How do languages influence each other? Studying cross-lingual data sharing during LM fine-tuning
Authors: Rochelle Choenni
Dan Garrette
Ekaterina Shutova
Venue: EMNLP 2023 Main (2023)
Keywords: cross-lingual influence
data sharing
training data attribution

Abstract: Multilingual language models (MLMs) are jointly trained on data from many different languages such that representation of individual languages can benefit from other languages' data. Impressive performance in zero-shot cross-lingual transfer shows that these models are able to exploit this property. Yet, it remains unclear to what extent, and under which conditions, languages rely on each other's data. To answer this question, we use TracIn (Pruthi et al., 2020), a training data attribution (TDA) method, to retrieve training samples from multilingual data that are most influential for test predictions in a given language. This allows us to analyse cross-lingual sharing mechanisms of MLMs from a new perspective. While previous work studied cross-lingual sharing at the model parameter level, we present the first approach to study it at the data level. We find that MLMs rely on data from multiple languages during fine-tuning and this reliance increases as fine-tuning progresses. We further find that training samples from other languages can both reinforce and complement the knowledge acquired from data of the test language itself.

How do languages influence each other? Studying cross-lingual data sharing during LM fine-tuning
Rochelle Choenni University of Amsterdam r.m. chwemnivven.... ml
Dan Garrette Google Research
Ekaterina Shutova University of Amsterdam e. shutova@uva.nn nl
dhgarrette@google.c. com
Abstract
language-neutral and language-specific compo- nents (Libovický al., 2020; Gonen al., 2020; Tanti et al., 2021). This naturally raises the ques- tion of how much models really benefit from mul- tilingual data and cross-lingual sharing, and under what conditions this occurs. Many works have stud- ied the encoding of cross-lingual patterns within MLMs by either focusing on probing for particu- lar cross-linguistic differences (Ravishankar et al., 2019; Choenni and Shutova, 2022), or by analyz- ing the distributional properties of representational language subspaces (Yang et al., 2021; Rajacc and Pilehvar, 2022; Chang et al., 2022; Chi et al., 2020). Yet, it is not straightforward how to trans- late these results into model behavior at inference time. We aim to directly study how much influence languages exert cross-lingually the predictions for individual languages.
Multilingual language models (MLMs) are jointly trained on data from many different lan- guages such that representation of individual languages can benefit from other languages' data. Impressive performance in zero-shot cross-lingual transfer shows that these models are able to exploit this property. Yet, it remains unclear to what extent, and under which condi- tions, languages rely on each other's data. To answer this question, we use TracIn (Pruthi et al., 2020), training data attribution (TDA) method, to retrieve training samples from mul- tilingual data that are most influential for test predictions in a given language. This allows us to analyse cross- lanss-linggal sharing mechanisms of MLMs from new perspective. While previous work studied cross- langull sharing at the model parameter level, we present the first approach study it at the data level. We find that MLMs rely on data from multiple languages during fine- fine-tuning and this reliance increases as fine- tuning progresses. We further find that training samples from other languages can both rein- force and complement the knowledge acquired from data of the test language itself.
In this study, we take step back the training pipeline to study the extent to which the model exploits its multilingual training data when mak- ing predictions. We hypothesise that if model performs cross- -oossllnngual information sharing, then it will base its inference-time predictions (to some ex- tent) on training data from multiple languages. An- alyzing the cross-lingual sharing mechanism from the data reliance perspective leads to set of inter- esting questions that we explore:
1 Introduction
Multilingual joint learning is often motivated by the idea that when multilingual language models (MLMs) learn information for multiple languages simultaneously, they can detect and leverage com- mon universal patterns across them. Thus, these models can exploit data from one language to learn generalisations useful for another, obtain- ing impressive performance on zero-shot cross- lingual transfer for many languages (Wu and Dredze, 2019). Various studies suggest that rep- resentations created by popular MLMs, such as mBERT and XLM-R (Conneau al., 2020), are not fully language-agnostic (Doddapaneni al.. 2021; Singh al., 2019), but instead strike a bal- ance between sagguagg-agnosticciis and captur- ing the nuances of different languages through
Given a test language A, does our MLM tend to base its predictions only on data from A itself, or does it also employ data from other languages that it was exposed to during task fine-tuning?
Do MLMS only employ data cross- lonsulligg out of necessity, e.g., scenarios where in- language fine-tuning data is unavailable or insufficient?
Do languages support each other by adding similar information to what relied upon from in-language data (i.e., reinforcing the

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model in what it already learns), or do they (also) provide complementary information?
prediction-based methods like Simfluence (Guu et al., 2023) base influence on the full training tra- jectory instead. TracIn (Pruthi et al., 2020), used in this paper, is somewhere in between these methods: rather than using a direct loss difference, it tracks the similarity between gradients of training and test samples over model checkpoints. In NLP, TDA methods have so far mostly been used for unveiling data artifacts and explainability purposes (Han and Tsvetkov, 2022), for instance, detect outlier data (Han et al., 2020), enable sestancesspecffi data fil- tering (Lam et al., 2022), or to fix erroncous model predictions (Meng et al., 2020; Guo et al., 2021).
4. How do cross-lingual sharing dynamics change over the course of fine-tuning?
5. Is the cross-lingual sharing behaviour similar when the test language was seen during fine- tuning compared to when it is used in zero- shot testing scenario?
To study this, use TracIn (Pruthi et al., 2020), training data attribution (TDA) method to identify set of training samples that are most informative for a particular test prediction. The influence of a training sample Etrain on test sample Etest can be formalized as the change in loss that would be observed for žiest if Ziain was omitted during training. Thus, it can be used as a measure of how influential Frain is when solving the task for Arest- To the best of our knowledge, we present the first approach to studying cross-lingual sharing at the data level by extending the use of a TDA method to the multilingual setting. We find that MLMs rely on data from multiple languages to a large extent, even when the test language was seen (or over-represented) during fine-tuning. This indi- cates that MLM representations might be more uni- versal than previous work suggested (Singh et al., 2019), in part explaining the 'surprising' effective- ness of cross- loogull transfer (Pires al., 2019; Wu and Dredze, 2019; Karthikeyan et al., 2020). More- over, we find that cross- looss-l sharing increases as fine-tuning progresses, and that languages can support one another by playing both reinforcing as well as complementary roles. Lastly, we find that the model exhibits different cross-lingual be- haviour in the zero-shot testing setup compared to when the test language is seen during fine-tuning.
2.2 Studying cross-lingual sharing
Many approaches have been used to study the cross- lingual abilities of MLMs (Doddapaneni et al., 2021). Pires et al. (2019) and Karthikeyan et al. (2020) showed that MLMs share information cross- lingually by demonstrating that they can perform zero-shot cross- lings-l transfer between languages without lexical overlap. This led to work under- standing how and where this sharing emerges.
One line of study focuses on how MLMs dis- tribute their parameters across languages by ana- lyzing the distributional properties of the resulting language representations. In particular, they aim understand to what extent MLMs exploit universal language patterns for producing input representa- tions in individual languages. As such, Singh et al. (2019) find that mBERT representations can be partitioned by language into subspaces, suggest- ing that little cross-lingual sharing had emerged. Yet others show that mBERT representations can be split into a language-specific component, and a language-neutra component that facilitates cross- lingual sharing (Libovický et al., 2020; Gonen et al., 2020; Muller et al., 2021). In addition, Chi et al. (2020) show that syntactic information is encoded within shared syntactic subspace, suggesting that portions of the model are cross-lingually aligned. Similarly, Chang al. (2022) more generally show that MLLMs encode information along orthogonal language-sensiiing and language-neutral axes.
2 Background and related work
2.1 Training data attribution methods
TDA methods aim to explain a model's predictions in terms of the data samples that it was exposed to during training. Proposed methods include measur- ing the similarity between learned model represen- tations from training and test samples (Rajani et al., 2020), and influence functions (Koh and Liang, 2017) that aim compute changes in the model loss through Hessian-basse approximations. While these methods compute influence between train- ing samples and the final trained model, discrete
While the previous works studied parameter shar- ing indirectly through latent model representation, Wang et al. (2020) explicitly test for the existence of language-specific and language-neutral parame- ters. They do so by employing a pruning method (Louizos et al., 2018) to determine the importance of model parameters across languages, and find that

