities between languages and their impact on cross-lingual models; we do this by mapping English to a Fake-English language, that is identical in all aspects to English but shares no word-pieces with any target language; ﬁnally, (iii) we develop a set of insights into B-BERT , along linguistic, architectural, and learning dimensions, that would contribute to further understanding and to the development of more advanced cross-lingual neural models.

Original:  B ACKGROUND 2. BERT
Revised:  B ACKGROUND 2. BERT

Original: BERT (Devlin et al., 2019) is a Transformer (Vaswani et al., 2017)
Revised: BERT (Devlin et al., 2019) is a Transformer-based (Vaswani et al., 2017)

Original: based pre-trained language representation model that has been widely used in the ﬁeld of Natural Language Processing.
Revised: pre-trained language representation model that has been widely used in the ﬁeld of Natural Language Processing.

Original: BERT is trained with Masked Language Modelling (MLM) (Taylor, 1953) and Next Sentence Prediction (NSP) objectives.
Revised: BERT is trained with Masked Language Modelling (MLM) (Taylor, 1953) and Next Sentence Prediction (NSP) objectives.

Original: Input to BERT is a pair of sentences 3 A and B, such that half of the time B comes after A in the original text and the rest of the time B is a randomly sampled sentence.
Revised: Input to BERT is a pair of sentences 3 A and B, such that half of the time B comes after A in the original text and the rest of the time B is a randomly sampled sentence.

Original: Some tokens from the input are randomly masked, and the MLM objective is to predict the masked tokens.
Revised: Some tokens from the input are randomly masked, and the MLM objective is to predict the masked tokens.

Original: The
Revised: The

Original: NSP objective is to predict whether B is the actual next sentence of A or not.
Revised: NSP objective is to predict whether B is the actual next sentence of A or not.

Original: (Devlin et al., 2019) argues that MLM enables a deep representation from both directions, and NSP helps understand the relationship between two sentences and can be beneﬁcial to representations.
Revised: Devlin et al. (2019) argues that MLM enables a deep representation from both directions, and NSP helps understand the relationship between two sentences and can be beneﬁcial to representations.

Original: BERT follows two-steps 1.
Revised: BERT follows two-steps 1.

Original: Pre-training and, 2.
Revised: Pre-training and, 2.

Original: Fine-tuning.
Revised: Fine-tuning.

Original: BERT is pre-trained using the above mentioned MLM and NSP objective on BooksCorpus and English Wikipedia text, and for any supervised downstream task, BERT is initialized with the pre-trained weights and ﬁne-tuned using the labeled data.
Revised: BERT is pre-trained using the above mentioned MLM and NSP objective on BooksCorpus and English Wikipedia text, and for any supervised downstream task, BERT is initialized with the pre-trained weights and ﬁne-tuned using the labeled data.

Original: BERT uses word-piece tokenization (Wu et al., 2016), which creates a sub-word vocabulary in a data-driven approach.
Revised: BERT uses word-piece tokenization (Wu et al., 2016), which creates a sub-word vocabulary in a data-driven approach.

Original: 2. M ULTILINGUAL BERT
Revised: 2. M ULTILINGUAL BERT

Original: Multilingual BERT is pre-trained in the same way as monolingual BERT except using Wikipedia text from the top 104 languages.
Revised: Multilingual BERT is pre-trained in the same way as monolingual BERT except using Wikipedia text from the top 104 languages.

Original: To account for the differences in the size of Wikipedia, some languages are sub-sampled, and some are super-sampled using exponential smoothing Devlin et al.
Revised: To account for the differences in the size of Wikipedia, some languages are sub-sampled, and some are super-sampled using exponential smoothing (Devlin et al., 2018).

Original: It’s worth mentioning that there are no cross-lingual objectives speciﬁcally designed nor any cross-lingual data, e.g. parallel corpus, used.
Revised: It’s worth mentioning that there are no cross-lingual objectives speciﬁcally designed nor any cross-lingual data, e.g. parallel corpus, used.

Original:  W HY M ULTILINGUAL BERT W ORKS
Revised:  W HY M ULTILINGUAL BERT W ORKS

Original: We present analysis for the cross-lingual ability of multilingual BERT (in our case B-BERT ) in three dimensions.
Revised: We present analysis for the cross-lingual ability of multilingual BERT (in our case B-BERT ) in three dimensions.

Original: (i) Linguistics (ii) Architecture and (iii) Input and Learning Objective.
Revised: (i) Linguistics (ii) Architecture and (iii) Input and Learning Objective.

Original:  D ATASETS AND E XPERIMENTAL S ETUP
Revised: 3. D ATASETS AND E XPERIMENTAL S ETUP

Original: In this work, we conduct all our experiments on two conceptually different downstream tasks – crosslingual Textual Entailment (TE) and cross-lingual Named Entity Recognition (NER).
Revised: In this work, we conduct all our experiments on two conceptually different downstream tasks – crosslingual Textual Entailment (TE) and cross-lingual Named Entity Recognition (NER).

