Data-driven Cross-lingual Syntax: - 麻省理工学院人工智能研究专业

Data-driven Cross-lingual Syntax:
An Agreement Study with Massively
Multilingual Models

Andrea Gregor de Varda
University of Milano-Bicocca
a.devarda@campus.unimib.it

Marco Marelli
University of Milano-Bicocca
m.marelli@unimib.it

Massively multilingual models such as mBERT and XLM-R are increasingly valued in Nat-
ural Language Processing research and applications, due to their ability to tackle the uneven
distribution of resources available for different languages. The models’ ability to process multiple
languages relying on a shared set of parameters raises the question of whether the grammatical
knowledge they extracted during pre-training can be considered as a data-driven cross-lingual
grammar. The present work studies the inner workings of mBERT and XLM-R in order to test
the cross-lingual consistency of the individual neural units that respond to a precise syntactic
现象, 那是, number agreement, in ﬁve languages (英语, 德语, 法语, Hebrew,
俄语). We found that there is a signiﬁcant overlap in the latent dimensions that encode
agreement across the languages we considered. This overlap is larger (A) for long- vis-`a-vis short-
distance agreement and (乙) when considering XLM-R as compared to mBERT, and peaks in the
intermediate layers of the network. We further show that a small set of syntax-sensitive neurons
can capture agreement violations across languages; 然而, their contribution is not decisive in
agreement processing.

1. 介绍

Massively multilingual models (MMMs) such as multilingual BERT (mBERT, Devlin
等人. 2019) and XLM-RoBERTa (XLM-R, Conneau et al. 2020A) are transformer-based
language representation models trained simultaneously on multilingual text in several
语言 (104 和 100, 分别). They do not involve any architectural changes
with respect to their monolingual counterparts (BERT and RoBERTa), nor any reliance
on any explicit cross-lingual signal. MMMs reach impressive performance scores in
tasks involving zero-shot cross-lingual transfer, a procedure that entails the ﬁne-tuning
of the model on supervised data in a language L1 and its application to a different

动作编辑器: Byron Wallace. 提交材料已收到: 27 六月 2022; 收到修订版: 24 九月
2022; 接受出版: 12 十月 2022.

https://doi.org/10.1162/coli a 00472

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计算语言学

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language L2, with no additional training.1 This procedure has been shown to be success-
ful across a variety of languages and downstream tasks (Pires, Schlinger, and Garrette
2019; Wu and Dredze 2019; Dufter and Sch ¨utze 2020; 刘等人. 2020; Lauscher et al. 2020;
see Doddapaneni et al. 2021 for a review). Although performance levels tend to be pos-
itively correlated with the typological similarity between the two languages (Lauscher
等人. 2020), zero-shot cross-lingual transfer yields surprising results in languages
written in different scripts (Pires, Schlinger, and Garrette 2019) and with little or no
(Karthikeyan et al. 2020); (Conneau et al. 2020乙) vocabulary overlap. With only a
subset of the world’s languages being properly represented in the evolving language
技术, the distribution of resources available for NLP researchers is extremely
asymmetrical (Joshi et al. 2020). Massively multilingual models represent an attempt
to temper the effects of this imbalance by exploiting the knowledge that can be shared
across languages.

The performance of MMMs in the transfer tasks hints at the possibility that their
internal representations might be inherently cross-lingual (Pires, Schlinger, and Garrette
2019; Dufter and Sch ¨utze 2020; Guarasci et al. 2022). Dufter and Sch ¨utze (2020) argue
that mBERT multilingualism might be due to its ﬁnite number of dimensions, 哪个
forces it to exploit common structures to compress representations across languages.
The question of whether a multilingual model induces a shared representational space
where abstract cross-linguistic regularities are encoded through a common set of pa-
rameters is remindful of the debate on the neural underpinning of linguistic knowledge
in multilingual individuals (see Dhar and Bisazza [2021] for similar considerations). 在
特别的, the problem is reminiscent of the question of whether the neural resources
allocated to different languages in a multilingual brain overlap (at least partially, 看
Perani et al. 1998; Abutalebi, Cappa, and Perani 2001; Perani and Abutalebi 2005; 绿色的
2008) or involve functionally independent neural populations (Kim et al. 1997; Tham
等人. 2005; Tan et al. 2011; 徐等. 2017). If we consider the possibility of looking
at artiﬁcial neural networks as a different “species” (Cummins and Schwarz 1988;
McCloskey 1991), in a fashion that reminds us of the study of animal models, the study
of the representations produced by these networks might offer novel insights into the
space of possible solutions to the cognitive question mentioned above.

A modest but increasing number of ﬁndings is contributing to the question of
whether MMMs develop a data-driven universal grammar through an analysis of their
internal states. A study targeting mBERT vector representations has shown that syntac-
tic trees can be retrieved from its intermediate representational subspaces, with these
subspaces being approximately shared across languages (志, Hewitt, and Manning
2020). These intermediate subspaces can be used in machine translation, by identifying
the nearest neighbor in different representation spaces given a sentence in a source
language and a set of candidates in a target language (Pires, Schlinger, and Garrette
2019). Other studies have performed representational similarity analysis comparing
encoded sentences in different languages; while most results suggested that MMMs
develop a cross-lingual space in the intermediate layers (Conneau et al. 2020乙; Del and
Fishel 2021; Muller et al. 2021), as shown by converging similarity between sentence
representations in deeper layers of the networks, contrasting results have documented
an opposed pattern when sentence representations are obtained through CLS pooling
instead of mean-pooling (Singh et al. 2019, although see Del and Fishel 2021 for a case
against the CLS pooling strategy).

1 Where L1 and L2 are typically a resource-rich and resource-poor language, 分别.

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de Varda and Marelli

Data-driven Cross-lingual Syntax

The work we reviewed insofar targeted vector representations as a whole, neglect-
ing the role of the individual parameters in the embeddings. 然而, while research
in NLP used to largely overlook the single dimensions in the neural representations,
a recent research line is starting to investigate the linguistic properties encoded in
individual neurons and attention weights (see for instance Karpathy, 约翰逊, 和
Fei-Fei 2015; 李等人. 2015; 雷德福, Jozefowicz, and Sutskever 2017; Tang et al. 2017;
Kementchedjhieva and Lopez 2018; Bau et al. 2018; Dalvi et al. 2019A; Lakretz et al.
2019; Pinter, Marone, and Eisenstein 2019; Serrano and Smith 2019). Aiming to ex-
tend this line of analysis to a multilingual setting, we isolated the contribution of the
individual neurons in mBERT and XLM-R, deﬁned as dimensions in the deep latent
陈述. While most studies assessing the models’ cross-lingualism considered
phrasal representations as a whole, without discerning between semantic and syntactic
特性 (Pires, Schlinger, and Garrette 2019; 刘等人. 2020; Del and Fishel 2021),
we restricted our study to number agreement, a structure-dependent phenomenon. 它
has been shown that BERT captures syntactic features in the intermediate
layers
(Jawahar, Sagot, and Seddah 2019), which are the same that show the highest repre-
sentational similarity across languages in the multilingual model (Del and Fishel 2021).
This layer-wise convergence of syntactic and cross-lingual knowledge in (米)BERT in-
spired our choice to constrain our study to a structural linguistic feature. The general
question of whether MMMs represent patterns that generalize across languages is
hereby framed as an inquiry into the cross-lingual stability of the neural units that
encode number agreement.

6, 9
(西德:75)

(西德:74)

2. 相关工作

A productive research line in computational linguistics has focused on the analysis of
the linguistic features learned by neural language models. This line of analysis aimed
at testing whether sequence processing networks were able to construct hierarchical
representations of the linguistic input, or either relied on local heuristics without ac-
quiring core knowledge of different grammatical phenomena. A popular trend within
this framework relied on the large-scale unsupervised training of a language model,
and the ﬁne-grained evaluation of the probabilities it assigned to different linguistic
units in a controlled setting as a “behavioral” correlate of its ability to capture the
regularities of a given language. Along this line of work, numerous studies have used
long-distance number agreement as a way of probing the networks’ ability to encode
structure-dependent relationships (扁豆, Dupoux, and Goldberg 2016; Bernardy and
Lappin 2017; Gulordava et al. 2018; Kuncoro et al. 2018; Marvin and Linzen 2018;
Goldberg 2019; 从斯海德尔, Mueller, and Linzen 2019; Lasri, Lenci, and Poibeau 2022).
While all the previous studies evaluated the models on their native tasks, Lakretz et al.
(2019) presented an ablation-based study of the inner mechanisms that underlie number
agreement processing in LSTMs at the single neuron level, showing that a very sparse
set of specialized units carried number features from the subject to the verb across the
intervening material. 与此相类似, Finlayson et al. (2021) have used causal analysis
to implicate speciﬁc neurons in transformer models.

With the debut of multilingual models, the previous studies were replicated in
different languages, showing that mBERT successfully captures syntax-sensitive agree-
ment patterns (Bacon and Regier 2019; Mueller et al. 2020). 然而, these experiments
limited their focus on the analysis of mBERT’s predictive behavior, overlooking the
functioning of its internal processes. A complementary line of analysis has investigated

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how multilingual models encode other linguistic attributes in their internal represen-
tations. 例如, Gonen, Ravfogel, and Goldberg (2022) have shown that gender
information is encoded in both language-speciﬁc and language-neutral subspaces in the
embeddings of mBERT. 此外, Antverg and Belinkov (2021) have investigated
the cross-lingual consistency in the units of mBERT and XLM-R that responded to
different morphological features, showing that there is a signiﬁcant overlap in the
latent dimensions that encode attributes such as gender, tense, and number. 相似地,
Stanczak et al. (2022) have probed the same models in 43 语言, and on a variety
of morphosyntactic categories. 然而, while these two studies have investigated the
encoding of number in MMMs, they have not investigated number agreement, 那是,
the structural relationship that is instantiated between a subject and a verb in a well-
formed sentence. To ﬁll this research gap, we tested whether the processes that underpin
number agreement computation across languages could be ascribed to an overlapping
set of latent dimensions in the structural embeddings of the models.

