Crosslingual Capabilities and Knowledge Barriers in Multilingual Large Language Models

## Abstract

Abstract Large language models (LLMs) are typically multilingual due to pretraining on diverse multilingual corpora. But can these models relate corresponding concepts across languages, effectively being crosslingual ? This study evaluates six state-of-the-art LLMs on inherently crosslingual tasks. We observe that while these models show promising surface-level crosslingual abilities on machine translation and embedding space analyses, they struggle with deeper crosslingual knowledge transfer, revealing a crosslingual knowledge barrier in both general (MMLU benchmark) and domain-specific (Harry Potter quiz) contexts. We observe
that simple inference-time mitigation methods offer only limited improvement. On the other hand, we propose fine-tuning of LLMs on mixed-language data, which effectively reduces these gaps, even when using out-of-domain datasets like WikiText. Our findings suggest the need for explicit optimization to unlock the full crosslingual potential of LLMs. Our code is publicly available at https://github.com/google-research/crosslingual-knowledge-barriers .

## 1 Introduction

Figure: Figure 1: LLMs pretrained on internet-scale corpora containing texts in different languages are typically multilingual. While they show promising crosslingual abilities on explicit tasks like machine translation, they struggle to bridge the language gap on knowledge-intensive tasks that require implicit crosslingual correlation, revealing a crosslingual knowledge barrier.
Refer to caption: x1.png

Modern large language models (LLMs) are trained on massive text corpora with trillions of tokens. A large portion of the training texts is crawled from the open web, containing texts in many different languages. As a result, many LLMs can operate in multiple languages. For example, Mistral-Large and Mixtral 8$\times$22B (Mistral, ) reported performance on the benchmark datasets (e.g., MMLU (Hendrycks et al., ), Arc Challenge (Clark et al., )) in multiple languages.

For humans, knowing multiple languages (*multilingual*) naturally implies knowing the correspondence between the words and phrases of the same meaning across those languages (*crosslingual*). This is because when exposed to different linguistic environments, people can develop crosslingual capabilities by grounding the languages in physical world interactions. For example, we can relate the English world “apple” to the Spanish word “manzana” because in both linguistic environments the corresponding words refer to the same fruit in the real world. On the other hand, modern LLMs are trained purely based on the statistical relations in the text corpus without any grounding in the real world. In specific tasks such as machine translation, in order to teach the models to correlate notions across different languages, it is common to train with *parallel corpora* — collections of pairs of texts with the same meaning but in different languages (Eisenstein, ). This motivates our central research question:

> How well do multilingual LLMs, not explicitly (^1^11This criterion allows the case when a small amount of parallel texts accidentally crawled from the web get mixed in the pretraining dataset, as it is nearly impossible to verify. We believe such presence, if it exists at all, would have negligible impact on the model given the size of the rest of the pretraining datasets.) trained on parallel corpora, exhibit crosslingual capabilities?

To state the problem more precisely, we define(^2^22 We leave some of the terms mathematically vague, as long as they are not conceptually ambiguous. E.g., to measure the performance with a given correct answer, depending on the specific task format, we could either ask the model to generate the specific sequence of tokens or to rank the correct answer among multiple choices.) the multilingual and crosslingual capabilities as follows.
Denote an instance of a given task $\mathsf{T}$ as a tuple $(\mathcal{K},\mathcal{C},\mathcal{O})$, where $\mathcal{K}$ is the (optional) knowledge learned from training data, $\mathcal{C}$ is a context, and $\mathcal{O}$ is the correct answer. The *multilingual performance* on $\mathsf{T}$ measures the average performance across each language $\ell$ on an evaluation set of task instances $\{(\mathcal{K}_{\ell},\mathcal{C}_{\ell},\mathcal{O}_{\ell})\}$, where the subscript $\ell$ indicates the realization of the knowledge/context/answer in a specific language. On the other hand, the *crosslingual performance* on $\mathsf{T}$ measures the average performance on an evaluation set of crosslingual task instances $\{(\mathcal{K}_{\ell},\mathcal{C}_{\ell^{\prime}},\mathcal{O}_{\ell^{\prime
\prime}})\}$, where $\ell,\ell^{\prime},\ell^{\prime\prime}$ can be different languages.