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some parameters are shared while others remain language-specifie. Moreover, Wang et al. (2020) focused on the negative interference effects (Ruder, 2017) of lingull sharing, i.e., parameter up- dates that help the model on one language, but harm its ability to handle another. They show that cross- lingual performance can be improved when param- eters are more efficiently shared across languages, leading to new studies finding language-specific and language-neutral subnetworks within MLMs to better understand (Foroutan al., 2022) and guide (Lin et al., 2021; Chocnni et al., 2022) cross-lingual sharing at the parameter level. contrast to these works, we do not study cross-lingual sharing at the model parameter level, but instead consider sharing at the data level. To the best of our knowledge, we are the first to explore this direction.
4 Methods
4.1 Models and fine-tuning
For all tasks, we add a classification head top of the pretrained XLM-R base model (Conneau al., 2020). The classifier is an MLP with one hidden layer and uses tanh activation. We feed the hidden representation corresponding to the beginning-on sequence token for each input sequence to the clas- sifier for prediction. We use learning rates of 2e-5, 9e-6, and 2c-5 for XNLI, PAWS-X, and MARC, and use AdamW (Loshchilov and Hutter, 2017) as optimizer. We fine-tune the full model on the concatenation 2K samples from 5 different lan- guages, i.e. 10K samples for each task. This allows us to limit the computational costs of computing influence scores (which increase linearly with the number of training samples), while still obtaining reasonable performance. We also reduce computa- tional costs by converting each task into simpler classification problem': for XNLI, we follow Han et al. (2020) by classifying "entailment or not" (i.c., mapping neutral and contradiction samples to a non-entailment label); for MARC, we collapse
3 Tasks and data
We conduct model fine-tuning experiments in three multilingual text classification tasks.
Natural language inference (NLI) The Cross- Lingual Natural Language Inference (XNLI) dataset (Conneau et al., 2018) contains premise- hypothesis pairs that are labeled with the relation- ship that holds between them: 'entailment', 'neu- tral' or 'contradiction'. The dataset contains paral- lel data in 15 languages. The original pairs come from English and were translated to the other lan- guages. We use English, French, German, Russian and Spanish for model fine-tuning and testing.
and 2 stars into a negative and and 5 stars into a positive review category. We train for 10 epochs and use early stopping (patience=3). We find that training converges at epoch 4 for XNLI, and at epoch 5 for PAWS-X and MARC, obtaining 78%, 83%, and 90% accuracy on their development sets.
4.2 TraeIn: Tracing Influence
Paraphrasing The Cross-Lingual Paraphrase Adversaries from Word Scrambling (PAWS-X) dataset (Yang et al., 2019) and task requires the model to determine whether two sentences are para- phrases of one another. To create this dataset, a sub- set of the PAWS development and test sets (Zhang et al., 2019) was translated from English to 6 other languages by professional translators, while the training data was automatically translated. We use English, French, German, Korean and Spanish.
We denote our training set D {z (ax ys) ) where each training sample z; consists of an input sequence Tú and a label yi. Koh and Liang (2017) show that we can compute how 'influential' each training sample 2; E D is to the prediction for a test sample Ziest : 0texst fā (Tww)) The influence score for training sample z; test sample Etest is defined as the change in loss Eie that would have incurred under the parameter estimates ʃa if the model was trained on D 2,. In practice, this prohibitively expensive to compute
Sentiment analysis The Multilingual Amazon Review Corpus (MARC) (Keung et al., 2020) con- tains Amazon reviews written by users in various languages. Each record in the dataset contains the review text and title, and star rating. The corpus is balanced across 5 stars, so each star rating con- stitutes 20% of the reviews each language. Note that this a non- non-parallel dataset. We use Chinese, English, French, German and Spanish.
requires
training the model [D] + times. Koh and Liang (2017) show that we can approximate it by mea- suring the change in loss on Ziest when the loss
'This reduces computational costs indirectly because sim- pler tasks require fewer training samples to obtain reasonably high performance for. As a result, we need to compute influ- ence scores between fewer training and test samples.