3. Materials and Methods

3.1 Language Models

Our experiments were performed utilizing the native masked language modeling com-
ponent of mBERT and XLM-R. The conﬁgurations of the models were left unaltered
with respect to their original releases (Devlin et al. 2019; Conneau et al. 2020A). In par-
针状的, we relied on the multilingual version of BERTBASE (cased) and on XLM-RBASE.
The two networks share an analogous structural conﬁguration: They are composed of
12 layers, 12 self-attention heads, and a hidden size of 768. 然而, while mBERT is
jointly trained with a masked language modeling and a next sentence prediction (NSP)
客观的, XLM-R drops the latter component, and increases the amount of training
数据. The networks did not undergo any ﬁne-tuning nor adaptation process, 像他们
were used as out-of-the-box masked language models. We did not mask any word
throughout this work.

3.2 Materials

The agreement data was obtained from the CLAMS dataset2 (Mueller et al. 2020), A
cross-linguistic resource for the syntactic evaluation of word prediction models. CLAMS
comprises subject-verb agreement challenge sets for English, 德语, 法语, 俄语,
and Hebrew, constructed by means of artiﬁcial grammars. Note that in abstract terms
these languages encode agreement patterns in a similar way, 那是, through a form of
morphological inﬂection that links subject and verb on account of their grammatical
数字. For the sake of simplicity, out of the seven syntactic constructions covered
in the original dataset we only included simple agreement and long-distance VP-
协调 (henceforth short- and long-distance agreement; 见图 1). We selected
these two conditions as they represent the settings with the shortest and the longest
dependency length between the subject and the verb, 分别. While in short-
distance agreement the two constituents are immediately adjacent, in long-distance

2 Publicly available at https://github.com/aaronmueller/clams.

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de Varda and Marelli

Data-driven Cross-lingual Syntax

(1)

(2)

(A)
(乙)

作者
*作者

smiles
smile

knows
knows

许多
许多

不同的
不同的

foreign
foreign

语言
语言

和
和

likes
喜欢

到
到

手表
手表

作者
*作者

(A)
(乙)
电视
电视

节目
节目

数字 1
English examples of grammatical (A) and ungrammatical (乙) sentences in the simple agreement
(1) and long-distance VP-coordination (2) 状况.

agreement they are separated by a large amount of intervening verbal material (即,
the VP projection of the main phrase and the coordinating conjunction).

3.3 程序

In order to identify the most relevant units with respect to the agreement task, 我们
adopted the Linguistic Correlation Analysis (生命周期评估) procedure (Dalvi et al. 2019A,乙),
a supervised method based on linear classiﬁcation. The ﬁrst step of LCA consists of
extracting the neuron activations from the model in response to the input words. 然后,
a logistic classiﬁer is trained to predict a label (in our case, the grammaticality of
the sentence obtained by including the word in the phrasal context) from the overall
internal state of the model, with cross-entropy loss and elastic net regularization as
additional loss term (Zou and Hastie 2005), with λ1 = λ2 = 0.001. The trained weights
of the classiﬁer are used as a measure of the relevance of the corresponding units with
respect to the linguistic property being investigated (IE。, the binary label of grammat-
ical acceptability); this allows sorting the neurons according to the absolute value of
their respective weights. In our study, we restricted our analyses to the activations in
response to the verb that should instantiate an agreement relationship with the subject
(例如, smiles/*smile, likes/*like in Figure 1). As a result of this choice, we trained the logistic
classiﬁers with the verb representations as input. In the case of multi-token verbs,
the activations corresponding to the two tokens were averaged, following Dalvi et al.
(2019A).

Probing classiﬁers have the undeniable advantage of being a ﬂexible analysis tech-
nique that can help researchers understand the roles and dynamics of the hidden
components of a network and diagnose potential problems (Alain and Bengio 2016).
然而, several shortcomings of probing classiﬁers have been highlighted in the liter-
ature. 例如, it has been emphasized that the probing framework might highlight
correlations between the representations generated by a language model and a given
linguistic property, but it does inform us on the role of this property in the predictions
of the model (Belinkov and Glass 2019; Belinkov 2022). Antverg and Belinkov (2021)
have proposed a methodology to rank individual neurons in language models without
the need for an external probe. This procedure involves the computation of the average
network activation q(z) for every categorical label z ∈ Z; 然后, a simple element-wise
subtraction between the centroids of each category is calculated to assess the differential
role of each neuron across classes. The ranking is then obtained by sorting the neurons
according to their absolute value in the vector difference. It has been shown that probe-
free rankings better identify neural units that are actually used by the language mod-
这, as demonstrated through selective interventions (Antverg and Belinkov 2021). 在

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order to complement the results we obtained with the linear probing, and to offset the
limitations that are inherent in the probing framework, we also experiment with such a
probeless method.3

The ranking processes were performed independently for (A) each ranking method
(linear and probeless), (乙) 每个型号 (mBERT and XLM-R), (C) each agreement condition
(长的- and short-distance), 和 (d) each individual language considered, 在一个 2 × 2 ×
2 × 5 design which allowed us to derive 40 distinct rankings. In all cases, the classiﬁer
was trained and tested on two subsets of the original data (80% 火车, 20% 测试). 在
order to license meaningful comparisons on the performances of the classiﬁers across
语言, we downsampled all the short-distance challenge sets to 280 项目 (224 在里面
training and 56 in the test set), and the long-distance datasets to 800 项目 (640 训练,
160 测试). All the procedures described above were implemented with the NeuroX toolkit
(Dalvi et al. 2019乙), a Python package to perform interpretation and analysis of deep
神经网络.

Once the neuron ranking was obtained, we evaluated the cross-lingual consistency
in the set of neural units computing agreement across languages. In order to do so,
we assessed the intersection between the top 100 neurons independently selected in
each language.4 In practice, we did not test the statistical signiﬁcance of the cross-
lingual overlap at the level of the whole architecture, since the estimate of our test
would have been biased by the sequential ﬂow of information within the network. 这
cross-lingual congruence of the neural units processing syntactic agreement could be
overestimated if one does not take into account the fact that similar processes with
a comparable degree of structural abstraction are likely to be processed in the same
layers. 直观地, a dimension in the ﬁrst layer of XLM-R or mBERT embeddings is less
likely to occupy a high position in the neuron ranking, since it is already known that
syntactic features are processed in the intermediate layers of the architecture (Jawahar,
Sagot, and Seddah 2019); because the probability associated with a given size of a set
intersection is critically dependent on the size of the population from which the sets are
sampled, a conservative approach to avoid a type-1 error is to consider a single layer
as the reference population. 因此, we previously searched for the layers that were more
relevant in the computation of cross-lingual agreement, and then evaluated the cross-
lingual overlap in the within-layer neural population. The statistical signiﬁcance of the
resulting intersection size was computed through the super exact test (王, 赵,
and Zhang 2015), a procedure for computing the distributions of multi-set intersections
based upon combinatorial theory.

4. 结果

4.1 Layer-wise Analyses

In order to restrict our intersection analysis to a pre-speciﬁed layer, we ﬁrst analyzed
the performance of a classiﬁer trained to predict the grammaticality label in response to
each layer’s activation. The results are summarized in Figure 2. In the case of mBERT,

3 We thank an anonymous reviewer for the suggestion.
4 We considered 100 units as Antverg and Belinkov (2021); 然而, following an anonymous reviewer’s
suggestion, we analyzed post hoc the ratio of weight mass that could be ascribed to these neurons. 这
顶部 100 units contribute to a substantial proportion of the weight mass of the layer (一般 45.46%),
while constituting only the 13.02% of the layer units (N= 768). We report a detailed analysis in
附录 1.

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Data-driven Cross-lingual Syntax

(A) Short-distance agreement, mBERT

(乙) Long-distance agreement, mBERT

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(d) Long-distance agreement, XLM-R

数字 2
Layer-wise performance of the logistic classiﬁer. The layer 0 includes the embedding layer
陈述. The vertical dashed line indicates the peak of the average accuracy obtained by
the classiﬁers in the ﬁve languages considered.

the highest average accuracy scores in the short- (2A) and the long-distance (2乙) 骗局-
ditions were obtained from the activations of the eighth (0.8707) and ninth (0.9505)
层, 分别. XLM-R showed a higher degree of congruence across conditions,
since the highest scores were obtained in the seventh layer both in the short- (0.8089,
2C) and in the long-distance datasets (0.98775, 2d). A clear pattern that emerges from
the graphs is that the accuracy curve is highly dependent on the language considered.
In the case of short-distance agreement, mBERT’s performance in Russian falls 0.1474
points below the average; in the long-distance condition, the performance levels in
Hebrew is 0.0880 points lower than the mean. The classiﬁers built upon the XLM-R
representations perform consistently worse in Hebrew, where their performance levels
是 0.1661 和 0.0420 points below average in the short- and in the long-distance con-
版本, 分别. These results corroborate the ﬁnding that mBERT does not learn
equally high-quality representations for its 104 语言 (Wu and Dredze 2020), 和
extends this observation to XLM-R. The relatively poor performance scores obtained in
Hebrew and Russian are also consistent with the results of the standard predictive tests
obtained by Mueller et al. (2020), where mBERT’s accuracy in the agreement tasks was
noticeably lower in the two languages written in non-Latin scripts. 尽管如此, 这
pattern of performance across layers seems to be stable across languages and models:
predictably, the activations extracted from the most shallow layers are not a solid basis

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for the detection of grammatical violations; the classiﬁcation accuracy increases in the
intermediate layers of the network, and declines in the deepest layers.

4.2 Intersections
4.2.1 Linguistic Correlation Analysis Rankings. Building upon these results, we conﬁned
our multi-set intersection analyses to the layers that achieved the best results in the
分类任务, 即, the seventh layer for XLM-R, and the eighth and the ninth
layer for mBERT (short- and long-distance agreement, 分别). The results of
the super exact test on the cross-lingual neural overlap are depicted in Figure 3, 和

(A) Short-distance, 层 8, mBERT

(乙) Long-distance, 层 9, mBERT

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(d) Long-distance, 层 7, XLM-R

数字 3
Set intersections of the top 100 neural units responsible for subject-verb agreement in the two
状况. The ﬁve concentric rings in the middle represent the ﬁve sets of top neurons relative
to each language, and the individual sections indicate the presence (绿色的) or the absence (灰色的)
of the sets in each intersection. Each circular sector corresponds to a particular conﬁguration of
set intersections. 例如, a sector with the ﬁrst and the last segment highlighted in green
corresponds to the German ∩ Russian intersection. The height of the bars in the outer layer is
proportional to the intersection sizes, which are made explicit by the numbers on the top. 这
color intensity of the bars represents the log-transformed p-value signiﬁcance of the
intersections, as computed with the super exact test. The white bars on the right of the diagrams
are not associated with FE and statistical signiﬁcance, and they simply report the number of
considered units for each language (N= 100). The segments are ordered counterclockwise by
intersection size.