For example, consider a task of $\mathsf{REPEAT}$. The multilingual performance simply measures the model’s capability of *copying* the context provided in different languages (i.e., $\mathcal{O}_{\ell}=\mathcal{C}_{\ell}$), whereas the crosslingual version of the task is equivalent to a much more challenging task of *translation* (i.e., $\mathcal{O}_{\ell^{\prime\prime}}=\text{Translate}_{\ell^{\prime}\Rightarrow
\ell^{\prime\prime}}(\mathcal{C}_{\ell^{\prime}})$). Another example task is question-answering (QA), where the crosslingual version requires the model to apply knowledge learned from one language to compute the answer in a different language.

With those definitions, we summarize the main studies and contributions as below:

Crosslingual capabilities (Section 2): We identify and formulate the question of multilingual vs crosslingual capabilities in LLMs without parallel-corpus training. Through both translation tests and embedding distance evaluations, we confirm that modern LLMs have strong crosslingual capabilities.

Crosslingual knowledge barrier (Section 3): We design crosslingual QA tasks, and observe a *crosslingual knowledge barrier*: LLMs have a significant performance gap in QA tasks formulated in a different language from the original language in which the knowledge is learned (see Figure 1 for an illustration). Via extensive experiments across six models, including both open-source and proprietary, we confirm a systematic presence of such barriers to knowledge learned both during the pretraining and fine-tuning stages.

Towards overcoming the barrier (Section 4): We propose a simple mixed-language training strategy and show that it can effectively reduce the knowledge barrier, significantly outperform other baseline methods based on prompt engineering, and further improve the few-shot learning performance. Furthermore, we show that even mixed-language training on out-of-domain data can be effective.

## 2 Multilingual LLMs have competitive crosslingual capabilities

In this section, we demonstrate the crosslingual capabilities of existing multilingual LLMs from two perspectives: machine translation performance (Section 2.1) and an analysis of multilingual text embeddings (Section 2.2). Specifically, our investigation focuses on five widely spoken languages: English (en), French (fr), German (de), Spanish (es), and Italian (it).

### 2.1 Machine translation performance

Evaluated multilingual language models. Our evaluation primarily considers six different LLMs that have exhibited strong multilingual capabilities. These include four open-source models: Llama2-7B, Llama2-13B (Touvron et al., ), Mistral-7B (Jiang et al., ), Llama3-8B (Meta, ), and two proprietary models: GPT-3.5 and GPT-4 (Achiam et al., ). Section B.1 provides HuggingFace links or endpoint specifications for all evaluated models. To perform machine translation tasks with the open-source models, we use the prompting format proposed by Xu et al. (). For proprietary models, we use the prompting template suggested on their official webpages.(^3^33[https://platform.openai.com/examples/default-translation](https://platform.openai.com/examples/default-translation))

Strong baselines. For reference we report two strong baselines: 1) the NLLB-3.3B model, the largest supervised encoder-decoder translation model from the NLLB family (Costa-jussà et al., ), which was trained on parallel corpus from various sources for 204 languages; and 2) the Google Translate API.

Multilingual LLMs achieve competitive performance in machine translation. We evaluate translation performance on a subset of $100$ examples from the FLoRes-101 benchmark (Goyal et al., ) for two directions per language: translating from English to the target language (en $\rightarrow$ X), and from the target language to English (X $\rightarrow$ en). We report the COMET score computed using the COMET-22 model (Rei et al., ), a metric designed to predict human judgments of machine translation quality, following previous work (Zhu et al., ; He et al., ; Xu et al., ).