Original: TE measures natural language understanding (NLU) at a sentence and sentence pair level, whereas NER measures
Revised: TE measures natural language understanding (NLU) at a sentence and sentence pair level, whereas NER measures

Original: NLU at a token level.
Revised: NLU at a token level.

Original: We use the Cross-lingual Natural Language Inference (XNLI)
Revised: We use the Cross-lingual Natural Language Inference (XNLI)

Original: (Conneau et al., 2018) dataset to evaluate cross-lingual TE performance and LORELEI dataset (Strassel & Tracey, 2016) for Cross-Lingual NER.
Revised: (Conneau et al., 2018) dataset to evaluate cross-lingual TE performance and LORELEI dataset (Strassel & Tracey, 2016) for Cross-Lingual NER.

Original: 3.1. C ROSS - LINGUAL N ATURAL L ANGUAGE I NFERENCE (XNLI)
Revised: 3.1. C ROSS - LINGUAL N ATURAL L ANGUAGE I NFERENCE (XNLI)

Original: XNLI is a standard cross-lingual textual entailment dataset that extends MultiNLI
Revised: XNLI is a standard cross-lingual textual entailment dataset that extends MultiNLI

Original: (Williams et al., 2018) dataset by creating a new dev and test set and manually translating into 14 different languages.
Revised: (Williams et al., 2018) dataset by creating a new dev and test set and manually translating into 14 different languages.

Original: Each input consists of a premise and hypothesis pair, and the task is to classify the relationship between premise and hypothesis into one of the three labels: entailment, contradiction, and neutral.
Revised: Each input consists of a premise and hypothesis pair, and the task is to classify the relationship between premise and hypothesis into one of the three labels: entailment, contradiction, and neutral.

Original: While training, both premise and hypothesis are in English, and while testing, both are in the target language.
Revised: While training, both premise and hypothesis are in English, and while testing, both are in the target language.

Original: XNLI uses the same set of premises and hypotheses for all the language, making the comparison across languages possible.
Revised: XNLI uses the same set of premises and hypotheses for all the language, making the comparison across languages possible.

Original: 3.1. C ROSS - LINGUAL N AMED E NTITY R ECOGNITION (NER)
Revised: 3.1. C ROSS - LINGUAL N AMED E NTITY R ECOGNITION (NER)

Original: Named Entity Recognition is the task of identifying and labeling text spans as named entities, such as people’s names and locations.
Revised: Named Entity Recognition is the task of identifying and labeling text spans as named entities, such as people’s names and locations.

Original: The NER dataset (Strassel & Tracey, 2016)
Revised: The NER dataset (Strassel & Tracey, 2016)

Original: we use consists of news and social media text labeled by native speakers following the same guideline in several languages, including English, Hindi, Spanish, and Russian.
Revised: we use consists of news and social media text labeled by native speakers following the same guideline in several languages, including English, Hindi, Spanish, and Russian.

Original: We subsample 80%, 10%, 10% of English NER data as training, development, and testing.
Revised: We subsample 80%, 10%, 10% of English NER data as training, development, and testing.

Original: We use the whole dataset of Hindi, Spanish, and Russian for testing purposes.
Revised: We use the whole dataset of Hindi, Spanish, and Russian for testing purposes.

Original: The vocabulary size is ﬁxed at 60000 and is estimated through the unigram language model in the SentencePiece library (Kudo, 2018).
Revised: The vocabulary size is ﬁxed at 60000 and is estimated through the unigram language model in the SentencePiece library (Kudo, 2018).

Original: 3.1. N OTATION AND E XPERIMENTAL SETUP
Revised: 3.1. N OTATION AND E XPERIMENTAL SETUP

Original: We denote B-BERT trained on language A and B as A-B, e.g., B-BERT trained on English ( en ) and
Revised: We denote B-BERT trained on language A and B as A-B, e.g., B-BERT trained on English ( en ) and

Original: Hindi ( hi ) as en - hi , similarly for Spanish ( es ) and Russian ( ru ).
Revised: Hindi ( hi ) as en - hi , similarly for Spanish ( es ) and Russian ( ru ).

Original: For pre-training, we subsample en , es , and ru Wikipedia to 1GB and use the entire Wikipedia for Hindi.
Revised: For pre-training, we subsample en , es , and ru Wikipedia to 1GB and use the entire Wikipedia for Hindi.

Original: Unless otherwise speciﬁed, for
Revised: Unless otherwise speciﬁed, for

Original: B-BERT training
Revised: B-BERT training

Original: , we use a batch size of 32 , a learning rate of 0 . 0001 , and 2 M training steps.
Revised: , we use a batch size of 32 , a learning rate of 0 . 0001 , and 2 M training steps.

Original: For XNLI, we use the same ﬁne-tuning approach as BERT uses in English and report accuracy.
Revised: For XNLI, we use the same ﬁne-tuning approach as BERT uses in English and report accuracy.