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reported in detail in Appendix 2 (Tables 2, 3 for mBERT; Tables 4, 5 for XLM-R). 全部
二-, three-, four-, and ﬁve-way combinations show an overrepresentation of the set
intersection relative to the random expectation. This overrepresentation is statistically
signiﬁcant in all but four intersections (在......之外 104); in the case of mBERT, the statistical
signiﬁcance of the fold enrichment (FE; IE。, the ratio between observed and expected
overlap5) exceeds the conventional threshold of α = .05 in the En6 ∩ He and De ∩ He
cases in the short-distance condition, and He ∩ Fr in the long-distance condition. 这
only combination with p > .05 in the intersections based on XLM-R is En ∩ He; 尤其,
Hebrew is present in all the non-signiﬁcant intersections.

In the case of the mBERT short-distance agreement results, the two-, three-, 和
four-way intersections associated with the highest fold enrichment are En ∩ Fr, En ∩ Fr
∩ Ge, and En ∩ Fr ∩ De ∩ Ru, 分别 (see Figure 3a). These three combinations
have in common the absence of the Hebrew set, and the presence of the English and
the French sets. 平均而言, the pairwise set intersections in the case of short-distance
agreement comprise 24.9 units; a striking number of 39 units is found in the En ∩ Fr
intersection (FE = 2.9952, p = 5.84 · 10–13). 值得注意的是, three neurons survived all the
ﬁve-way set intersections, occupying a high position in all the ﬁve language-speciﬁc
rankings (FE = 104.3677, p = 3.39 · 10–6). In the case of long-distance agreement, 这
highest fold enrichment for each N2 . . . 4-way intersection is found in Fr ∩ Ru, Fr ∩ En
∩ Ge, and Fr ∩ En ∩ De ∩ Ru, with Hebrew being again the absent language in the
three combinations and French appearing in all of them (see Figure 3b). The average
pairwise intersection size is 28.4; the ﬁve-way intersection in the long-distance condition
includes four neurons, with FE = 139.1569 and p = 1.01 · 10–10. 全面的, 协议-
related information displays a greater degree of convergence in the long- vis-`a-vis the
short-distance condition. 的确, in the former case intersection sizes are consistently
bigger, and associated with higher FE (一般, the FE for the pairwise intersections
是 1.8893 in the short-distance condition, 和 2.1811 in the long-distance condition).

The results obtained by XLM-R mirror the ones derived from mBERT: 长的-
distance agreement is characterized by larger intersections in the top-100 neuron rank-
英格斯, showing signs of a stronger cross-lingual alignment. 的确, the average pairwise
FE is 2.1965 in the short-distance condition, 和 3.3333 in the long-distance condition.
The N2 . . . 4-way intersections with highest FE in the short-distance condition are En ∩
Fr, He ∩ Fr ∩ Ru, and De ∩ En ∩ Fr ∩ Ru (see Figure 3c); in the long-distance condition,
the combinations that share the highest number of neurons are De ∩ Fr, De ∩ Fr ∩ Ru,
and De ∩ En ∩ Fr ∩ Ru (see Figure 3d). While Hebrew appears in one top combination
in the short-distance condition, most of the best scoring intersections do not include it.
The number of neurons that are present in the top-100 sets across all ﬁve languages is
remarkably high: In the short-distance condition, we found six cross-lingual neurons
(FE = 208.7354, p = 3.87 · 10–13), whereas in the long-distance condition the number rises
to ten (FE = 347.8924, p = 1.29 · 1023, by far the highest FE score we obtained in our
学习). The overall congruence in the neural units responding to agreement violations
is stronger in XLM-R with respect to mBERT; this disparity is particularly evident in the
long-distance condition, where the neurons surviving through the ﬁve-way intersection
are more than double.

5 With the observed overlap being equal, higher-degree set intersections—which have lower expected

overlap—will have higher FE.

6 For readability purposes, the set of the top 100 units selected for a given language is reported with the

国际标准化组织 639-1 code of that language (英语: En; 德语: 的; 俄语: Ru; 法语: Fr; Hebrew: 他).

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4.2.2 Probeless Rankings. As with the LCA method, we restricted our multi-set analyses to
the individual units populating the seventh layer in the case of XLM-R, and the eighth
and ninth layers for mBERT (长的- and short-distance agreement). The results of the
super exact test based on the probeless rankings are graphically depicted in Figure 4,
and reported in detail in Appendix 2 (Tables 6, 7 for mBERT; Tables 8, 9 for XLM-R).
From a qualitative standpoint, the results obtained with the probeless ranking method
are analogous to those described in the previous section. Intersection sizes show a
general overrepresentation of units with respect to what would be expected by chance;
的确, when considering short-distance agreement, in all the set intersections the size
of the observed overlap exceeds the size of the expected overlap by a signiﬁcant margin
with the exception of very few combinations, most of which include the Hebrew set
(mBERT: En ∩ He; XLM-R: Fr ∩ Ru, He ∩ Fr, En ∩ He, De ∩ He, De ∩ He ∩ Ru, De ∩
He ∩ Fr). In the long-distance condition there are no exceptions to this trend, 与

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(A) Short-distance, 层 8, mBERT

(乙) Long-distance, 层 9, mBERT

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(d) Long-distance, 层 7, XLM-R

数字 4
N2 . . . 5-way intersection statistics derived from the rankings obtained with the probeless
方法.

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FE associated with all intersections being statistically signiﬁcant, regardless of model
类型. 再次, intersection sizes tend to be bigger in the long-distance condition,
showing signs of a stronger representational alignment across languages. Restricting
our focus to pairwise overlap, the average FE is higher in the long-distance intersection
数据 (mBERT, short: 2.7421; mBERT, 长的: 3.2947; XLM-R, short: 1.8586; XLM-R, 长的:
4.416). 此外, the cross-lingual overlap is more pronounced when considering
the embeddings of the RoBERTa-based encoder (see above), in line with the LCA-based
结果.

In the case of mBERT, the intersections with the highest overrepresentation of the
fold for each degree are En ∩ Fr, En ∩ Fr ∩ De, En ∩ Fr ∩ De ∩ He (short-distance), 和
Fr ∩ Ru, Fr ∩ Ru ∩ De, Fr ∩ Ru ∩ De ∩ En (long-distance). In the case of XLM-R, 这
intersections with the highest FE are En ∩ Fr, En ∩ Fr ∩ De, En ∩ Fr ∩ De ∩ Ru (两个都
长的- and short-distance). While Hebrew appears in one top combination in the short-
distance condition (mBERT), all the other best scoring intersections do not include it; 在
另一方面, they all include the French set, in line with the results obtained with the
linear classiﬁer.

5. 讨论

Number agreement is a syntactic phenomenon that crucially relies on a proper parse
of the structure of a sentence. In all ﬁve languages we considered, number agreement
is made explicit through a form of morphological inﬂection that links subject and verb
by virtue of their syntactic relationship and their shared grammatical number. 给定
the similarity of the underlying grammatical process, a truly multilingual neural model
should display some degree of cross-lingual consistency in the neural units computing
协议. Our analyses showed that indeed there is a correspondence in the encoding
of agreement patterns across languages, not only in terms of the layer-wise convergence
of information, but also in terms of the organization of the neural units within a single
层. In the layer-wise analyses, a linear classiﬁer built upon both mBERT and XLM-R
embeddings was able to detect syntactic anomalies from the intermediate layers of the
网络. The classiﬁcation accuracy decreased in the deepest layers of the networks, 在
line with results obtained with monolingual models (Jawahar, Sagot, and Seddah 2019);
关键地, this quadratic concave trend was coherent across the languages included
在我们的研究中. The structural alignment of different language pairs was susceptible to
systematic differences affecting in particular Hebrew, a low-resource language that
also obtains lower performance scores in layer-wise classiﬁcation. We speculate that
this difference in results might be due, at least in part, to the typological relations
between the languages included in our study. 的确, 英语, 德语, 法语, 和
Russian are Indo-European languages. Hebrew, 另一方面, is a Semitic lan-
guage belonging to the Afroasiatic family,7 despite exhibiting some Indo-European
inﬂuences (Zuckermann 2006). 此外, differently from the others, Hebrew is a
language characterized by a templatic morphology: Verbs and nouns can be inﬂected
by modifying a consonantal root, adding vowels between the consonants. 因此, A
linear segmentation of the input into sub-word units (as the one underlying mBERT and
XLM-R tokenizers) might not capture the full morphological complexity of the words
(Klein and Tsarfaty 2020). This entails that two inﬂected forms of the same root might
not share any sub-word token more frequently than in languages with concatenative

7 Following the Omniglot classiﬁcation of languages at https://omniglot.com/writing/langfam.htm.

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morphological systems, making agreement computations more difﬁcult and based on
representational properties that are different from the other considered languages. 我们
thus speculate that the weaker correspondence in the neural unit processing agreement
in Hebrew might be motivated by these typological and morphological differences.

Despite a certain degree of language speciﬁcity in the intersection patterns, 这
independent selection of language-speciﬁc relevant units can nonetheless identify a
shared substrate underlying number agreement processing. Across model types and
ranking methods, the size of this shared substrate is consistently larger with increased
distance between the two hierarchically dependent words, as evidenced by the higher
FE in the long-distance condition. The greater distance between subject and verb, 作为
well as the contingent introduction of attractors between them, makes the task of
word prediction more difﬁcult, as evidenced by standard predictive tests (Mueller et al.
2020). 因此, the comparison between the results obtained in the two agreement con-
ditions suggests that cross-lingual alignment is favored by more complex sentence
陈述. A possible objection to this observation lies in the fact that both the
training and the test set in the long-distance condition comprised more items than in
the short-distance condition (参见章节 3.3). This asymmetry in training data might
have resulted in a more precise ranking in the long-distance case, which in turn could
have identiﬁed more efﬁciently the cross-lingual components in the network. To rule
out this possible confound, we repeated all our analyses after downsampling the long-
distance set,8 and still found a more consistent unit-level convergence with increased
distance between the two interdependent constituents (see Appendix 3). Another factor
that inﬂuenced the cross-lingual convergence of syntactic information was model type:
The intersection sizes derived from the XLM-R-based ranks were much larger than the
ones obtained from its predecessor, regardless of the neuron ranking algorithm (in line
with previous results on probing with MMMs, see Antverg and Belinkov [2021] 和
Stanczak et al. [2022] for similar results). The two models are minimally different: 这
main attributes that distinguish them are the larger amount of training data and the
absence of the NSP objective in XLM-R. This suggests that the NSP loss is not a crucial
determinant of cross-lingual convergence, and that more trained and better performing
multilingual models have stronger language-neutral internal components (see also Del
and Fishel 2021).