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associated with z; is upweighted by some value:
I
Sentence pair
Tabaci es una vertienee
Leunda Kumania.
test
El rio Leurda es un alluente del rio Tubuci en Rumania.
I (Zis Zrest) -VoL(Znes 2) H H
4.19
Borcut
Rumania.
El rio Colnici es un afluente del rio Dercut en Rumania.
VoL(zz, 0)
4.15
Colnici alluente
Borcui Rumania.
El rio Bogcut era un allugate del ri Colnici en Rumanin.
rivirre Slatina est un
rivière Rouanmic
4.10
La rivibre Cochirleanca est un afficnt de la Roemanie.
where Hgg is the Hessran of the loss C(D, with respect to 0, i.c. (D)
Table I: The top 3 most positively influential training samples retrieved Spanish test input from PAWS-X, and their corresponding influence scores (Z). Note that the last training samples are truncated to fit in the table.
However, computing H is still expensive. this method requires further approximations if the model is non-convex, and they can be less accurate when used on deep learning models (Basu et al., 2021). Pruthi et al. (2020) find a similar, but first- order, solution that we use in this study, TracIn:
PAWSX
Aeg. 5% confidionce
[[zi Frest) VoL(Zieat 0e) VoL VoL(zz, 0e) (2)
-0
20
20
where 0g is the checkpoint of the model at each training epoch. The intuition behind this is to approximate the total reduction in the test loss (Zrest 0) during the training process when the training sample 2j is used. This gradient prod- uct method essentially drops the H. term and reduces the problem to the dot product between the gradicnts of the training and test point loss.
50
75
100
125
150
175
200
225
250
Figure Average percentage of decrease in model con- fidence across test samples and fine-tuning languages when removing the top k most positively influential training samples for PAWS-X.
Normalization A problem of gradient products is that they can be dominated by outlier training samples of which the norm of their gradients is significantly larger than the rest of the training sam- plcs (Yu et al., 2020). This could lead TracIn to deem the same set of outlier samples as most in- fluential to a large number of different test points (Han et al., 2020). In the multilingual setup, we know that dominating gradients is a common prob- lem (Wang al., 2020). Barshan et al. (2020) propose simple modification that we adapt: sub- stituting the dot product with cosine similarity, thus normalizing by the norm of the training gradients.
samples with the highest influence scores and refer to them as the set of the most positively influential samples. Similarly, we refer to the top training samples with the most negative influence scores as the most negatively influential samples. Note that negative cosine similarity between gradients are commonly referred to as gradient conflicts (Yu et al., 2020) and have been shown to be indicative of negative interference in the multilingual setting (Wang al., 2020; Choenni et al., 2022).
To pick the test samples for which we will com- pute influence scores, we select from the set of sam- ples that the model labeled correctly, i.c. we study which training samples (and the languages they come from) positively and negatively influenced the model in making the correct prediction. For XNLI and PAWS-X, we train on parallel data; thus, as the content in our fine-tuning data is identical across languages, each language has equal oppor- tunity to be retrieved amongst the most influential samples. Hence, we can ascribe the influence from each influential sample the specific language that coming from as well as to the content of the sample itself (through the number of translations retrieved irrespective of the source language).
5 Experimental setup
After fine-tuning models (see Section 4.1), in turns, use 25 test samples from each language for testing and compute influence scores between each test sample and all 10K training samples. For each test sample, we then retrieve the top training
FFro experiments using nonmaleddl FastFF (Guo al,, 2021), we found that outlier fine-tuning languages (e.g. Korean) would suspiciously often be ranked on top.
'Note that, despite using a NVIDIA A100 GPU, this is still computationally expensive because we have to recompute the influence scores between each test sample and all 10K training samples separately for each model checkpoint.

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ID
Sentence pair
Winarsky es micmboo TERE, Kappa, ACMy y Sigma Winursky os miembro de ACM, IEEE. Pli Beta Kappa Signa XL.
es lest
Bernical spricht neben Englisch auch Russisch. Hindi Franzisisch. Bemient spricht nehen Englisch auch Pranzüssch, Hindi und Russisch.
de345
2.3
The festival 's main partners UBS Manor Heineken. Vaudoise Assunances and Parmigiani Fleurier.
en987
The main partners of this festival are Farmigiani Fleurier, Manor, Heiinkeen. Vaudoise and UBS.
Les principaux partenaires du festival sont UBS, Manor, Heineken. Vandoise Assurances Parmigiani Hleurier. principaux partenaires
f1987
2.04
festival sont Parmigiani Pleurier, Manor, Heinekon, Vaudalse UBS.
Il est le fils de luan, trois fiéres: Danilo lr, Antonio, Danilo Repadas er Cerila Ropadas ainsi que ses socians Roberta et Christina. est le fils de Dunilo Rapadas el de Cerila Rapadas, 11 trois freres, Dunilo Jt. Antonio, Juan el ses socurs Roberia et Christina. 7 Juan9] o o Danilo Antomio, Dunilo Rapudas, Cetila Rupuln
es115
2.16
s) 2] Roberta.) Christina?: 22 G 41C. Danilo Rapadas:) Cerila Rapadas:]] oi R. Danilo Jr. Antonio, Juan 18 x @l Reberaa9 Christina?); # c). Ademass de Michael Patrick, âlbum inclaye contribuciones musicales de Diana, John, Chick, Sianley. contiene contribucionos musicales Chick, Stanley, John Michael Patrick.
kol15
-2.13
es1771
22006
Ademis
Table 2: The top 3 most positively (top) and negatively (bottom) influential samples retrieved for a random test input from the PAWS-X dataset. + indicates correct paraphrase and incorrect one. Also, correct re-ordered words are denoted by orange, incorrect ones by red and the respective words in the original sentence by green.
6 Quality of most influential samples
verges, we conclude that the remaining samples do not exert much influence anymore, and we stop analyzing the ranking after this point.
We qualitatively test the plausibility of our influ- ence scores. In Table 1, we show a Spanish test input from PAWS-X and the corresponding top 3 most positively influential samples retrieved using TracIn. We see that TracIn ranks extremely similar samples with the same label as most influential. In Table 2, we also observe some evidence of cross- lingual sharing. The 3 most positively influential samples do not come from the test language, but they clearly test the model for the same knowledge: if the order of an unstructured list is slightly altered, do we get a correct paraphrase? In each case, this is correct. Yet, for the negatively influential samples. similar alterations are performed (i.e. changing the order of names), but in these cases this does cru- cially change the meaning of the sentences.
Results Figure 1 shows the effect of retraining the model on PAWS-X while removing the top k most positively influential samples. We find that af- ter k=100, the decrease in model confidence starts to level off. The same found for negatively influential samples and XNLL Thus, all further ex- periments focus on analysing the top 100 most in- fluential samples (see Appendix A for more details on selecting k). Yet, while for XNLI removing the top 100 most positively influential results in clear decrease in model confidence, removing the most negative ones does not result in similar confidence increase. Thus, compared to PAWS-X, negative interference effects seem less strong in XNLI given our 5 fine-tuning languages. This is also reflected Table where we report the aver- age influence scores between all training and test samples per language pair and task, and on aver- age observe much higher scores for XNLI than for PAWS-X (see Appendix B for more statistics on the influence scores).
Effect of is on model confidence We run quan- titative tests to assess the quality of our influence scores, and to select the optimal number for the top k most influential samples to analyze in our further experiments. We hypothesize that only a subset of our fine-tuning data will substantially influence predictions, while a long tail of training samples will have little influence (either positively or nega- tively). To find this threshold value k, we select the top k E (50, 100, 150, 200, 250) most influential samples to test how our model confidence changes when leaving out these sets of samples from our fine-tuning data in turns. If our influence scores are meaningful, removing the top l most positively in- fluential samples will reduce the model confidence (i.e. the class probability) in the correct prediction, while removing the top k most negatively influen- tial samples should increase it. When we find the k value for which the change in confidence con-
7 Cross-language influence
We now study how much each test language relies fine-tuning data from other languages at test time for parallel and non-parallel datasets. Figure shows, for all datasets, the percentage of training samples that contributed to the top 100 most posi- tively and negatively influential samples based on their source language.