Original: For
Revised: For

Original: NER, we extract BERT representations as features and ﬁne-tune a Bi-LSTM CRF model (without character-wise embeddings) and report F 1 score averaged from 5 runs and its standard deviation.
Revised: NER, we extract BERT representations as features and ﬁne-tune a Bi-LSTM CRF model (without character-wise embeddings) and report F 1 score averaged from 5 runs and its standard deviation.

Original: 3. L INGUISTICS
Revised: 3. L INGUISTICS

Original: Pires et al.
Revised: Pires et al.

Original: (2019) hypothesizes that the cross-lingual ability of M-BERT arises because of the shared word-pieces between source and target languages.
Revised: (2019) hypothesizes that the cross-lingual ability of M-BERT arises because of the shared word-pieces between source and target languages.

Original: However, our experiments show that B-BERT is cross-lingual even when there is no word-piece overlap.
Revised: However, our experiments show that B-BERT is cross-lingual even when there is no word-piece overlap.

Original: Similarly, (Wu & Dredze, 2019) hypothesizes that source language should be selected such that it shares more word-pieces with the target language while our experiment suggests that structural similarity (e.g. word-ordering) is much more important.
Revised: Similarly, (Wu & Dredze, 2019) hypothesizes that source language should be selected such that it shares more word-pieces with the target language while our experiment suggests that structural similarity (e.g. word-ordering) is much more important.

Original: Motivated by the above hypotheses, in this section, we study the contribution of wordpiece overlap and structural similarity for the cross-lingual ability of B-BERT .
Revised: Motivated by the above hypotheses, in this section, we study the contribution of wordpiece overlap and structural similarity for the cross-lingual ability of B-BERT .

Original: 3.2. W ORD - PIECE O VERLAP
Revised: 3.2. W ORD - PIECE O VERLAP

Original: M-BERT is trained using Wikipedia text from 104 languages, and the texts from different languages share some common word-piece vocabulary (like numbers, links, etc.. including actual words, if they have the same script), we refer to this as word-piece overlap.
Revised: M-BERT is trained using Wikipedia text from 104 languages, and the texts from different languages share some common word-piece vocabulary (like numbers, links, etc.. including actual words, if they have the same script), we refer to this as word-piece overlap.

Original: Previous work (Pires et al., 2019) hypothesizes that M-BERT generalizes across languages because these shared word-pieces force the other word-pieces to be mapped to a same shared space
Revised: Previous work (Pires et al., 2019) hypothesizes that M-BERT generalizes across languages because these shared word-pieces force the other word-pieces to be mapped to a same shared space

Original: [Table]
Revised: [Table]

Original: In this section
Revised: In this section

Original: [Table]
Revised: [Table]

Original: we perform experiments to compare cross-lingual performance with and without word-piece overlap.
Revised: we perform experiments to compare cross-lingual performance with and without word-piece overlap.

Original: We construct a new corpus – Fake-English ( enfake ), by shifting the Unicode of each character in English Wikipedia text by a large constant so that there is strictly no character overlap with any other Wikipedia text 4 .
Revised: We construct a new corpus – Fake-English ( enfake ), by shifting the Unicode of each character in English Wikipedia text by a large constant so that there is strictly no character overlap with any other Wikipedia text 4 .

Original: We may consider Fake-English as a different language than
Revised: We may consider Fake-English as a different language than

Original: English, but having the exact same properties except word surface forms
Revised: English, but having the exact same properties except word surface forms

Original: [Table]
Revised: [Table]

Original: We measure the contribution of word-piece overlap as the drop in performance when the word-piece overlap is removed.
Revised: We measure the contribution of word-piece overlap as the drop in performance when the word-piece overlap is removed.

Original: From Table 1, we can see B-BERT is cross-lingual even when there is no wordpiece overlap .
Revised: From Table 1, we can see B-BERT is cross-lingual even when there is no wordpiece overlap .

Original: We can also see that the contribution of word-piece overlap is very small, which is quite surprising and contradictory to the hypothesis by (Pires et al., 2019; Wu & Dredze, 2019).
Revised: We can also see that the contribution of word-piece overlap is very small, which is quite surprising and contradictory to the hypothesis by (Pires et al., 2019; Wu & Dredze, 2019).

Original: 3.2. W ORD -O RDERING S IMILARITY
Revised: 3.2. W ORD -O RDERING S IMILARITY

Original: Words are ordered differently between languages.
Revised: Words are ordered differently between languages.

Original: For example, English has a Subject-Verb-Object order, while Hindi has a Subject-Object-Verb order.
Revised: For example, English has a Subject-Verb-Object order, while Hindi has a Subject-Object-Verb order.

Original: We analyze whether similarity in how words are ordered affects learning cross-lingual transferability.
Revised: We analyze whether similarity in how words are ordered affects learning cross-lingual transferability.