From a methodological standpoint, the qualitative convergence in the results ob-
tained with LCA and the probeless ranking method shows that our ﬁndings are not
biased by the inherent limitations of the probing framework, such as the conﬂation
between the information learned by the model and by the probe (Antverg and Belinkov
2021). 的确, the main outcomes of our study—such as the greater cross-lingual con-
vergence in long- versus short-distance agreement and the stronger alignment in the
RoBERTa-based encoder—are robust regardless of the neuron ranking method applied.

6. 跟进: The Depth of the Cross-lingual Syntax

In the previous sections, we started from the implicit assumption that the most relevant
layers for computing agreement within a single language would show the highest con-
sistency in their inner organization across languages. In the present follow-up study, 我们

8 We chose to rule out this confound a posteriori instead of performing our analyses on balanced sets from
the beginning in order to derive more precise estimates for the log-distance condition, where more data
were available.

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Data-driven Cross-lingual Syntax

empirically tested this premise. 第一的, we examined the weights assigned by the linear
classiﬁers to the highest scoring individual neurons across layers, and their dispersion
across languages (6.1). 然后, as a control, we also analyzed the layer-wise correla-
tions between the weight matrices learned by the classiﬁers in the ﬁve different lan-
guages9 (6.2).

6.1 Top Neurons Across Layers

Whereas in our previous experiments we adopted a maximally conservative approach
by extracting ﬁve language-speciﬁc independent neuron rankings for each condition,
here we used a more exploratory procedure by jointly searching for relevant cross-
lingual neurons in each layer. We reasoned that a cross-lingual neuron responding to
agreement should satisfy two necessary conditions. 第一的, it should have, 一般, A
high impact on the prediction of the grammaticality label. 第二, the measures of that
neuron’s impact in the ﬁve languages considered should be comparable: Its relevance
should not be driven by a subset of the languages, but rather be cross-linguistically
稳定的. Following this line of reasoning, we operationalized the cross-lingual relevance
of each unit with respect to the task by averaging the absolute value of its weights
learned by the ﬁve language-speciﬁc classiﬁers. This procedure allowed us to construct
a global, language-neutral ranking of the neurons. 然后, for each layer, we considered
the neural unit with the highest average weight, and observed the relative standard
deviation of its value across languages. We performed our analyses independently for
short- and long-distance agreement, and for either model type.

(西德:74)

The results of our follow-up tests are depicted in Figure 5. The general pattern that
clearly emerges from the four plots is an initial increase in average weight, 这是
steeper in the long-distance condition; the average weights then decrease in the last
layers. The growth in the average weight is associated with a contingent reduction
in the cross-lingual measure of dispersion, as indicated by the error bars. In the case
8, 9
of mBERT, this rise in the average weight reaches its peak in the intermediate
(西德:75)
layers. In the short-distance condition, the highest weight is obtained in the eighth
layer by neuron 6533 (5A); this neuron’s weights also exhibit a contained amount of
variation across languages (although the top neurons in the embedding and in the
seventh layer display an even smaller amount of dispersion). The best candidate cross-
lingual neuron is easier to identify in the long-distance condition: 神经元 7674 在里面
ninth layer exhibits at the same time the two preconditions identiﬁed above, being both
the one with the highest weight and the one with the lowest cross-lingual deviation
(5乙). XLM-R neurons behave in an analogous way, but reach their maximal cross-lingual
convergence in earlier layers. In the short-distance condition, the highest mean weight
is obtained in the seventh layer by neuron 5621 (5C); this neuron also displays contained
cross-lingual variation, although the weights of neuron 6545 in the eighth layer are more
stable across languages. In the long distance condition, neuron 5066 in the sixth layer is
the most relevant agreement-responding unit (5d); while neurons 5666, 6928, 和 7931
are slightly more stable across languages, 5066 clearly marks the weight peak. 在里面
case of XLM-R, the weight-by-layer growth curve is steeper if compared with mBERT,
especially in the long-distance condition: While the weights of the top neurons in the
ﬁrst ﬁve layers are close to zero and highly variable across languages, from the sixth
layer we have an almost sudden increment.

9 We thank the anonymous reviewers for the suggestion.

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(A) Short-distance, mBERT

(乙) Long-distance, mBERT

(d) Long-distance, XLM-R

数字 5
Mean weight of each layer’s top neuron, averaged over ﬁve languages. The error bars indicate
the relative standard variation of the weight across the ﬁve languages, rescaled by a 102 因素
for readability purposes. The numbers annotated over the error bars specify the ID of the neuron
whose metrics are depicted in the graph. Note that the y axis scale varies across plots, 为了
highlight the layer-wise progression of the average weights.

6.2 Correlation Between Weight Matrices Across Layers

In the previous section, we considered the individual units of each layer that were
assigned the highest average weight by the linear classiﬁer, in order to draw conclusions
about the layer-wise encoding of agreement across languages. This approach allowed
us to identify a set of individual units that are cross-lingually associated with number
协议; 然而, this procedure neglects the vast majority of the network’s units.
因此, as a sanity check, we also analyzed the cross-lingual correlation between the
weights assigned by the linear classiﬁers to the neurons of each layer. The weights of the
classiﬁer are supposed to reﬂect the relevance of each unit with respect to the linguistic
property being investigated, 即, grammatical agreement. 因此, a cross-lingual
correlation in the classiﬁer weights reﬂects how similarly two given languages encode
agreement relations. Differently from our previous results, this analysis considers all
the neural units within a layer, and not only the top neurons. Following our previous
结果, we predicted an increase in cross-lingual weight correlation in the ﬁrst layers
of the networks, followed by a plateau in the intermediate layers, and a ﬁnal decrease
toward the deepest layers of the models.

The layer-wise results of our weight correlation analysis are reported in Figure 6;
note that each point in the plot reﬂects the average weight correlation obtained across

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数字 6
Layer-wise progression of cross-lingual weight correlations, grouped by model and condition.

the ten combinations of language pairs. All the pairwise correlations are reported in
detail in Appendix 4 (数字 10). The results of the correlation analyses are largely con-
sistent with what we reported in the previous section. Across model types and condi-
系统蒸发散, the cross-lingual correlation in the weight matrices (henceforth CCWM) 增加
in the intermediate layers of the models, reaching its peak in the seventh (XLM-R, short-
distance agreement) and eighth layer (mBERT, short- and long-distance agreement;
XLM-R, long-distance agreement). 然后, the CCWM progressively decreases toward
the deepest layers of the models. While the localization of the correlation peaks does
not coincide exactly with the weight maxima identiﬁed in § 6.1, from a qualitative
standpoint the layer-wise progression of the CCWM is mostly coherent with our previ-
ous observations, when considering the effects of both agreement condition and model
类型. 的确, the increase in CCWM is steeper (A) when considering long- as opposed
to short-distance dependencies, 和 (乙) when analyzing XLM-R as opposed to mBERT
嵌入.

合在一起, these layer-wise patterns strengthen our previous ﬁndings in two
方法. 第一的, they conﬁrm the premise of our ﬁrst experiment concerning the layer-wise
ﬂow of cross-lingual syntactic information within the network, supporting our choice
to constrain our tests to the middle layers of the network. 第二, they clearly show
that there is a cross-lingual convergence in the encoding of grammatical structures in
the middle-to-deep layers of the networks. This means that MMMs such as mBERT and
XLM-R progressively develop a cross-lingual space where language-neutral individual
units respond to similar grammatical structures in different languages. 全面的, 这些
results are consistent with the view that identiﬁes the ﬁrst layers of an MMM as a
multilingual encoder (Del and Fishel 2021), where syntactic features are progressively
elaborated and converge toward the same units in the middle-to-deep layers. 然后, 这
subsequent decline is coherent with the view of MMMs as the stacking of two sub-
网络: a multilingual encoder followed by a task-speciﬁc decoder, which has little
importance in the transfer (Muller et al. 2021).

6.3 Single Neurons Encode Grammatical Structures

In § 6.1, we identiﬁed four candidate cross-lingual neurons. These units were assigned
on average a high weight by the linear classiﬁer, and their relevance was characterized

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计算语言学

体积 49, 数字 2

by a reduced variation across languages. 在这个部分, we studied their individual
behavior in response to well-formed and agreement-violating sentences. 更确切地说,
we tested whether their activation patterns alone were sufﬁcient and necessary to predict
the grammaticality of such sentences. 这样做, we assessed whether (A) the activations
of those units alone could predict agreement violations, 和 (乙) the activations of their
respective layers could predict grammaticality when these units were zeroed out. 到
increase the generalizability of our results, we measured their responses to agreement
in another condition of the CLAMS dataset, across a Prepositional Phrase (例如, “这
surgeons behind the architect *smiles/smile”). This condition was chosen as it falls
between the long-distance VP coordination and the short-distance condition in terms of
the distance between subject and verb. A total of 11,200 sentences from this condition10
were selected and divided in a train and a test set (80% 火车, 20% 测试). 然后, 我们
extracted the activations of the models in the verb position, 和 (A) selected the output
of the four units identiﬁed in the previous section (神经元 7674 和 6533 in the case of
mBERT, and neurons 5066 和 5621 for XLM-R), 或者 (乙) zeroed out their activations in the
layers output. In the former case (A), we used the output of each of these neurons taken
singularly as a predictor in a logistic regression model, with the dummy-coded label of
grammatical acceptability as dependent variable. We then computed the classiﬁcation
accuracy in the test set, and assessed the statistical signiﬁcance of our results against
chance level with a binomial test. As an additional baseline, we also randomly sampled
30 neural units from the corresponding layers in the two models (layers 8 和 9 为了
mBERT, 和 7 和 6 for XLM-R), and evaluated their average accuracy in predicting the
grammaticality label on the same dataset.11 In the second case (乙), we used as predictors
in the logistic regression models all the layer units except for the neuron of interest;
we then compared the results obtained with the full layer embedding with the results
obtained with the ablated layer by means of a McNemar test, a statistical test utilized
on paired nominal data.