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Train
Train
40
-40
tu
23
19
18
20
de
.431
442
.25
434
.418
de
.244
226
.241
.237
.155
35
35
6.99
610
.008
.285
5663
.603
597
5877
.542
68
221
.256
1223
.218
.146
6
.514
540
525
-529
499
fr
320
.35
.325
.323
.189
tu
.651
.667
.52
.660
.611
ko
.14
146
.141
.40
.166
18
20
16
22
20
(a) XNLI
(b) PAWS-X
22
18
22
15
22
16
19
23
15
fr
ru
fr
Table 3: For each language pair (o, 6), we compute the
(a) XNLI
average influence score between all 2K training samples from the fine-tuning language a and all the test samples from the test language b.
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7.1 Parallel datasets
11
13
49
12
12
58
10
10
For XNLI and PAWS-X, across all test languages, the retrieved sets of most-influential training sam- ples contain relatively high numbers of samples from languages other than the test language. This high degree of cross- languag influence provides strong evidence of cross-lingue information shar- ing within the models. Korean (PAWS-X) is the only exception, which is least surprising as it is also least similar to the other fine-tuning languages and might therefore be processed by the model in relative isolation. Yet, tributes cross-lingually some extent (~13% to the most positively influential samples on average). However, after further inspection we find that only in ~ 11% % of these Korean samples the sentences are fully written in the Hangul script; in all other cases, code-switching might be responsible for the cross-lingual alignment. Moreover, we observe that all test languages across both tasks mostly rely data from their own language most positively influential. Yet, the opposite does not hold: for in- stance, for PAWS-X we see that Korean is always the largest negative contributor irrespective of the test language, nicely showcasing the problem of negative interference (Ruder, 2017). Lastly, we find that while English obtains the highest aver- age influence score across all training samples (see Table 3), this is not representative of its actual influ- ence when judged by the most influential samples.
on
en
ko
trein
trai
(b) PAWS-X
40
44
34
19
20
26
26
19
15
35
36
33
10
28
15
text
12
25
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49
fr
fr
dh
(C) MARC
Figure 2:
For each test language. we show the per- centage of samples that each fine-tuning language con- tributed the top 100 most positively (lefi) and neg- atively (right) influential training samples averaged across test samples.
that Korean still con-
languages, thus artificially boosting cross-lingual sharing within the models. Therefore, we also train model on the non-parallel MARC dataset that con- tains user- aser-written product reviews. In Figure 2c, we see that while languages indeed seem to rely more strongly on their own data for MARC compared to PAWS-X X and XNLI (s*+10%) strong evidence for cross-lingual sharing is still observed. Moreover, similar language pair effects can be seen across tasks, e.g. French and Spanish rely each other's data the most for both PAWS-X and MARC. Yet we also find interesting differencess such as that for both parallel datasets, English contributes to the negatively influential samples the least, while for MARC it is instead the largest contributor. Given that our fine-tuning data is balanced across lan- guages, it is possible that we are seeing the effect of translation here, i.e. parallel data is translated from English, which results in the other language data conforming more to English, phenomena known as "translationese" (Koppel and Ordan, 2011). This is also supported by Table 3, where we found that on average the training samples from English ob- tained the highest influence scores, but for MARC
This confirms our hypothesis that there is a long tail of training samples that are of little influence.
7.2 Non-parallel dataset
While parallel datasets allow for fair comparison across languages in terms of the content that they were exposed to, this setting is not representative of most scenarios as most datasets are not paral- lel. Also, the translation of training samples across languages might decrease the variation between

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Translarions (%)
de
fr
ko
XNNJ
PAWSX
XNLI
NEG
60
61
62
62
PAWS.X
NEG
45 50 46 46
32
42-
40
15
Table 4: For the positively and negatively influential samples the top 100 each test language, we report how many of the samples coming from other fine-tuning languages are translations of the most influential sam- ples from own language (i.e. % reinforeing samples).
23
20
Traning spach
Thariig
Figure 3: For each test language, we plot the percentage of samples coming from their own language that were included in the most positively influential training sam- ples, i.e. the extent to which the model relies on its own language and how this changes over fine-tuning epochs.
we find that Spanish most often obtains the highest scores instead (see Appendix B, Table 6).
8 Further analysis
the model requires some knowledge of grammat- ical structure, e.g. identical paraphrases can take different forms across languages, thus the model might learn from cross- moss-lingual sharing differently.
We further analyze cross-lingual sharing for the tasks with parallel datasets since some of our anal- ysis requires translation retrieval.
8.1 Complementary vs. reinforcing samples Now that we have seen that our models rely on data from languages other than the test language, we study how these samples might contribute to the model performance, i.e., are they reinforcing the model with similar knowledge that it has seen from the test language, do these samples somehow encode complementary knowledge that the model did not retrieve on from its language? In or- der to make this distinction, we look at whether the most influential samples retrieved in other lan- guages are translations of the most influential sam- ples retrieved from the test language itself.
8.2 Sharing dynamics during fine-tuning
As explained in Section 4.2, TracIn approximates influence over training, obtaining separate scores after each fine-tuning epoch. While in previous results we reported the sum of these scores, we now analyze them separately per fine-tuning epoch. Blevins et al. (2022) study cross-lingual pretraining dynamics of multilingual models to see when cross- lingual sharing emerges. We instead study whether different patterns emerge when looking at language influence across fine-tuning.
Results In Figure 3, we plot, for each test language, what percentage of samples from in- language data were included in the top 100 most influential samples across different fine-tuning epochs. From this, we see that for both tasks, the languages start relying less their own fine- tuning data after epoch 2. Thus conclude that on average the models gradually start to per- form more cross-lingual sharing as fine-tuning pro- gresses. Moreover, in line with previous find- ings (Blevins et al., 2022), we observe that the amount of cross-lingual sharing between differ- ent language pairs fluctuates during fine-tuning (see Appendix C for results). To test whether the ranked influence scores between epochs are statisti- cally significantly different, we apply the Wilcoxon signed-rant test (Wilcoxon, 1992). and confirm that between all epochs this holds true (p-value < 0.05).
Results We report these percentages in Table 4, and find that for XNLI, over half of the contribu- tions from different languages are translations of the most influential training samples from the re- spective test language, indicating that the model largely benefits from reinforcing data from other languages. For PAWS-X, this is not the case, indi- cating that here the biggest benefit of gross-lingual sharing can more likely be attributed to the model learning to pick up on new, complementary. in- formation from other languages. As XNLI re- quires deep semantic understanding, we speculate that the model does not need to learn language- specific properties, but only needs to capture the content from data (possibly creating more universal representations to induce implicit data augmenta- tion). Thus, the most influential samples might more often be translations since some samples are content- wise more influential, and samples across languages can contribute equally. Yet, for PAWS-X,
8.3 Zero-shot testing
Another interesting testbed is zero-shot cross- lingual testing, in which no samples from the test