Original: We study the effect of word-ordering similarity by destroying the word-ordering structure through randomly permuting some percentage of words in sentences during pre-training.
Revised: We study the effect of word-ordering similarity by destroying the word-ordering structure through randomly permuting some percentage of words in sentences during pre-training.

Original: We permute both source (Fake-English) and target language (although permuting any one of them would also be sufﬁcient).
Revised: We permute both source (Fake-English) and target language (although permuting any one of them would also be sufﬁcient).

Original: This way, the similarity of word-ordering is hidden from B-BERT .
Revised: This way, the similarity of word-ordering is hidden from B-BERT .

Original: We quantify the amount of permutation by sampling 25% , 50% , 100% of the (cid:0) L 2 (cid:1) pairs of word-pieces in a sentence with L word-pieces, and swap each pair (e.g. wp i , ..., wp j becomes wp j , ..., wp i ).
Revised: We quantify the amount of permutation by sampling 25% , 50% , 100% of the (cid:0) L 2 (cid:1) pairs of word-pieces in a sentence with L word-pieces, and swap each pair (e.g. wp i , ..., wp j becomes wp j , ..., wp i ).

Original: This way of shufﬂing by no means generates a uniform random distribution on permutations, but provides a roughly good way to control the randomness.
Revised: This way of shufﬂing by no means generates a uniform random distribution on permutations, but provides a roughly good way to control the randomness.

Original: Note that for each word-piece, the other word-pieces that appear in its context (other word-pieces in the sentence) are not changed, although the order is changed.
Revised: Note that for each word-piece, the other word-pieces that appear in its context (other word-pieces in the sentence) are not changed, although the order is changed.

Original: We also do not permute during ﬁne-tuning, as we only want to control cross-lingual ability gained during pre-training.
Revised: We also do not permute during ﬁne-tuning, as we only want to control cross-lingual ability gained during pre-training.

Original: [Table]
Revised: [Table]

Original: From Table
Revised: From Table

Original: [Table]
Revised: [Table]

Original: we can see that the performance drops signiﬁcantly when we curtail the word-order similarity between the two languages.
Revised: we can see that the performance drops signiﬁcantly when we curtail the word-order similarity between the two languages.

Original: However
Revised: However

Original: [Table]
Revised: [Table]

Original: the cross-lingual performance is still signiﬁcantly better than random, which indicates that there are other components of structural similarity, which could contribute to the cross-lingual ability of B-BERT .
Revised: the cross-lingual performance is still signiﬁcantly better than random, which indicates that there are other components of structural similarity, which could contribute to the cross-lingual ability of B-BERT .

Original: 3.2. W ORD - FREQUENCY S IMILARITY
Revised: 3.2. W ORD - FREQUENCY S IMILARITY

Original: We also study whether only knowing unigram word frequency allows for good cross-lingual representations.
Revised: We also study whether only knowing unigram word frequency allows for good cross-lingual representations.

Original: Indeed, Zipf’s law indicate that words appear with different frequency, and one may suggest similar meaning words appear with relatively similar frequency in a pair of languages, helping B-BERT learn cross-lingually.
Revised: Indeed, Zipf’s law indicate that words appear with different frequency, and one may suggest similar meaning words appear with relatively similar frequency in a pair of languages, helping B-BERT learn cross-lingually.

Original: We collect the frequency of words in the target language and generate a new monolingual corpus by sampling words based on the frequency, i.e., each sentence is a set of random words sampled from the original unigram frequency.
Revised: We collect the frequency of words in the target language and generate a new monolingual corpus by sampling words based on the frequency, i.e., each sentence is a set of random words sampled from the original unigram frequency.

Original: The only information B-BERT learns from the languages is their unigram frequency, and perhaps sub-word level information and distribution of lengths of sentences.
Revised: The only information B-BERT learns from the languages is their unigram frequency, and perhaps sub-word level information and distribution of lengths of sentences.

Original: We train B-BERT using Fake-English and this newly generated target corpus.
Revised: We train B-BERT using Fake-English and this newly generated target corpus.

Original: From Table 3, we can see that the performance is very poor.
Revised: From Table 3, we can see that the performance is very poor.

Original: Therefore, unigram frequencies alone don’t contain enough information for cross-lingual learning.
Revised: Therefore, unigram frequencies alone don’t contain enough information for cross-lingual learning.

Original: [Table]
Revised: [Table]

Original: 3.2. S TRUCTURAL S IMILARITY
Revised: 3.2. S TRUCTURAL S IMILARITY

Original: We deﬁne the structure of a language as every property of an individual language that is invariant to the script of the language (e
Revised: We deﬁne the structure of a language as every property of an individual language that is invariant to the script of the language (e

Original: [Table]
Revised: [Table]

Original: g., morphology, word-ordering, word frequency are all parts of structure of a language).
Revised: g., morphology, word-ordering, word frequency are all parts of structure of a language).