6.3.1 Single Neurons Are Sufﬁcient to Compute Agreement. The results of our experiment
are reported in Figure 7. 全面的, the neurons that we identiﬁed in the previous section
were signiﬁcantly predictive of grammaticality across languages, providing a sanity
check for our procedure. In the case of mBERT, the activation of neuron 7674, 哪个
had been singled out in the long-distance condition, was sufﬁcient to signiﬁcantly
classify sentences as agreement-violating in all the languages considered, with an av-
erage accuracy of 0.59 (7A). 不出所料, accuracy was lower in the Russian and
Hebrew datasets, but nonetheless the performance levels were still above chance. 这
activation of neuron 6533 achieved a rather inferior performance, as it reached statistical
signiﬁcance only in German and French, with an average cross-lingual accuracy of 0.53.
As in all the tests we reported so far, the results obtained with XLM-R were more
solid, as both neuron 5066 和 5621 were signiﬁcant predictors of grammaticality in all
语言 (7乙), with the exception of neuron 5621 in French, which was only marginally
signiﬁcant (p = 0.056). The logistic classiﬁer based on neuron 5066 achieved an average
准确度 0.64; 尤其, its output alone was sufﬁcient to reach an accuracy level of
0.84 in French. Similarly to mBERT, the neuron identiﬁed in the short-distance condition
(5621) was less strongly associated with the label in most languages, but it still obtained

10 The number of instances was chosen to match the smallest challenge set (in Hebrew) for cross-lingual

comparability.