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PAWSX: -k
imbalance during training
27
24
25
18
30
65
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Figure 5: The percentage of data contributing to either the most positively (left) or negatively (right) influential samples for particular language when adding % of data on top of that language's 's data during fine-tuning,
Figure 4: Percentage of samples that each fine-tume tne-tuning language contributed to the top 100 most influential sam- ples for Korean and Spanish during zero-shot testing.
fine-tuning languages for our zero-shot models. We find that the models still rely on cross-lingual shar- ing, and while Korean was previously processed in isolation (i.e., mostly relying on its own fine-tuning data), it now benefits from multiple languages.
language are seen during fine-tunings here, the model must rely solely on samples from other languages. Thus, for a language we compare the influential- -amples ranking from the model for which was included the fine-tuning languages T, for- to that of a model for which it was ex- cluded, Jery. We check for two potential differ- ences: (1) Will fory replace l-samples that were highly influential in fer with translations of those same samples?; and (2) Will fory rely the same non-l samples that were highly influential in fe,? As Korean was found to be the most isolated language for PAWS-X (i.e., it relies on data from other languages the least), while Spanish relies on cross-lingual sharing the most, we in turns retrain our model without Korean and Spanish, obtaining 74% and 81% % accuracy respectively, and recom- pute the influence scores. We then compare the top 100 most influential samples from the two zero- shot models those of føg. and report how many translations of the samples from the test language vs. the other languages are covered.
8.4 Sharing as an effect of data-imbalance
An important aspect that can affect -ross-lingual sharing is the (im)balance of language data during fine-tuning. For instance, if some languages are over-represented during training, then they might end up exerting stronger influence over other train- ing languages, while languages that are under- represented might end up benefiting more from cross-lingual sharing (Wu and Dredze, 2020). To study how much the cross-lingual sharing effects observed so far can be ascribed to data scarcity, we perform experiments in which, for each lan- guage in turn, we fine-tune on PAWS-X XX but with E {25, 50, 75, 1003% additional I data included, thus ensuring that language is over-represented with respect to the other fine-tuning languages.
Results Surprisingly, we find that, in the zero- shot setup, the models barely rely the specific training samples that were found when the test lan- guage was included during fine-tuning. For Korean, only 5% the most positively influential samples from the zero-shot model are direct translations of the Korean samples that were retrieved when it was included during training. Moreover, only 4% of training samples from the other languages that were retrieved were deemed most influential again in the zero-shot setup. The same trend was found for Spanish, albeit translations of 14% of the Spanish and 13% from the other languages were recovered. Lastly, in Fig- ure 4, we show the data reliance distribution across
Results In Figure 5, we plot the percentage of in-language training samples that contribute to the of most influential samples for the respective test language as an effect of data imbalance. For all languages, we see a clear trend: as the data gets more biased towards one language, training samples from that language increase in influence- both positive and negative-withh the model. Yet we also see that this trend does not always steadily increase (e.g. for French and German). Morcover, for all languages except Korean, even when the lan- guage's data has fully doubled (+100%), its most influential samples set is still more than 50% from other mne-ttnnng languages. This indicates that even with data imbalances, the model largely ben-
lesser extent, where

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efits from cross-lingual sharing. An interesting outlier is English, for which we see that positive influence from its own data rapidly increases (sim- ilar to Korean); we hypothesize that this could be due to being considerably overrepresented during pretraining, nudging the model towards processing this language in isolation well.
(e.g. text generation or sequence labelling). In such tasks, the model could learn rely on cross-lingual sharing to a lesser extent. Jain al. (2022) recently extended influence functions to sequence tagging tasks to allow for more fine-grained analysis on the segment-level. Even though this further increases computational costs, it would be good direction for future work on cross- cross-lingual sharing.
9 Conclusion
Finally, focus our analysis on the fine-tuning stage. However, pre-training and fine-tuning ef- fects are hard to disentangle. As such, it would be reasonable to study the emergence of cross-lingual abilities during pre-training as well. However, in practice, this is difficult to achieve using TDA meth- ods due to the large amount of training samples seen during pre-training. It requires (1) access to the full pre- pre-training data, and (2) sufficient com- putational resources to compute influence scores between each test sample and (an informative sub- set of) training samples. Yet, given that many re- searchers are actively working on more efficient TDA methods, and our approach to studying cross- lingual data sharing can generally be coupled with any type of TDA method, we expect that similar studies that focus on the pre-training stage will be possible in the future as well.
To the best of our knowledge, we are the first to study the extent to which multilingual models rely on cross-lingual sharing the data level. We show that languages largely influence one another cross- lingually, and that this holds under various condi- tions. Moreover, we find that cross-lingual sharing increases as fine-tuning progresses, and that lan- guages can support one amother both by playing a reinforcing well as a complementary role. Lastly, we show how TracIn can be used to study data shar- ing in LMs. We hope that this paper can inspire future work on studying the sharing mechanism within multi-task and multi-modal models as well.
10 Limitations
One limitation of this study is that the experiments are computationally expensive to run, resulting in us only studying the effect on 125 test samples. Previous works have used more efficiency tricks to limit computational costs, for instance, by only computing influence scores between the test sam- ples and the k most similar training samples as found based on k nearest neighbour search on their representations (Rajani et al., 2020; Guo et al., 2021; Jain et al., 2022). However, limiting the pool of training samples will bias us to retrieving samples based on the similarity between the hidden model representations from the final trained model. As one of our main goals is to study cross-lingual sharing from a new perspective, we opted against using such methods, and instead compute influence scores over the full training set.
Acknowledgement
This project was in part supported by Google PhD Fellowship for the first author. We want to thank Ian Tenney for his thorough feedback and insights.
References
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A Selecting k for different tasks
XNU Negative samples removal
confidencee increase
Selecting a right threshold value for k is not trivial as the number of most influential samples varies across languages and specific test samples, More- over, in many cases, the top & most positively influ- ential training samples have the same label as the test instance, while the opposite holds true for the most negatively influential samples. Thus, when selecting value for k that is too large, we might not be able to distinguish between the effect of re- moving the most influential samples and the effect of data imbalance on our model. Thus, we opt for more careful approach and select the smallest pos- sible value of k for which we observe consistent change in model confidence.
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Figure 8: Average percentage (%) of decrease in model confidence across test samples and fine-tuning lan- guages when removing the top k most positively in- fluential training samples for the XNLI dataset.
B Influence score statisties
Figures 9, 10 and 11, show how for each task the influence scores between fine-tuning and test lan- guages distributed. We show separate plots for the distributions of positive and negative influence scores. Table we show an example of ran- dom test input from XNLI and its corresponding top 3 most positively and negatively influential sam- ples. In Table 6, we report average influence scores between training and test samples for MARC.
Positive samples removal
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koo de
Figure 6: Average percentage (%) of decrease in model confidence across test samples and fine-tuning lan- guages when removing the top i most positively in- fluential training samples for the XNLI dataset.
Distribution of positive Influence scores
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ko
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Figure 7: Average percentage (%) of increase in model confidence across test samples and fine-tuning lan- guages when removing the top & most negatively in- fluential training samples from the PAWS-X dataset.
Figure 9: The distribution of influence scores for PAWS- X for all training samples from language.