Original: From Table 1, we can see that BERT transfers very well from Fake-English to
Revised: From Table 1, we can see that BERT transfers very well from Fake-English to

Original: English.
Revised: English.

Original: Also note that, despite not sharing any vocabulary, Fake-English transfers to Spanish,
Revised: Also note that, despite not sharing any vocabulary, Fake-English transfers to Spanish,

Original: Hindi, Russian almost as well as English.
Revised: Hindi, Russian almost as well as English.

Original: On XNLI, where the scores between languages can be compared, the cross-lingual transferability from Fake-English to Spanish is much better than from
Revised: On XNLI, where the scores between languages can be compared, the cross-lingual transferability from Fake-English to Spanish is much better than from

Original: Fake-English to Hindi/Russian.
Revised: Fake-English to Hindi/Russian.

Original: Since they do not share any word-pieces, this better transferability comes from the structure similarity being closer between Spanish and Fake-English.
Revised: Since they do not share any word-pieces, this better transferability comes from the structure similarity being closer between Spanish and Fake-English.

Original: Through Section 3.2.2 we know that between two languages, even when there are no word-piece overlap, nor any particular order of words in a sentences, B-BERT still learns some cross-lingual features.
Revised: Through Section 3.2.2 we know that between two languages, even when there are no word-piece overlap, nor any particular order of words in a sentences, B-BERT still learns some cross-lingual features.

Original: Section 3.2.3 shows from the other side that if B-BERT is given only little information (unigram frequency), B-BERT learns nearly no cross-lingual features.
Revised: Section 3.2.3 shows from the other side that if B-BERT is given only little information (unigram frequency), B-BERT learns nearly no cross-lingual features.

Original: These results suggest that we should shed more light on studying the structural similarity between languages, for example, higher order of k − gram or k − co-occur frequencies (notice that the word ordering experiment can be seen as giving B-BERT k − co-occurrence word frequencies where k is the length of the longest sentence in the corpus).
Revised: These results suggest that we should shed more light on studying the structural similarity between languages, for example, higher order of k − gram or k − co-occur frequencies (notice that the word ordering experiment can be seen as giving B-BERT k − co-occurrence word frequencies where k is the length of the longest sentence in the corpus).

Original: In this study, we don’t further dissect the structure of language.
Revised: In this study, we don’t further dissect the structure of language.

Original: Despite its amorphous deﬁnition, our experiment clearly shows that structural similarity is crucial for cross-lingual transfer.
Revised: Despite its amorphous deﬁnition, our experiment clearly shows that structural similarity is crucial for cross-lingual transfer.

Original: 3. A RCHITECTURE
Revised: 3. A RCHITECTURE

Original: From Section 3.2, we observe that B-BERT recognizes the language structure effectively.
Revised: From Section 3.2, we observe that B-BERT recognizes the language structure effectively.

Original: In this section, we envisage that BERT potentially gains the ability to recognize language structure also because of its architecture.
Revised: In this section, we envisage that BERT potentially gains the ability to recognize language structure also because of its architecture.

Original: In this section, we study the contribution of different components of
Revised: In this section, we study the contribution of different components of

Original: B-BERT architecture namely (i) depth, (ii) multi-head attention and, (iii) the total number of parameters.
Revised: B-BERT architecture namely (i) depth, (ii) multi-head attention and, (iii) the total number of parameters.

Original: The motivation is to understand which components are crucial for its cross-lingual ability.
Revised: The motivation is to understand which components are crucial for its cross-lingual ability.

Original: We perform all our cross-lingual experiments on the XNLI dataset with Fake-English as the source and Russian as the target language; we measure cross-lingual ability by the difference between the performance of Fake-English and Russian (lesser the difference better the cross-lingual ability).
Revised: We perform all our cross-lingual experiments on the XNLI dataset with Fake-English as the source and Russian as the target language; we measure cross-lingual ability by the difference between the performance of Fake-English and Russian (lesser the difference better the cross-lingual ability).

Original: 3.3. D EPTH
Revised: 3.3. D EPTH

Original: We presume the ability of B-BERT to extract good semantic and structural features is a crucial reason for its cross-lingual effectiveness, and the deepness of B-BERT helps it extract good language features.
Revised: We presume the ability of B-BERT to extract good semantic and structural features is a crucial reason for its cross-lingual effectiveness, and the deepness of B-BERT helps it extract good language features.

Original: In this section, we study the effect of depth on both the monolingual and cross-lingual performance of B-BERT .
Revised: In this section, we study the effect of depth on both the monolingual and cross-lingual performance of B-BERT .

Original: We ﬁx the number of attention heads and change the size of hidden units and intermediate units such that the total number of parameters are almost the same (size of intermediate units is always 4 × size of hidden units).
Revised: We ﬁx the number of attention heads and change the size of hidden units and intermediate units such that the total number of parameters are almost the same (size of intermediate units is always 4 × size of hidden units).