11 We thank an anonymous reviewer for the suggestion.

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de Varda and Marelli

Data-driven Cross-lingual Syntax

(A) mBERT, cross-lingual neurons

(乙) XLM-R, cross-lingual neurons

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(d) XLM-R, random neurons

数字 7
Accuracy of the classiﬁers based on the neurons identiﬁed in Section 6 (top row) and average
performance obtained by 30 units randomly sampled from the same layer (bottom row),
grouped by language. The asterisks indicate the statistical signiﬁcance of the results against
chance level, with p < 0.001***, p < 0.01**, p < 0.05*. an average accuracy of 0.57. If compared to randomly sampled units from the same layers, which in theory could be expected to respond to similar linguistic phenomena, the neurons extracted with our procedure were generally more effective in predicting the well-formedness of a sentence. Across both model types, the neurons identiﬁed in the long-distance condition (7674 and 5066) consistently outperformed in classiﬁ- cation accuracy the randomly sampled units extracted from their respective layers, with the only exception the Russian data, where the outcomes were comparable. Once again, the results in the short-distance condition are less clear-cut. In the case of mBERT, neuron 6533 outperformed the randomly sampled baseline only in German and French, but when considering the RoBERTa-based transformer, neuron 5621 outperformed the baseline in all the languages but French. However, it should be noted that the neurons that we randomly sampled from the relevant layers generally obtained above-chance performance scores in the classiﬁcation task, suggesting that number agreement com- putations are spread out across the middle layers of the network. 6.3.2 Single Neurons Are not Necessary to Compute Agreement. Once veriﬁed that the four interlingual neurons we singled out in § 6.1 were sufﬁcient to capture agreement 277 Computational Linguistics Volume 49, Number 2 Table 1 Comparison of the results of the classiﬁer obtained with the full layer and the ablated layer. The ﬁrst two columns indicate the language and the agreement condition where the units were identiﬁed (see § 6.1). The following ﬁve columns specify the results obtained with mBERT, and in particular the target neuron that was zeroed out, the respective layer, the accuracy obtained with the full layer embedding, the accuracy obtained with the ablated layer, and the statistical signiﬁcance of the McNemar test. The last ﬁve columns report the same indexes, but relative to the XLM-R model. *In contrasting the accuracy of the full and the ablated layer, the standard χ2 calculation was used instead of the binomial test, as the number of observations per cell in the contingency table was higher than 25. mBERT XLM-R Language Cond. Neuron L Acc French French English English Hebrew Hebrew Russian Russian German German Short Long Short Long Short Long Short Long Short Long 6533 7674 6533 7674 6533 7674 6533 7674 6533 7674 8 9 8 9 8 9 8 9 8 9 1.0000 1.0000 0.9464 0.9549 0.9013 0.8933 0.9821 0.9754 1.0000 1.0000 Accabl 1.0000 1.0000 0.9451 0.9558 0.9013 0.8942 0.9821 0.9754 1.0000 1.0000 p Neuron L Acc 1.0000 1.0000 0.2500 0.6250 1.0000 0.6880 1.0000 1.0000 1.0000 1.0000 5621 5066 5621 5066 5621 5066 5621 5066 5621 5066 7 6 7 6 7 6 7 6 7 6 1.0000 1.0000 0.9527 0.9049 0.8710 0.8299 0.9254 0.8777 1.0000 1.0000 Accabl 1.0000 1.0000 0.9527 0.9040 0.8705 0.8326 0.9259 0.8790 1.0000 1.0000 p 1.0000 1.0000 1.0000 0.7540 1.0000* 0.4170 1.0000 0.6640 1.0000 1.0000 violations with an above-chance performance, we aimed to test whether their contribu- tion was necessary for the task. The results of these analyses are summarized in Table 1. As can be seen in the table, the ablation of the candidate cross-lingual units did not show a signiﬁcant impact on the results obtained by the classiﬁers in any of the languages considered in the analyses, regardless of model type. This result is largely consistent with our previous observation that number agreement processing is not restricted to a small number of specialized units in multilingual transformer models, but it is encoded with redundancy in the network’s embeddings. While the activation patterns of the neurons we set apart in our cross-lingual search do encode agreement to a signiﬁcant extent, their role is not decisive in agreement processing. 6.4 Testing in an Unseen Language In the previous section, we tested the four candidate interlingual neurons we identiﬁed in § 6.1 in a novel condition of the CLAMS dataset, showing that our selection procedure was robust to small changes in the sentential structure of the agreement data. To further assess the cross-lingual abilities of those units, we further extended the analyses to measure their predictive power in detecting agreement violations in an unseen language, that is, Italian. Since the CLAMS dataset did not include any other language beyond the ones that we had previously considered, we artiﬁcially created a new agreement dataset in a rule-based fashion, and replicated our previous analyses in this dataset. 6.4.1 Dataset Creation and Analyses. To generate an agreement dataset in Italian, we started from a set of 2 determiners (deﬁnite and indeﬁnite; D), 20 nouns (N), 20 verbs (10 transitive, 10 intransitive; V), and 15 temporal prepositional modiﬁers (M). Then, we created a corresponding plural set for each of D, N, and V (Dp, Np, Vp). Starting 278 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 de Varda and Marelli Data-driven Cross-lingual Syntax from those samples, we created four agreement conditions by computing the Cartesian products between the three sets:12 (a) (b) (c) (d) Singular agreement: D × N × V Plural agreement: Dp × Np × Vp Violated singular agreement: D × N × Vp Violated plural agreement: Dp × Np × V where each condition consisted of 800 items. We then inserted one modiﬁer sampled from M after the nouns, to increase the distance between subject and verb to an amount comparable to the CLAMS condition we used in § 6.3 (across a Prepositional Phrase). Conditions (a) and (b) were then merged and labeled as grammatical, whereas condi- tions (c) and (d) were codiﬁed as ungrammatical. This method allowed us to generate 3,200 labeled sentences, which were then divided in a train (80%) and a test set (20%). Following our previous procedures, we used the two transformer models to extract their internal activations in the verb position; then, we selected from the obtained embeddings the output of the four candidate cross-lingual units (mBERT: 6533, 7674; XLM-R: 5621, 5066). We then trained four different logistic regression models—one for the output of each neuron—in the training set data, and evaluated their accuracy in the test set. Beside contrasting the model accuracy against chance level with a binomial test, we implemented a second baseline with 30 neural units randomly sampled from the same layers as the target neurons. 6.4.2 Results. The neural units that we consider in this study were generally successful in detecting agreement violations in Italian. When considering mBERT, the neuron identiﬁed in the short-distance condition (6533) reached an accuracy score of 0.57 (p = 0.0001); the unit that had been singled out in the long-distance condition (7674) obtained an accuracy of 0.52, although the binomial test was not signiﬁcant (p = 0.1258). On the other hand, both the units that were identiﬁed in the XLM-R model signiﬁcantly outperformed chance level (5621: 0.60, p = 1.56 · 10–7; 5066: 0.64, p = 1.63 · 10–13). The randomly sampled units obtained instead a rather inferior performance in the Italian test set, with the exception of the sample based on the ninth layer of mBERT (mBERT, layer 8: 0.53, p = 0.0525; mBERT, layer 9: 0.53, p = 0.0446; XLM-R, layer 7: 0.54, p = 0.0219; XLM-R, layer 6: 0.51, p = 0.3319). Taken together, these results strengthen the validity of our methodology, showing that the neural units that were associated with agreement in a set of languages can successfully capture the same property in a different language which did not concur in the unit selection. The performance of individual neurons in predicting well-formedness demon- strates that explicit knowledge emerges in a quasi-symbolic format in the neural units we identiﬁed in the previous experiment. Interestingly, simply training a transformer model on a masked language modeling objective on multilingual data causes the emergence of syntax-sensitive units that respond to the same linguistic phenomenon in different languages. The knowledge encoded in these units is also sufﬁciently abstracted 12 Note that the agreement relationship between D and N was set to always be grammatical, so that the only structure-dependent relationship that could be violated was subject-verb number agreement. 279 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Computational Linguistics Volume 49, Number 2 from the low-level features of the input that can be captured even in settings that differ from the one employed during unit selection, both in terms of agreement condi- tions (across a Prepositional Phrase) and languages (Italian). However, the comparison with randomly sampled neurons further shows that while some units are particularly responsive to agreement violations, this grammatical phenomenon is encoded with redundancy in the network’s embeddings. Indeed, other randomly sampled dimensions in the activation matrix still respond to the same structure-dependent relationship, although with lower levels of association with the label (see Dalvi et al. [2020] for an analysis of redundancy in transformer language models). This ﬁnding is congruent with the layer ablation results, where we showed that the activation patterns of the target neurons were not necessary to reach near-perfect accuracy in the classiﬁcation task. 7. Conclusion This study presents the ﬁrst single-neuron analysis aimed at assessing the cross-lingual nature of mBERT and XLM-R agreement processing mechanisms. Our ﬁndings are in line with the view that the very large neural capacity in MMMs leads to multilingual representations that have both language-neutral and language-speciﬁc components (see also Doddapaneni et al. 2021; Gonen, Ravfogel, and Goldberg 2022). While the majority of the networks’ units shows a heterogeneous cross-lingual relevance, several neurons in the structural embeddings of mBERT and XLM-R respond to syntactic features in two or more languages. We argue that those neurons can be considered as the implementa- tional substrate that supports number agreement computations across languages. The independent neuron rankings, while far from being identical, display an above-chance level of cross-lingual consistency. This consistency is stronger for long- vis-`a-vis short- distance agreement, suggesting that more complex structures tax more strongly the language-neutral components of the networks. Our results are also informative in terms of model comparison: While most research efforts considered a single model—generally mBERT—when assessing the eventual cross-lingual nature of its representations (Singh et al. 2019; Chi, Hewitt, and Manning 2020; Dufter and Sch ¨utze 2020; Muller et al. 2021; Guarasci et al. 2022, although see Del and Fishel 2021), our results contrast two prominent MMMs, showing