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ID/
Premise and hypothesis
nicht Ich bin mir besüglich des Grundes sicher.
warum.
test
nicht, Lösung
0:935/2.40
Ich habe eine perfokie Vorstallung davon, was zu run ist yeah
why
cn1699/2.34
know why.
no1696/2.0
stteao, пооexxy.
33r30 nonewyy:
caída del comunismo, Congreso aprohi amplias régimen aparthedd Sudáfrica.
es758/
Congresso no apuyó el apartheid en Sudifricu.
But there place where Will's journalism does
maiter. where daes baseball.
Will's articles are only good in regurds to sports
Pero lugur donde el periodismo de will parece importar, donde tira héishol. anticulos will sãlo son buenos en lo que se refiere los deportes
181-11111114
Table 5: An sample of the top most positively (top) and negatively (bottom) influential samples retrieved for a random test input from the XNLI dataset. Note that indicates correct entailment and contradiction.
Training lanuuage
Thaining language
Distribution of positive influence scores
Distribution of positive Influence scores
Infuence score
Distribution of negative influence scores
Distribution of negative influence scores
0.0
AM
-0.5
Influence score
Influance
-1.5
-2.0
-2.5
de
de
2/
60
Test
Test
Figure 10: The distribution of influence scores for XNLI for all training samples from a language.
Figure II: The distribution of influence scores for MARC for all training samples from a language.
C Cross-language influence dynamics over fine-tuning epochs
Train
In Figures 12 and 13, we show the full influence dy- namics between all fine-tuning and test languages after different epochs during fine-tuning, Note that, to compare whether ranked influence scores between different epochs statistically signifi- cantly different, we applied the Wilcoxon signed- rank test (Wilcoxon, 1992), and we can confirm that between all fine-tuning epochs this holds true (p-value < 0.05).
de
fr
zh
de
.554
550
.589
.582
.455
en
.50
.554
.593
.582
.458
Test
es
.539
.536
.607
.582
.440
fr
.561
.556
.618
.617
.454
zh
.535
.544
.577
.576
.542
Table 6: For each language pair, we show the average influence score between all training samples from fine-tuning language and each test sample (from the respective test language) for the MARC dataset.

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Figure 12: Full overview of how much each fine-tuning language exerts influence on each test language across the different fine-tuning epochs. We report percentages for which each fine-tuning language was represented the test language's top 100 most positively (green) and negatively (purple) influential training samples.
PAWSX Epoch
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Figure 13: Full overview of how much each fine-tuning language exerts influence each test language across the different fine-tuning epochs. We report percentages for which each fine-tuning language was represented in the test language's top 100 most positively (green) and negatively (purple) influential training samples.