Original: From Table 4, we can see that a deeper model not only perform better on English but are also better cross-lingual.
Revised: From Table 4, we can see that a deeper model not only perform better on English but are also better cross-lingual.

Original: We can also see a strong correlation between performance on English and crosslingual ability ( ∆ ), which further supports our assumption that the ability to extract good semantic and structural features is a crucial reason
Revised: We can also see a strong correlation between performance on English and crosslingual ability ( ∆ ), which further supports our assumption that the ability to extract good semantic and structural features is a crucial reason

Original: [Table]
Revised: [Table]

Original: 3.3. M ULTI - HEAD ATTENTION
Revised: 3.3. M ULTI - HEAD ATTENTION

Original: In this section
Revised: In this section

Original: [Table]
Revised: [Table]

Original: we study the effect of multi-head attention on the cross-lingual ability of B-BERT .
Revised: we study the effect of multi-head attention on the cross-lingual ability of B-BERT .

Original: We ﬁx the depth and the total number of parameters – which is a function of depth and size of hidden and intermediate layers and study the performance for the different number of attention heads.
Revised: We ﬁx the depth and the total number of parameters – which is a function of depth and size of hidden and intermediate layers and study the performance for the different number of attention heads.

Original: From
Revised: From

Original: Table
Revised: Table

Original: [Table]
Revised: [Table]

Original: we can see that the number of attention heads doesn’t have a signiﬁcant effect on crosslingual ability( ∆ ) – B-BERT is satisfactorily cross-lingual even with a single attention head, which is in agreement with the recent study on monolingual BERT (Voita et al., 2019; Clark et al., 2019)
Revised: we can see that the number of attention heads doesn’t have a signiﬁcant effect on crosslingual ability( ∆ ) – B-BERT is satisfactorily cross-lingual even with a single attention head, which is in agreement with the recent study on monolingual BERT (Voita et al., 2019; Clark et al., 2019)

Original: [Table]
Revised: [Table]

Original: 3.3. T OTAL N UMBER OF P ARAMETERS
Revised: 3.3. T OTAL N UMBER OF P ARAMETERS

Original: Similar to depth, we also anticipate that a large number of parameters could potentially help
Revised: Similar to depth, we also anticipate that a large number of parameters could potentially help

Original: B-BERT extract good semantic and structural features.
Revised: B-BERT extract good semantic and structural features.

Original: We study the effect of the total number of parameters on cross-lingual performance by ﬁxing the number of attention heads and depth; we change the number of parameters by changing the size of hidden and intermediate units (size of intermediate units is always 4 × size of hidden units).
Revised: We study the effect of the total number of parameters on cross-lingual performance by ﬁxing the number of attention heads and depth; we change the number of parameters by changing the size of hidden and intermediate units (size of intermediate units is always 4 × size of hidden units).

Original: From Table
Revised: From Table

Original: [Table]
Revised: [Table]

Original: we can see that the total number of parameters is not as signiﬁcant as depth; however, below a threshold
Revised: we can see that the total number of parameters is not as signiﬁcant as depth; however, below a threshold

Original: [Table]
Revised: [Table]

Original: the number of parameters seems signiﬁcant
Revised: the number of parameters seems signiﬁcant

Original: [Table]
Revised: [Table]

Original: which suggests that B-BERT requires a certain minimum number parameters to extract good semantic and structural feature.
Revised: which suggests that B-BERT requires a certain minimum number parameters to extract good semantic and structural feature.

Original: 3.3. G ENERALIZATION TO BERT WITH MORE LANGUAGES
Revised: 3.3. G ENERALIZATION TO BERT WITH MORE LANGUAGES

Original: Here we show that the results for model structure hold also for a more multilingual case; to further illustrate this, we experiment on four language BERT (en, es, hi, ru).
Revised: Here we show that the results for model structure hold also for a more multilingual case; to further illustrate this, we experiment on four language BERT (en, es, hi, ru).

Original: From Table 7, we can see that the performance on XNLI is comparable even with just 15% of parameters
Revised: From Table 7, we can see that the performance on XNLI is comparable even with just 15% of parameters

Original: [Table]
Revised: [Table]

Original: and just 1 or 3 attention heads when the depth is good enough, which is in agreement with our observations in the main text.
Revised: and just 1 or 3 attention heads when the depth is good enough, which is in agreement with our observations in the main text.

Original: 3. I NPUT AND L EARNING O BJECTIVE
Revised: 3. I NPUT AND L EARNING O BJECTIVE

Original: In this section, we study the effect of input representation and learning objectives on cross-lingual ability of B-BERT .
Revised: In this section, we study the effect of input representation and learning objectives on cross-lingual ability of B-BERT .

Original: BERT is a Transformer model trained with Masked Language Modeling (MLM) and Next Sentence Prediction (NSP) objectives.
Revised: BERT is a Transformer model trained with Masked Language Modeling (MLM) and Next Sentence Prediction (NSP) objectives.