that the RoBERTa-based transformer excels in cross-lingual alignment. With respect to the previous literature, our study is novel in that it measures the convergence of cross-lingual signal in the syntactic domain. Previous studies often used a coarse-grained approach to cross-lingual coherence; indeed, the emergence of an interlingual space was often measured as the layer-wise progression of sentence similarity scores across languages, thus conﬂating syntactic and semantic features (e.g., Singh et al. 2019; Del and Fishel 2021; but see Chi, Hewitt, and Manning 2020). In this study, we extended the previous ﬁndings by showing that even when narrow- ing the scope of our analyses to subtle structure-dependent phenomena, the mod- els consistently allocate an overlapping set of resources to similar processes across languages. In the Introduction, we mentioned how the study of the convergence of information in a multilingual neural model could inform the debate on the neural underpinnings of linguistic knowledge in multilingual individuals. In that respect, our study shows that the optimal solution that naturally emerges from priorless sequence processing networks is a partial overlap of resources, which is dependent on the typo- logical similarity between languages. The very existence of language-neutral components in mBERT and XLM-R shows that the models address the high surface inconsistency of the multilingual input through 280 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 de Varda and Marelli Data-driven Cross-lingual Syntax strong generalization—hence, leveraging truly multilingual knowledge. Once acknowl- edged that the representation space exploited by MMMs is multilingual in nature, the study of their predictive behavior could provide us with unique insights into the struc- tural symmetries that are instantiated across languages, and inform us on the nature of language as a system beyond the surface discrepancies shown by single languages. We hope that this investigation will pave the way to future studies inspecting the MMMs’ learned representation spaces to acquire novel knowledge on the properties that are shared across languages and language families. 8. Limitations and Further Directions This study showed that number agreement is partly encoded by a language-neutral set of parameters in the structural embeddings of mBERT and XLM-R. However, two important caveats must be made. First, the syntactic relationship we analyze is a circum- scribed expression of the variety of grammatical phenomena that characterize natural languages. While restricting our analyses to a speciﬁc class of grammatical instances increases the experimental control over our study, it should be noted that the gener- alizability of our ﬁndings to other linguistic structures should be properly assessed in future research. Second, the phenomenon we investigate is expressed in our language sample in a rather consistent way, when analyzed in abstract terms: Subject and verb are paired through a form of morphological inﬂection—which is mainly concatenative in four out of the ﬁve languages considered—on account of their structural dependency and their grammatical number. We leave for future research an assessment of whether our results hold when considering a more typologically diverse language sample that conveys agreements relationships in fundamentally different ways. Appendix 1. Weight Mass Analyses In § 4, we considered the number of top 100 units that were shared among two or more languages to draw conclusions on the neuron-level cross-lingual convergence of agreement information in the networks. However, the threshold we used, while congruent with previous research (Antverg and Belinkov 2021), needs to be motivated. In particular, it is necessary to ensure that the top neurons that are considered in the analyses effectively account for a sufﬁciently ample proportion of the weight mass. In other words, it is critical to verify that (a) the weight distribution is sufﬁciently skewed to motivate the selection of N top neurons, and (b) N = 100 is a sensible threshold that includes the most relevant units, and does not include too many of the non- relevant ones. To verify these premises, we plot the weight distribution of the different model × condition × language combinations, and examine the ratio of the cumulative weight mass13 accounted for by the top 100 units. The outcomes of these analyses are summarized in Figure 8. As can be clearly seen from the ﬁgure, the weight distributions are highly skewed, with a small number of units that are assigned high weights, and a long right tail of less relevant neurons. In general, 100 neurons—which only constitute 13.02% of the layer units—contribute to a substantial proportion of the weight mass of the layer (on average 45.46%). This proportion is lower when considering mBERT 13 (cid:80)100 (cid:80)768 i=1 wi j=1 wj 281 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Computational Linguistics Volume 49, Number 2 (a) Short-distance, mBERT, layer 8 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o (b) Long-distance, mBERT, layer 9 Figure 8 Weights (y axis) associated by the linear classiﬁer to the individual units (x axis) of the relevant layers. The percentage superimposed on the graph indicates the cumulative weight mass accounted for by the top 100 units in each individual language. l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 282 de Varda and Marelli Data-driven Cross-lingual Syntax (c) Short-distance, XLM-R, layer 7 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 (d) Long-distance, XLM-R, layer 7 (short-distance: 35.21%; long-distance: 43.36%) as opposed to XLM-R (short-distance: 49.45%; long-distance: 57.81), and with short- as opposed to long-distance dependencies between subject and verb (see above). This suggests that both model type and subject- verb distance contribute to the sparseness of the encoding of the phenomenon under scrutiny, with XLM-R and long-distance dependencies causing the emergence of fewer specialized units that respond to agreement violations, and mBERT and short-distance agreement promoting more distributed and possibly redundant encoding patterns. However, despite a certain amount of variability across models and conditions, 100 units generally contribute to a large amount of the weight mass, justifying a posteriori the choice of our threshold. 283 Computational Linguistics Volume 49, Number 2 Appendix 2. Super Exact Test Results in Detail 2.1. Linguistic Correlation Analysis Table 2 Results of the super exact test relative to all N2 . . . 5-way intersections of the top 100 neurons in the short-distance agreement condition (mBERT, LCA). Intersection Degree Obs. overlap Exp. overlap FE Fr ∩ Ru He ∩ Ru He ∩ Fr En ∩ Ru En ∩ Fr En ∩ He De ∩ Ru De ∩ Fr De ∩ He De ∩ En He ∩ Fr ∩ Ru En ∩ Fr ∩ Ru En ∩ He ∩ Ru En ∩ He ∩ Fr De ∩ Fr ∩ Ru De ∩ He ∩ Ru De ∩ He ∩ Fr De ∩ En ∩ Ru De ∩ En ∩ Fr De ∩ En ∩ He En ∩ He ∩ Fr ∩ Ru De ∩ He ∩ Fr ∩ Ru De ∩ En ∩ Fr ∩ Ru De ∩ En ∩ He ∩ Ru De ∩ En ∩ He ∩ Fr De ∩ En ∩ He ∩ Fr ∩ Ru 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 5 28 26 19 25 39 14 17 34 15 29 8 10 6 9 10 5 7 6 17 5 4 3 5 3 5 3 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 0.2208 0.2208 0.2208 0.2208 0.2208 0.0287 2.1504 1.9968 1.4592 1.9200 2.9952 1.0752 1.3056 2.6112 1.1520 2.2272 4.7186 5.8982 3.5389 5.3084 5.8982 2.9491 4.1288 3.5389 10.027 2.9491 18.1194 13.5895 22.6492 13.5895 22.6492 104.3677 p 1.21 · 10–05 1.17 · 10–04 4.47 · 10–02 3.34 · 10–04 5.84 · 10–13 4.28 · 10–01 1.34 · 10–01 3.03 · 10–09 3.10 · 10–01 3.54 · 10–06 2.29 · 10–04 4.68 · 10–06 6.33 · 10–03 3.50 · 10–05 4.68 · 10–06 2.59 · 10–02 1.30 · 10–03 6.33 · 10–03 1.58 · 10–13 2.59 · 10–02 6.82 · 10–05 1.38 · 10–03 2.59 · 10–06 1.38 · 10–03 2.59 · 10–06 3.39 · 10–06 284 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 de Varda and Marelli Data-driven Cross-lingual Syntax Table 3 Long-distance agreement condition (mBERT, LCA). Intersection Degree Obs. overlap Exp. overlap FE Fr ∩ Ru He ∩ Ru He ∩ Fr En ∩ Ru En ∩ Fr En ∩ He De ∩ Ru De ∩ Fr De ∩ He De ∩ En He ∩ Fr ∩ Ru En ∩ Fr ∩ Ru En ∩ He ∩ Ru En ∩ He ∩ Fr De ∩ Fr ∩ Ru De ∩ He ∩ Ru De ∩ He ∩ Fr De ∩ En ∩ Ru De ∩ En ∩ Fr De ∩ En ∩ He En ∩ He ∩ Fr ∩ Ru De ∩ He ∩ Fr ∩ Ru De ∩ En ∩ Fr ∩ Ru De ∩ En ∩ He ∩ Ru De ∩ En ∩ He ∩ Fr De ∩ En ∩ He ∩ Fr ∩ Ru 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 5 40 24 18 26 38 21 35 27 24 31 9 16 8 10 16 12 9 15 17 11 6 6 10 6 7 4 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 0.2208 0.2208 0.2208 0.2208 0.2208 0.0287 3.0720 1.8432 1.3824 1.9968 2.9184 1.6128 2.6880 2.0736 1.8432 2.3808 5.3084 9.4372 4.7186 5.8982 9.4372 7.0779 5.3084 8.8474 10.0270 6.4881 27.1791 27.1791 45.2985 27.1791 31.7089 139.1569 p 8.85 · 10–14 8.90 · 10–04 8.03 · 10–02 1.17 · 10–04 3.64 · 10–12 1.13 · 10–02 6.17 · 10–10 3.90 · 10–05 8.90 · 10–04 2.51 · 10–07 3.50 · 10–05 2.50 · 10–12 2.29 · 10–04 4.68 · 10–06 2.50 · 10–12 5.83 · 10–08 3.50 · 10–05 3.59 · 10–11 1.58 · 10–13 5.54 · 10–07 7.95 · 10–08 7.95 · 10–08 1.22 · 10–14 7.95 · 10–08 2.00 · 10–09 2.12 · 10–08 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 285 Computational Linguistics Volume 49, Number 2 Table 4 Short-distance agreement condition (XLM-R, LCA). Intersection Degree Obs. overlap Exp. overlap FE Fr ∩ Ru He ∩ Ru He ∩ Fr En ∩ Ru En ∩ Fr En ∩ He De ∩ Ru De ∩ Fr De ∩ He De ∩ En He ∩ Fr ∩ Ru En ∩ Fr ∩ Ru En ∩ He ∩ Ru En ∩ He ∩ Fr De ∩ Fr ∩ Ru De ∩ He ∩ Ru De ∩ He ∩ Fr De ∩ En ∩ Ru De ∩ En ∩ Fr De ∩ En ∩ He En ∩ He ∩ Fr ∩ Ru De ∩ He ∩ Fr ∩ Ru De ∩ En ∩ Fr ∩ Ru De ∩ En ∩ He ∩ Ru De ∩ En ∩ He ∩ Fr De ∩ En ∩ He ∩ Fr ∩ Ru 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 5 32 30 31 32 35 25 21 23 28 29 16 14 13 14 9 12 13 12 14 15 9 7 7 9 11 6 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 0.2208 0.2208 0.2208 0.2208 0.2208 0.0287 2.4576 2.3040 2.3808 2.4576 2.6880 1.9200 1.6128 1.7664 2.1504 2.2272 9.4372 8.2575 7.6677 8.2575 5.3084 7.0778 7.6677 7.0779 8.2575 8.8474 40.7686 31.7089 31.7089 40.7686 49.8283 208.7354 p 6.13 · 10–08 9.74 · 10–07 2.52 · 10–07 6.13 · 10–08 6.17 · 10–10 3.34 · 10–04 1.14 · 10–02 2.22 · 10–03 1.21 · 10–05 3.54 · 10–06 2.50 · 10–12 4.68 · 10–10 5.51 · 10–09 4.68 · 10–10 3.50 · 10–05 5.84 · 10–08 5.51 · 10–09 5.84 · 10–08 4.68 · 10–10 3.59 · 10–11 7.79 · 10–13 2.01 · 10–09 2.01 · 10–09 7.79 · 10–13 1.69 · 10–16 3.87 · 10–13 286 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 de Varda and Marelli Data-driven Cross-lingual Syntax Table 5 Long-distance agreement condition (XLM-R, LCA). Intersection Degree Obs. overlap Exp. overlap FE Fr ∩ Ru He ∩ Ru He ∩ Fr En ∩ Ru En ∩ Fr En ∩ He De ∩ Ru De ∩ Fr De ∩ He De ∩ En He ∩ Fr ∩ Ru En ∩ Fr ∩ Ru En ∩ He ∩ Ru En ∩ He ∩ Fr De ∩ Fr ∩ Ru De ∩ He ∩ Ru De ∩ He ∩ Fr De ∩ En ∩ Ru De ∩ En ∩ Fr De ∩ En ∩ He En ∩ He ∩ Fr ∩ Ru De ∩ He ∩ Fr ∩ Ru De ∩ En ∩ Fr ∩ Ru De ∩ En ∩ He ∩ Ru De ∩ En ∩ He ∩ Fr De ∩ En ∩ He ∩ Fr ∩ Ru 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 5 54 34 30 48 48 18 54 57 26 52 22 36 13 15 42 19 21 38 35 13 12 17 30 11 12 10 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 0.2208 0.2208 0.2208 0.2208 0.2208 0.0287 4.1472 2.6112 3.3040 3.6864 3.6864 1.3824 4.1472 4.3776 1.9968 3.9936 12.9761 21.2337 7.6677 8.8474 24.7726 11.2067 12.3863 22.4133 20.6438 7.6677 54.3582 77.0074 135.8955 49.8283 54.3582 347.8924 p 5.84 · 10–28 3.03 · 10–09 9.74 · 10–07 