Reviews:
[{"review_id": "d28BhDX4Mf", "reviewer": "Reviewer_FsHG", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": 4, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for the positive review.\n\nWhile we acknowledge that larger models have come out since XLM-R, it was useful for this work to study XLM-R specifically as this model’s cross-lingual abilities has been widely studied at the parameter level in previous studies. Analyzing a different model wouldn’t allow us to directly contrast our findings to existing knowledge about multilingual models.  Moreover, we believe that studying smaller models like XLM-R can still yield insightful results that can guide design decisions for larger ones as well (especially since they all still largely rely on the same training strategies and the transformer architecture). Though, given the recent advancements in NLP, we agree that it might be more suited now to call XLM-R a language model instead of a large language model. We will adjust this accordingly. \n\nAlso, while it is true that we can not directly generalize the results from XLM-R to other LMs, we would like to point out that the fact that XLM-R is successfully able to perform cross-lingual data sharing, makes it very unlikely that larger, stronger, LLMs would not have the ability to learn this property as well. Whether it also uses it would be a question for future work.\n\nLastly, to better clarify the usefulness of this study: We believe that interpretability studies like these will help us understand the current limitations of multilingual models. In turn, this can help us guide design decisions and future research directions. Had we, for instance, found that cross-lingual sharing does not already happen at the data level, it would make sense to focus future efforts on forcing  the model to rely more on cross-lingual data sharing in the hope to further improve performance. Also, as Reviewer qo5L nicely pointed out, we could use this approach as an intrinsic measure for testing the cross-lingual abilities of LMs. Moreover, we could, for instance, test to what extent cross-lingual data sharing correlates with better downstream task performance, i.e. testing to what extent cross-lingual data sharing actually benefits performance. In short, we believe that this approach opens up the possibility of exploring many new research questions.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "- The paper is well written, with figures and tables that enhance comprehension.\n- The experiments section is very well done. There is a big variety of experiments covering all possible settings. Every time I was thinking about an experiment that would be interesting to try, the authors had already included it in one of the following sections.\n- The authors explore different datasets and variety of languages, including different alphabets.\n- The conclusions drawn after each experiment are clear and well supported by the experiments.", "reasons_to_reject": "Affected my rating:\n- The model used is a XLM-R model (Conneau et al., 2020), which I consider old in the field of LMs considering recent advancements. \n- The title and abstract of the paper state the analysis is done on a *Large* Language Model, which again considering recent advancements, is not how I would define a XLM-R model. I understand that the TDA methods used are very computationally expensive, and therefore it would be hard to apply them on bigger models because of potential resources limitations. However, then the paper should not talk about *Large* Language Models, and just about Language Models instead.\n\nDid not affect my rating:\n- The authors explore just one model, therefore it is not clear if this results would extend to other language models. This is understandable due to the resources needed to obtain the attributions.\n- Limited impact. It is an interesting exploratory analysis, but some previous work had obtained similar conclusions and I don't see how the results could be used for further research.", "questions_to_authors": "", "paper_topic_and_main_contributions": "The paper analyses how multilingual training data is used by a XLM-R model specifically fine-tuned for binary classification tasks. The authors use a Training Data Attribution (TDA) method to understand which samples of a training corpus are more influential when making predictions in given languages. The authors explore a big variety of experiments. They start analysing the differences between using a parallel corpus across languages, or a non-parallel one. Using the parallel dataset they analyse if data of different languages reinforce or complement each other in a prediction. They also analyse how the language-sharing varies during the training, what happens in zero-shot conditions and with an unbalanced training set. The contribution of the paper is gaining insights on how the multilingual data is leveraged in the stated settings. In general, the authors observe that the model frequently relies on data from different languages, and not only in the given one for the prediction. They see that the sharing increases as the fine-tuning progresses and that the shared information both reinforces and complements the data of the test language.", "excitement": 3, "reproducibility": 5, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "sXLX3ycn44", "reviewer": "Reviewer_JCHa", "summary": "", "questions": "I'm more curious if this conclusion can be generalized for the pre-training phase of MLLMs? Or can it only be limited to the fine-tuning stage, as the authors say?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 4, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for the positive review.\n\nWhile it is possible that models with e.g. larger sizes would behave differently, we believe that it is already an interesting finding that at least one popular LM can rely on cross-lingual data sharing. It would be unlikely that better and larger models would not have the ability to learn this as well. Though, what we could instead find is that larger models do not need to do it because of their increased capacity. As this was outside the scope of this project, we hope that the approach proposed in this paper will enable such follow up studies.\n\nAlso, given the recent advancements in the field, we will change our use of large language models to just language models.\n\nLastly, while running experiments to study the effect during pre-training would be very interesting, the problem with this would be that at the pre-training phase too many training samples are seen to  compute influence scores for. We would need to re-run pre-training to make sure that we know what exact training samples were seen and compute influence scores between each training and test sample (or an informative subset of training samples – though even computing scores for just e.g. 1% of the pre-training data will already be expensive). We can imagine that other research groups will have the compute power to do something like that in the future though, especially since researchers are in parallel actively working on more efficient TDA methods, and our approach to studying cross-lingual data sharing can generally be coupled with any type of TDA method.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "1. This paper attempts to explore the question of how much models really benefit from multilingual data and cross-lingual sharing, and under what conditions this occurs. The question explored in this paper is very interesting and important, and while some works have tried to explore this question and given some conclusions, this work presents a new perspective to analyze the question. While it is not difficult to think of analyzing this question from a data perspective, it is nice that this work succeeds in implementing this idea.\n2. This paper hypothesizes that if a model performs cross-lingual information sharing, then it will base its inference-time predictions (to some extent) on training data from multiple languages. This hypothesis appears to be correct, while the authors conduct reasonable experiments based on this hypothesis.\n3. This paper is well-written and clear.", "reasons_to_reject": "1. My only point of concern is that this paper only conducts experiments on one MLLM, the XLM-R base. For the question the paper wants to explore, will different MLLMs or different model size behave differently?\n2. It would not generally be considered that the XLM-R base is an LLM, which seems a bit of an overstatement. Also, I think the authors should add other types of PLMs to make their statement more strong, such as decoder-only PLMs", "questions_to_authors": "I'm more curious if this conclusion can be generalized for the pre-training phase of MLLMs? Or can it only be limited to the fine-tuning stage, as the authors say?", "paper_topic_and_main_contributions": "1. This paper attempts to explore the question of how much models really benefit from multilingual data and cross-lingual sharing, and under what conditions this occurs. \n2. They use a training data attribution method, to retrieve training samples from multilingual data that are most influential for test predictions in a given language.\n3. In this way, this paper analyzes cross-lingual sharing mechanisms of MLLMs in the data level instead of model parameter level. Then this paper points out that MLLMs rely on data from multiple languages during fine-tuning and this reliance increases as fine-tuning progresses. Meanwhile, this paper also finds that training samples from other languages can both reinforce and complement the knowledge acquired from data of the test language itself.", "excitement": 4, "reproducibility": 3, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "bxACBENnXy", "reviewer": "Reviewer_3fXq", "summary": "", "questions": "\nDear Authors, thank you for the work. Please find below a few questions:\n * L248: How making it a binary classification helps with the computational cost? Arguably making it a multi-classification task is not more expensive. More generally, it seems most of experiments in this paper rely on XLM-R, which with its 550M parameters can easily be run on a modern single MacBook Pro/comparable laptop. L311: Authors report using an A100 GPU. Can you elaborate more about the 'very expensive' cost?\n* Table 1: Why the last sample in Table 1 has '..'. Does that indicate a truncation or is that the sample?\n* Do you plan to release the code used for the experiments? All the models and datasets are open-source. Releasing the code would allow the community to reproduce/replicate the results presented in this work. ", "limitations": "", "rating": 4, "confidence": 3, "soundness": 4, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for your review and appreciation of our paper.\n\nThe problem with the compute expense is that we need to get the gradients of the loss for each training and test sample to compute the dot product between them. Though it is not possible to simply store the gradients of ~10K training samples into memory. Therefore, we need to re-compute the gradient for each training sample for every test sample. Moreover, note that you have to do this for each model checkpoint (in our case we use 4-5 checkpoints). Also, computing the dot products between such high dimensional vectors is expensive. We would like to point out, however, that while we focused on retrieving high quality influence scores on the full training set for this first explorative study (such that we wouldn’t miss any training sample or bias the results), researchers are in parallel actively working on various efficiency tricks that can be used to speed up the process. Given that our approach to studying cross-lingual data sharing can be coupled with any type of TDA method, we hope that many interesting follow up experiments will be possible using faster methods as well. \n\nRE the binary classification: It reduces computational costs indirectly because it simplifies the task and thus requires fewer training samples (only 10K) to obtain reasonably high performance on the task. Therefore we need to compute influence scores between fewer training and test samples which reduces computational costs. We will clarify this in the paper.