Original: We study the effect of NSP as recent works (Lample & Conneau, 2019; Joshi et al., 2019; Liu et al., 2019) show that the NSP objective hurts the performance on several monolingual tasks.
Revised: We study the effect of NSP as recent works (Conneau & Lample, 2019; Joshi et al., 2019; Liu et al., 2019) show that the NSP objective hurts the performance on several monolingual tasks.

Original: To verify whether B-BERT can learn in language agnostic settings, We also study the use of language identity markers.
Revised: To verify whether B-BERT can learn in language agnostic settings, We also study the use of language identity markers.

Original: We are also interested in studying the effect of tokenization and language representation – using characters and words vocabulary instead of word-pieces.
Revised: We are also interested in studying the effect of tokenization and language representation – using characters and words vocabulary instead of word-pieces.

Original: 3.4. N EXT SENTENCE P REDICTION (NSP)
Revised: 3.4. N EXT SENTENCE P REDICTION (NSP)

Original: The input to the BERT is a pair of sentences separated by a special token such that half the time the second sentence is the next and rest half the time, it is a random sentence.
Revised: The input to the BERT is a pair of sentences separated by a special token such that half the time the second sentence is the next and rest half the time, it is a random sentence.

Original: The NSP objective of
Revised: The NSP objective of

Original: BERT ( B-BERT ) is to predict whether the second sentence comes after the ﬁrst one in the original text.
Revised: BERT ( B-BERT ) is to predict whether the second sentence comes after the ﬁrst one in the original text.

Original: We study the effect of NSP objective by comparing the performance of B-BERT pre-trained with and without this objective.
Revised: We study the effect of NSP objective by comparing the performance of B-BERT pre-trained with and without this objective.

Original: From Table 8, we can see that the NSP objective hurts the crosslingual performance even more than monolingual performance.
Revised: From Table 8, we can see that the NSP objective hurts the crosslingual performance even more than monolingual performance.

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table]
Revised: [Table]

Original: 3.4. L ANGUAGE I DENTITY M ARKER
Revised: 3.4. L ANGUAGE I DENTITY M ARKER

Original: In Section 3.
Revised: In Section 3.

Original: [Table]
Revised: [Table]

Original: we argue that B-BERT is cross-lingual because of its ability to recognize language structure similarities, and hence we presume adding a language identity marker doesn’t affect its cross-lingual ability.
Revised: we argue that B-BERT is cross-lingual because of its ability to recognize language structure similarities, and hence we presume adding a language identity marker doesn’t affect its cross-lingual ability.

Original: Even if we don’t add a language identity marker, BERT learns language identity (Wu & Dredze, 2019).
Revised: Even if we don’t add a language identity marker, BERT learns language identity (Wu & Dredze, 2019).

Original: To incorporate language identity in the input, we add a different end of string tokens([SEP]) for different languages (i
Revised: To incorporate language identity in the input, we add a different end of string tokens([SEP]) for different languages (i

Original: [Table]
Revised: [Table]

Original: e., our input format is [CLS] SENT1 [SEP-A] SENT [SEP-B], where A and B are languages corresponding to SENT1 and SENT2 respectively).
Revised: e., our input format is [CLS] SENT1 [SEP-A] SENT [SEP-B], where A and B are languages corresponding to SENT1 and SENT2 respectively).

Original: From
Revised: From

Original: Table 9, we can see that adding language identity marker doesn’t affect cross-lingual performance.
Revised: Table 9, we can see that adding language identity marker doesn’t affect cross-lingual performance.

Original: [Table]
Revised: [Table]

Original: 3.4. C HARACTER VS . W ORD -P IECE VS . WORD
Revised: 3.4. C HARACTER VS . W ORD -P IECE VS . WORD

Original: We compare the performance of B-BERT with character, word-piece, and word tokenized input.
Revised: We compare the performance of B-BERT with character, word-piece, and word tokenized input.

Original: For character B-BERT , we use all the characters as vocabulary
Revised: For character B-BERT , we use all the characters as vocabulary

Original: [Table]
Revised: [Table]

Original: and for word B-BERT , we use the most frequent 100000 words as vocabulary.
Revised: and for word B-BERT , we use the most frequent 100000 words as vocabulary.

Original: From Table 10, we can see that the cross-lingual performance (difference between source and target language performance) of B-BERT with wordpiece tokenized is similar to that of word tokenized, while both are better than character tokenized.
Revised: From Table 10, we can see that the cross-lingual performance (difference between source and target language performance) of B-BERT with wordpiece tokenized is similar to that of word tokenized, while both are better than character tokenized.

Original: We believe that this is because word-pieces and words carry much more information than characters, allowing B-BERT to learn similarities between the two languages easier.
Revised: We believe that this is because word-pieces and words carry much more information than characters, allowing B-BERT to learn similarities between the two languages easier.