2.94 · 10–21 2.94 · 10–21 8.04 · 10–02 5.84 · 10–28 1.12 · 10–31 1.18 · 10–04 1.28 · 10–25 4.42 · 10–20 6.28 · 10–43 5.51 · 10–09 3.59 · 10–11 1.29 · 10–54 4.90 · 10–16 1.07 · 10–18 1.07 · 10–46 4.33 · 10–41 5.51 · 10–09 2.04 · 10–18 9.49 · 10–29 1.52 · 10–60 1.69 · 10–16 2.04 · 10–18 1.29 · 10–23 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 287 Computational Linguistics Volume 49, Number 2 2.2. Probeless Table 6 Short-distance agreement condition (mBERT, probeless). Intersection Degree Obs. overlap Exp. overlap FE Fr ∩ Ru He ∩ Ru He ∩ Fr En ∩ Ru En ∩ Fr En ∩ He De ∩ Ru De ∩ Fr De ∩ He De ∩ En He ∩ Fr ∩ Ru En ∩ Fr ∩ Ru En ∩ He ∩ Ru En ∩ He ∩ Fr De ∩ Fr ∩ Ru De ∩ He ∩ Ru De ∩ He ∩ Fr De ∩ En ∩ Ru De ∩ En ∩ Fr De ∩ En ∩ He En ∩ He ∩ Fr ∩ Ru De ∩ He ∩ Fr ∩ Ru De ∩ En ∩ Fr ∩ Ru De ∩ En ∩ He ∩ Ru De ∩ En ∩ He ∩ Fr De ∩ En ∩ He ∩ Fr ∩ Ru 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 5 26 30 31 21 54 18 30 50 23 48 11 13 9 15 16 14 13 10 35 11 6 7 7 6 8 3 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 0.2208 0.2208 0.2208 0.2208 0.2208 0.0287 1.9968 3.3040 2.3808 1.6128 4.1472 1.3824 3.3040 3.8400 1.7664 3.6864 6.4881 7.6677 5.3084 8.8474 9.4372 8.2575 7.6677 5.8982 20.6438 6.4881 27.1791 31.7089 31.7089 27.1791 36.2388 104.3677 p 1.18 · 10–04 9.74 · 10–07 2.52 · 10–07 1.14 · 10–02 5.84 · 10–28 8.04 · 10–02 9.74 · 10–07 2.19 · 10–23 2.22 · 10–03 2.94 · 10–21 5.55 · 10–07 5.51 · 10–09 3.5 · 10–05 3.59 · 10–11 2.5 · 10–12 4.68 · 10–10 5.51 · 10–09 4.69 · 10–06 4.33 · 10–41 5.55 · 10–07 7.95 · 10–08 2.01 · 10–09 2.01 · 10–09 7.95 · 10–08 4.28 · 10–11 3.39 · 10–06 288 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 de Varda and Marelli Data-driven Cross-lingual Syntax Table 7 Long-distance agreement condition (mBERT, probeless). Intersection Degree Obs. overlap Exp. overlap FE Fr ∩ Ru He ∩ Ru He ∩ Fr En ∩ Ru En ∩ Fr En ∩ He De ∩ Ru De ∩ Fr De ∩ He De ∩ En He ∩ Fr ∩ Ru En ∩ Fr ∩ Ru En ∩ He ∩ Ru En ∩ He ∩ Fr De ∩ Fr ∩ Ru De ∩ He ∩ Ru De ∩ He ∩ Fr De ∩ En ∩ Ru De ∩ En ∩ Fr De ∩ En ∩ He En ∩ He ∩ Fr ∩ Ru De ∩ He ∩ Fr ∩ Ru De ∩ En ∩ Fr ∩ Ru De ∩ En ∩ He ∩ Ru De ∩ En ∩ He ∩ Fr De ∩ En ∩ He ∩ Fr ∩ Ru 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 5 60 42 38 37 36 26 52 57 36 45 30 27 17 17 39 26 24 26 29 17 13 18 22 13 14 10 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 0.2208 0.2208 0.2208 0.2208 0.2208 0.0287 4.608 3.2256 2.9184 2.8416 2.7648 1.9968 3.9936 4.3776 2.7648 3.4560 17.6947 15.9253 10.027 10.027 23.0031 15.3354 14.1558 15.3354 17.1049 10.027 58.888 81.5373 99.6567 58.888 63.4179 347.8924 p 1.21 · 10–35 1.7 · 10–15 3.64 · 10–12 2.14 · 10–11 1.18 · 10–10 1.18 · 10–04 1.28 · 10–25 1.12 · 10–31 1.18 · 10–10 2.92 · 10–18 2.29 · 10–32 1.64 · 10–27 1.59 · 10–13 1.59 · 10–13 1.25 · 10–48 5.85 · 10–26 5.94 · 10–23 5.85 · 10–26 1.02 · 10–30 1.59 · 10–13 2.19 · 10–20 5.93 · 10–31 3.45 · 10–40 2.19 · 10–20 2.09 · 10–22 1.29 · 10–23 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 289 Computational Linguistics Volume 49, Number 2 Table 8 Short-distance agreement condition (XLM-R, probeless). Intersection Degree Obs. overlap Exp. overlap FE Fr ∩ Ru He ∩ Ru He ∩ Fr En ∩ Ru En ∩ Fr En ∩ He De ∩ Ru De ∩ Fr De ∩ He De ∩ En He ∩ Fr ∩ Ru En ∩ Fr ∩ Ru En ∩ He ∩ Ru En ∩ He ∩ Fr De ∩ Fr ∩ Ru De ∩ He ∩ Ru De ∩ He ∩ Fr De ∩ En ∩ Ru De ∩ En ∩ Fr De ∩ En ∩ He En ∩ He ∩ Fr ∩ Ru De ∩ He ∩ Fr ∩ Ru De ∩ En ∩ Fr ∩ Ru De ∩ En ∩ He ∩ Ru De ∩ En ∩ He ∩ Fr De ∩ En ∩ He ∩ Fr ∩ Ru 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 5 16 26 15 19 47 13 21 37 10 38 5 10 5 9 11 4 4 10 24 5 4 4 8 4 4 4 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 0.2208 0.2208 0.2208 0.2208 0.2208 0.0287 1.2288 1.9968 1.1520 1.4592 3.6096 0.9984 1.6128 2.8416 0.7680 2.9184 2.9491 5.8982 2.9491 5.3084 6.4881 2.3593 2.3593 5.8982 14.1558 2.9491 18.1194 18.1194 36.2388 18.1194 18.1194 139.1569 p 2.12 · 10–01 1.18 · 10–04 3.11 · 10–01 4.48 · 10–02 3.12 · 10–20 5.54 · 10–01 1.14 · 10–02 2.14 · 10–11 8.71 · 10–01 3.64 · 10–12 2.59 · 10–02 4.69 · 10–06 2.59 · 10–02 3.5 · 10–05 5.55 · 10–07 8.78 · 10–02 8.78 · 10–02 4.69 · 10–06 5.94 · 10–23 2.59 · 10–02 6.82 · 10–05 6.82 · 10–05 4.28 · 10–11 6.82 · 10–05 6.82 · 10–05 2.13 · 10–08 290 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 de Varda and Marelli Data-driven Cross-lingual Syntax Table 9 Long-distance agreement condition (XLM-R, probeless). Intersection Degree Obs. overlap Exp. overlap FE Fr ∩ Ru He ∩ Ru He ∩ Fr En ∩ Ru En ∩ Fr En ∩ He De ∩ Ru De ∩ Fr De ∩ He De ∩ En He ∩ Fr ∩ Ru En ∩ Fr ∩ Ru En ∩ He ∩ Ru En ∩ He ∩ Fr De ∩ Fr ∩ Ru De ∩ He ∩ Ru De ∩ He ∩ Fr De ∩ En ∩ Ru De ∩ En ∩ Fr De ∩ En ∩ He En ∩ He ∩ Fr ∩ Ru De ∩ He ∩ Fr ∩ Ru De ∩ En ∩ Fr ∩ Ru De ∩ En ∩ He ∩ Ru De ∩ En ∩ He ∩ Fr De ∩ En ∩ He ∩ Fr ∩ Ru 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 5 69 53 47 61 74 35 61 68 38 69 40 58 31 34 56 33 33 52 62 29 31 31 51 27 29 27 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 0.2208 0.2208 0.2208 0.2208 0.2208 0.0287 5.2992 4.0704 3.6096 4.6848 5.6832 2.6880 4.6848 5.2224 2.9184 5.2992 23.593 34.2098 18.2845 20.054 33.0301 19.4642 19.4642 30.6709 36.5691 17.1049 140.4253 140.4253 231.0223 122.3059 131.3656 939.3093 p 3.46 · 10–49 8.92 · 10–27 3.12 · 10–20 5.01 · 10–37 6.89 · 10–58 6.17 · 10–10 5.01 · 10–37 1.49 · 10–47 3.64 · 10–12 3.46 · 10–49 1.36 · 10–50 1.77 · 10–91 4.77 · 10–34 2.78 · 10–39 2.17 · 10–86 1.66 · 10–37 1.66 · 10–37 1.22 · 10–76 4.19 · 10–102 1.02 · 10–30 2.94 · 10–63 2.94 · 10–63 1.99 · 10–125 1.26 · 10–52 7.23 · 10–58 5.53 · 10–78 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 291 Computational Linguistics Volume 49, Number 2 Appendix 3. Long-distance Condition Downsampled (a) Long-distance agreement, mBERT (b) Long-distance agreement, XLM-R l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o (c) Long-distance, layer 9, LCA, mBERT (d) Long-distance, layer 7, LCA, XLM-R l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 (e) Long-distance, layer 9, probeless, mBERT (f) Long-distance, layer 7, probeless, XLM-R Figure 9 Layer-wise performance of the logistic classiﬁer (top) and N2 . . . 5-way intersection statistics obtained with LCA (middle) and probeless ranking (bottom) on the downsampled long-distance agreement data. 292 de Varda and Marelli Data-driven Cross-lingual Syntax In this section, we report the results we obtained by downsampling the long- distance condition to match the number of items available in the short-distance dataset—224 in the training (80%) and 56 in the test set (20%). Given the rather limited number of instances available in this condition, we decided to report in the article the results obtained with the larger dataset. Nonetheless, because we also comment on the short- vs. long-distance comparison, it is necessary to rule out the possible confound of the different amount of training data.14 The peak of performance is obtained in the same layers as in the non-downsampled analyses (layers 9 and 7 for mBERT and XLM-R, respectively, see Figure 9a, 9b). The multi-set intersection analysis also shows a coherent pattern of results with respect to what we reported above. Indeed, in the case of mBERT the N2 . . . 4-way intersections with the highest FE are Fr ∩ Ru, Fr ∩ Ru ∩ (En ⊕ De), and Fr ∩ En ∩ De ∩ Ru, with Hebrew being absent in three combinations and French appearing in all of them (see Figure 9c, Table 10). Similarly, in the case of XLM-R the highest FE is obtained in De ∩ Fr, De ∩ Ru ∩ (En ⊕ Fr), and Fr ∩ En ∩ De ∩ Ru (Figure 9d, Table 11). Crucially, intersection sizes are consistently bigger in the downsampled long- distance condition (Figure 9c, 9d) than in the short-distance condition (Figure 3a,3a) across both model types. Table 10 Downsampled long-distance condition, mBERT. Intersection Degree Obs. overlap Exp. overlap FE Fr ∩ Ru He ∩ Ru He ∩ Fr En ∩ Ru En ∩ Fr En ∩ He De ∩ Ru De ∩ Fr De ∩ He De ∩ En He ∩ Fr ∩ Ru En ∩ Fr ∩ Ru En ∩ He ∩ Ru En ∩ He ∩ Fr De ∩ Fr ∩ Ru De ∩ He ∩ Ru De ∩ He ∩ Fr De ∩ En ∩ Ru De ∩ En ∩ Fr De ∩ En ∩ He En ∩ He ∩ Fr ∩ Ru De ∩ He ∩ Fr ∩ Ru De ∩ En ∩ Fr ∩ Ru De ∩ En ∩ He ∩ Ru De ∩ En ∩ He ∩ Fr De ∩ En ∩ He ∩ Fr ∩ Ru 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 5 46 22 23 37 41 24 42 37 25 41 13 27 12 11 27 14 13 26 23 13 9 10 19 10 9 8 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 0.2208 0.2208 0.2208 0.2208 0.2208 0.0287 3.5328 1.6896 1.7664 2.8416 3.1488 1.8432 3.2256 2.8416 1.9200 3.1488 7.6677 15.9252 7.0779 6.4881 15.9252 8.2575 7.6677 15.3354 13.5660 7.6677 40.7686 45.2985 86.0671 45.2985 40.7686 278.3139 14 We thank the anonymous reviewers for bringing this issue to our attention. p 3.11 · 10–19 5.20 · 10–03 2.22 · 10–03 2.14 · 10–11 1.27 · 10–14 8.90 · 10–04 1.70 · 10–15 2.14 · 10–11 3.34 · 10–04 1.27 · 10–14 5.51 · 10–09 1.64 · 10–27 5.84 · 10–08 5.54 · 10–07 1.64 · 10–27 4.68 · 10–10 5.51 · 10–09 5.85 · 10–26 1.69 · 10–21 5.51 · 10–09 7.79 · 10–13 1.23 · 10–14 3.36 · 10–33 1.23 · 10–14 7.79 · 10–13 3.13 · 10–18 293 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Computational Linguistics Volume 49, Number 2 Table 11 Downsampled long-distance condition, XLM-R. Intersection Degree Obs. overlap Exp. overlap FE Fr ∩ Ru He ∩ Ru He ∩ Fr En ∩ Ru En ∩ Fr En ∩ He De ∩ Ru De ∩ Fr De ∩ He De ∩ En He ∩ Fr ∩ Ru En ∩ Fr ∩ Ru En ∩ He ∩ Ru En ∩ He ∩ Fr De ∩ Fr ∩ Ru De ∩ He ∩ Ru De ∩ He ∩ Fr De ∩ En ∩ Ru De ∩ En ∩ Fr De ∩ En ∩ He En ∩ He ∩ Fr ∩ Ru De ∩ He ∩ Fr ∩ Ru De ∩ En ∩ Fr ∩ Ru De ∩ En ∩ He ∩ Ru De ∩ En ∩ He ∩ Fr De ∩ En ∩ He ∩ Fr ∩ Ru 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 5 54 34 30 48 48 18 54 57 26 52 22 36 13 15 42 19 21 38 35 13 12 17 30 11 12 10 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 13.0208 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 1.6954 0.2208 0.2208 0.2208 0.2208 0.2208 0.0287 2.9952 3.1488 2.0736 3.1488 2.7648 1.9200 3.6096 3.7632 1.9968 3.3792 10.6168 12.3863 11.7965 7.6677 15.9252 11.7965 9.4372 15.9252 14.7456 8.8474 49.8283 63.4179 77.0074 58.8880 49.8283 347.8924 p 5.85 · 10–13 1.27 · 10–14 3.90 · 10–05 1.27 · 10–14 1.18 · 10–10 3.34 · 10–04 3.12 · 10–20 2.62 · 10–22 1.18 · 10–04 2.59 · 10–17 9.22 · 10–15 1.07 · 10–18 2.39 · 10–17 5.50 · 10–09 1.64 · 10–27 2.39 · 10–17 2.50 · 10–12 1.64 · 10–27 1.94 · 10–24 3.59 · 10–11 1.69 · 10–16 2.09 · 10–22 9.49 · 10–29 2.19 · 10–20 1.69 · 10–16 1.29 · 10–23 294 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 de Varda and Marelli Data-driven Cross-lingual Syntax Appendix 4. Pairwise Correlations in the Weight Matrices (a) Short-distance, mBERT (b) Long-distance, mBERT (c) Short-distance, XLM-R (d) Long-distance, XLM-R Figure 10 Pairwise correlation coefﬁcients between the weights learned by the classiﬁers, divided by layer, condition, and model type. 295 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / c o l i / l a r t i c e - p d f / / / / 4 9 2 2 6 1 2 1 2 5 5 6 5 / c o l i _ a _ 0 0 4 7 2 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Computational Linguistics Volume 49, Number 2 References Abutalebi, Jubin, Stefano F. Cappa, and Daniela Perani. 2001. The bilingual brain as revealed by functional neuroimaging. Bilingualism: Language and Cognition, 4(2):179–190. https://doi.org/10.1017 /S136672890100027X Alain, Guillaume and Yoshua Bengio. 2016. Understanding intermediate layers using linear classiﬁer probes. arXiv preprint arXiv:1610.01644. Antverg, Omer and Yonatan Belinkov. 2021. 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