\n\nRE table 1: Yes, this is just a truncation to make the example fit in the Table. We will clarify this in the caption.\n\nRE the code: Yes, we will release our code upon publication.\n\nTypos Grammar Style And Presentation Improvements:\n- L339: A enumerated list seems to be introduced in L339 with a 'First', however the second item seems to be not present. If this is not a list of findings, I suggest to remove \"First\".\n\nWe will remove it.\n\n- Figure 1: k starts at 50. Is that intended?\n\nYes, we started by trying to remove the top 50 most influential samples.\n\n- Figure 4 is not readable. Could you vectorize it like the other pictures/figures?\n\nThank you for pointing this out, we will make sure to improve the readability in the camera-ready version.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": " * Paper is well written and presented. All questions and findings are presented in Section 1. Formal notations are correctly introduced in subsequent sections, and they are consistent between each other.  \n * The work presented seems to be the first to use a training data-first approach to study cross-lingual aspects. Previous lines of work have studied cross-lingual abilities of LM at the parameters or prediction/probing level. \n * Experiments are clear and well documented. Additional experiments are added in Section 8 and details in Appendix. Great point as well to note: many examples are given and manually analyzed. \n * Results presented are interesting for the community as they highlight that LM cross-lingual representations may be more universal that what previous works suggested. \n\nOverall this paper is well written and experiments are correctly conducted and presented. Results are interesting and could interest as well the rest of the research community. ", "reasons_to_reject": "* Multiple times the authors mention the expensive cost related to their experiments. However, looking at the models involved (XLM-R with 550M parameters), this seems far away from today standards (> 4B parameters, with 'small' models like FlanT5-xl). This raises some concerns: \n    (a) It is not extremely clear in the paper why this computational cost seems so expensive. Adding measurements (e.g. estimated FLOP per experiment) would have helped grasping the problem. \n    (b) If the cost is indeed expensive, this seems to limit importantly the scope of this work as model like XML-R are fairly small. ", "questions_to_authors": "\nDear Authors, thank you for the work. Please find below a few questions:\n * L248: How making it a binary classification helps with the computational cost? Arguably making it a multi-classification task is not more expensive. More generally, it seems most of experiments in this paper rely on XLM-R, which with its 550M parameters can easily be run on a modern single MacBook Pro/comparable laptop. L311: Authors report using an A100 GPU. Can you elaborate more about the 'very expensive' cost?\n* Table 1: Why the last sample in Table 1 has '..'. Does that indicate a truncation or is that the sample?\n* Do you plan to release the code used for the experiments? All the models and datasets are open-source. Releasing the code would allow the community to reproduce/replicate the results presented in this work. ", "paper_topic_and_main_contributions": "Many of the previous works studying multilingual capabilities of LLM have proposed to look at cross-lingual capabilities by probing or by analyzing distributional properties of language subspace. In this work authors propose to take a step back in the training pipeline and study in which extent the model exploits its multilingual training data to make cross-lingual predictions. \n\nAuthors use the TracIn method previously published, which allows to identify the most informative training samples. The tasks are fairly standard for the topic (XNLI, cross-lingual paraphrasing, cross-lingual Sentiment Analysis), choice that helps for comparison with prior works. Results presented are interesting and highlight that LM cross-lingual representations may be more universal that what previous works suggested. ", "excitement": 4, "reproducibility": 3, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {"Typos_Grammar_Style_and_Presentation_Improvements": "* L339: A enumerated list seems to be introduced in L339 with a 'First', however the second item seems to be not present. If this is not a list of findings, I suggest to remove \"First\". \n* Figure 1: k starts at 50. Is that intended? \n* Figure 4 is not readable. Could you vectorize it like the other pictures/figures?"}}, {"review_id": "7gO3NtoXUe", "reviewer": "Reviewer_qo5L", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": 4, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for the positive review.\n\nWhile pre-training definitely affects the behavior of the model at the fine-tuning stage, studying the effects of different pre-training runs on the fine-tuning behavior would be a different study. Studying the pre-training phase can not directly tell us about the predictions that are made at test time as: (1) we typically need to first fine-tune the model on a downstream task and (2) during fine-tuning the way in which the model learns can change. Moreover, studying the fine-tuning stage allows us to compare cross-lingual data sharing for different downstream tasks and datasets. This allowed us to pose a set of interesting questions about which types of tasks elicit more sharing and the effect that the dataset properties could have on this (e.g. parallel vs non-parallel data).  Thus, given the wide range of experiments reported on in the paper already, studying the pre-training effects was left for future work. \n\nMoreover, while we do not perform experiments at the parameter level ourselves, we do compare our findings to those obtained from previous studies at the parameter level. For instance, in line with previous studies at the parameter level, we find that cross-lingual sharing increases during fine-tuning and that the amount of sharing between language pairs fluctuate over training. While running more experiments at the parameter level ourselves would be interesting, we believe that the set of experiments we picked to conduct at the data-level already tells an interesting, complete, story on its own. Also, since we are limited to 8 pages, we do not think that it would be feasible to add more experiments to the paper. Though, we do believe that directly contrasting results at the parameter and data level could result in an interesting follow up paper. \n\nLastly, thank you for the feedback on the structure of the methods and experiments section. We will incorporate all of your suggestions in the camera-ready version.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "- The first data approach to studying cross-lingual sharing at the data level.\n- This data-level study of cross-lingual sharing is very important to the multilingual NLP community as it will help design MLLMs in such a way as to maximize cross-lingual sharing by understanding the underlying factors that encourage or limit that. It could also be directly used as a measure of the intrinsic performance and cross-lingual capabilities of those models. \n- The quality of the approach chosen allows an unbiased measuring of the influence over fine-tuning data. I like how the paper chooses quality over quantity (as explained in the limitations).", "reasons_to_reject": "- Shedding light on the mechanism of cross-lingual sharing in MLLMs should involve more studying their biases at the pre-training stage and incorporating an understanding or measure of those to assess the true influence of languages at the fine-tuning stage. I think without that the study is a bit lacking and inconclusive in that.\n- While this is the first study of cross-lingual sharing at the data level, it could help to compare those insights to the parameter level to see how complementary or orthogonal they are.\n- While I think the ideas are clear, the paper could benefit from another round of restructuring especially when it comes to making a distinction between the methodology and experimental setup (check comments below).", "questions_to_authors": "", "paper_topic_and_main_contributions": "This paper studies cross-lingual sharing mechanisms during fine-tuning at the data level. They leverage a technique called TracIn the influence of each training language on test predictions in a given language. This sheds light on very important aspects of cross-lingual data-sharing dynamics including to what extent languages influence each other, complementarity and reinforcement nature of the interactions between languages, and how all of that plays out in data-scarce and zero-shot scenarios.", "excitement": 3, "reproducibility": 4, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {"Typos_Grammar_Style_and_Presentation_Improvements": "- Section 3: this should go into the experimental setup\n- Section 4.1: some parts of it should also go into the experimental setup. \n- You could start by Section 4.2 which is the main approach of the paper then leave describe just the methodology of different evaluation tasks after that in the methods section. After that, you can talk about the different hyperparameters of those tasks and stats of datasets in the experimental setup. You basically want to decouple your approach for studying/quantifying the influence of languages from the downstream tasks that are used as use cases for this analysis and make your approach look as generic enough to be used to understand any downstream task that the NLP community is willing to study next. \n- Table 1: what the first column? explain in the caption.\n- Line 377 Results: could be merged with the previous paragraph \n- Section 7: you should explain here that the next subsections will talk about two types of datasets all in Figure 2\n- Table 3: table not well introduced or explained in main text\n\n\n"}}]

Author rebuttal:

Meta-review: In the context of multilingual masked language models, this paper focuses on understanding the importance of specific training (i.e. fine-tuning) data samples at test time (referred to as cross-lingual data sharing). More specifically, it measures and analyzes the importance of the training samples and their language distribution using TracIn (Prudi et al. 2020) for the multilingual and cross-lingual performance of XLM-R across three tasks.

Reasons to accept:
- Very well-written paper (with beautiful plots) that addresses an under-studied question: the importance of specific samples seen during fine-tuning at test time in the multilingual and cross-lingual settings.
- Many settings and dimensions of the problem are analyzed and discussed, such as sample importance in the multilingual setting, in the zero-shot cross-lingual setting, and the impact of fine-tuning dynamics on cross-lingual data sharing.

Reasons to Reject:
- None

Suggestion:
- Given the emergence of LLMs as an essential framework in NLP, discussing how this method could be applied to pretrained LLMs (without task-specific fine-tuning) and their multilingual generalization would be highly beneficial for the paper.
Decision: Accept-Main