Original:  D ISCUSSION AND F UTURE WORK
Revised:  D ISCUSSION AND F UTURE WORK

Original: This paper provides a systematic empirical study addressing the cross-lingual ability of B-BERT .
Revised: This paper provides a systematic empirical study addressing the cross-lingual ability of B-BERT .

Original: The analysis covers three dimensions: (1) Linguistics properties and similarities of the source and target languages, (2) Neural Architecture, and (3) Input representation and Learning Objective.
Revised: The analysis covers three dimensions: (1) Linguistics properties and similarities of the source and target languages, (2) Neural Architecture, and (3) Input representation and Learning Objective.

Original: In order to gauge the language similarity aspect needed to make B-BERT successful, we created a new language – Fake-English – and this allows us to study the effect of word-piece overlap while maintaining all other properties of the source language.
Revised: In order to gauge the language similarity aspect needed to make B-BERT successful, we created a new language – Fake-English – and this allows us to study the effect of word-piece overlap while maintaining all other properties of the source language.

Original: Our experiments reveal some interesting 
Revised: Our experiments reveal some interesting and

Original: [Table]
Revised: [Table]

Original: and surprising results like the fact that word-piece overlap on the one hand, and multi-head attention on the other, are both not signiﬁcant, whereas structural similarity and the depth of B-BERT are crucial for its cross-lingual ability.
Revised: surprising results. The most notable ﬁnding is that word-piece overlap on the one hand, and multihead attention on the other, are both not signiﬁcant, whereas structural similarity and the depth of B-BERT are crucial for its cross-lingual ability.

Original: While, in order to better control interference among languages
Revised: While in order to better control interference among languages

Original: [Table]
Revised: [Table]

Original: we studied the cross-lingual ability of B-BERT instead of those of M-BERT , it would be interesting now to extend this study, allowing for more interactions among languages.
Revised: we studied the cross-lingual ability of B-BERT instead of those of M-BERT , it would be interesting now to extend this study, allowing for more interactions among languages.

Original: We leave it to future work to study these interactions.
Revised: We leave it to future work to study these interactions.

Original: In particular, one important question is to understand the extent to which adding to M-BERT languages that are related to the target language, helps the model’s cross-lingual ability.
Revised: In particular, one important question is to understand the extent to which adding to M-BERT languages that are related to the target language, helps the model’s cross-lingual ability.

Original: We introduced the term Structural Similarity , despite its obscure deﬁnition, and show its signiﬁcance in cross-lingual ability.
Revised: We introduced the term Structural Similarity , despite its obscure deﬁnition, and show its signiﬁcance in cross-lingual ability.

Original: Another interesting future work could be to develop a better deﬁnition and, consequently, a ﬁner set of experiments, to better understand the Structural similarity and study its individual components.
Revised: Another interesting future work could be to develop a better deﬁnition and, consequently, a ﬁner set of experiments [Table] to better understand the Structural similarity and study its individual components.

Original: Finally
Revised: Finally

Original: [Table]
Revised: [Table]

Original: we note an interesting observation made in Table 11.
Revised: we note an interesting observation made in Table 11.

Original: We observe a drastic drop in the entailment performance of B-BERT when the premise and hypothesis are in different languages.
Revised: We observe a drastic drop in the entailment performance of B-BERT when the premise and hypothesis are in different languages.

Original: (This data was created using XNLI when in the original form the languages contain  same premise and hypothesis pair).
Revised: (This data was created using XNLI where in the original form the languages contain the same premise and hypothesis pair).

Original: One of the possible explanations could be that BERT is learning to make textual entailment decisions by matching words or phrases in the premise to those in the hypothesis.
Revised: One of the possible explanations could be that BERT is learning to make textual entailment decisions by matching words or phrases in the premise to those in the hypothesis.

Original: This question, too, is left as a future direction
Revised: This question, too, is left as a future direction

Original: [Table]
Revised: [Table]

Original: A CKNOWLEDGMENTS
Revised: A CKNOWLEDGMENTS

Original: This work was supported by Contracts W911NF-15-1-0461, HR0011-15-C-
Revised: This work was supported by Contracts W911NF-15-1-0461, HR0011-15-C-

Original: [Table]
Revised: [Table]

Original: and HR0011-182-0052 from the US Defense Advanced Research Projects Agency (DARPA), by Google Cloud, and by Cloud TPUs from Googles TensorFlow Research Cloud (TFRC).
Revised: and HR0011-182-0052 from the US Defense Advanced Research Projects Agency (DARPA), by Google Cloud, and by Cloud TPUs from Googles TensorFlow Research Cloud (TFRC).

Original: The views expressed are those of the authors and do not reﬂect the ofﬁcial policy or position of the Department of Defense or the
Revised: The views expressed are those of the authors and do not reﬂect the ofﬁcial policy or position of the Department of Defense or the

Original: U.S. Government or Google.
Revised: U.S. Government or Google.