As shown in Table 1, even though the evaluated multilingual LLMs are not directly trained on parallel corpora, their translation ability is quite competitive when compared to translation models explicitly trained on parallel corpora or industrial-grade translation APIs. Notably, these models generally perform better when translating non-English text into English, but worse in the opposite direction, potentially suggesting that they are more proficient with the English translations.
Those results are consistent with previous papers that focus on improving machine translation with pretrained LLMs (Zhu et al., ; He et al., ; Xu et al., ). However, our evaluation has a different goal of comprehensively examining LLMs’ crosslingual capabilities beyond translation.

**Table 1: COMET scores for machine translation tasks evaluated on a FloRes-101 subset benchmark using multilingual LLMs (Llama2-7B, Mistral-7B, Llama2-13B, Llama3-8B, GPT-3.5, and GPT-4), models trained on parallel corpora (NLLB-3.3B), and an industrial-grade translation API (Google Translate). Multilingual LLMs achieve competitive translation performance against dedicated translation models and the translation API.**
|  | English (en) $\rightarrow$ other languages | Other languages $\rightarrow$ English (en) |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  | en $\rightarrow$ de | en $\rightarrow$ fr | en $\rightarrow$ es | en $\rightarrow$ it | Avg | de $\rightarrow$ en | fr $\rightarrow$ en | es $\rightarrow$ en | it $\rightarrow$ en | Avg |
| Llama2-7B | $83.93$ | $85.82$ | $85.93$ | $84.67$ | $85.09$ | $86.94$ | $88.70$ | $85.52$ | $86.73$ | $86.97$ |
| Llama2-13B | $71.63$ | $79.91$ | $81.00$ | $76.68$ | $77.81$ | $88.26$ | $88.91$ | $85.83$ | $86.99$ | $87.50$ |
| Mistral-7B | $77.94$ | $78.23$ | $79.13$ | $78.13$ | $78.36$ | $87.48$ | $88.38$ | $85.64$ | $86.75$ | $87.06$ |
| Llama3-8B | $83.24$ | $86.56$ | $84.99$ | $85.98$ | $85.19$ | $89.22$ | $88.84$ | $87.04$ | $87.78$ | $88.22$ |
| GPT-3.5 | $87.53$ | $86.97$ | $86.40$ | $86.46$ | $86.84$ | $89.14$ | $89.42$ | $87.47$ | $88.41$ | $88.61$ |
| GPT-4 | $87.29$ | $87.56$ | $86.49$ | $86.64$ | $87.00$ | $89.27$ | $89.66$ | $87.53$ | $88.42$ | $88.72$ |
| NLLB-3.3B | $87.33$ | $87.44$ | $86.88$ | $88.26$ | $87.48$ | $79.65$ | $87.44$ | $85.64$ | $84.13$ | $84.72$ |
| Google Translate | $89.13$ | $88.77$ | $87.25$ | $89.21$ | $88.59$ | $89.96$ | $90.15$ | $87.47$ | $88.80$ | $89.10$ |

### 2.2 Embedding of mixed translated sentences

We further investigate the explicit crosslingual ability of multilingual LLMs by probing their text embeddings. Specifically, we aim to verify whether the embeddings for a given text in English are similar to the embeddings when some words are presented in different languages. We focus primarily on open-source models due to the cost associated with querying embeddings from proprietary models.

Experimental setup. We randomly sample $1,000$ examples from the WikiText-103 corpus (Merity et al., ). For each example, we create two versions: (1) The original text in English; (2) Mixed-language-translated: for each word, with a probability of $p=0.8$ it is unchanged; and with a probability of $1-p$, the word is (independently) translated, using Google Translate API, into a random language selected from the set {en, fr, de, es, it}. In other words, each word has a $0.16$ probability of being translated into a non-English language.
We then obtain sentence embeddings from the LLM for both versions of each example.

To establish baselines for comparison, we consider two scenarios representing an “upper bound” on the distance when perturbations are *unrelated* to the original content: (1) Random Token Replacement: with a probability of $p=0.16$, each token is replaced with a random different token from the vocabulary; and (2) Random Token Dropout: with a probability of $p=0.16$, a token is completely masked out by disallowing any attention to it.

The original embedding size is 4096. To visualize and compare the embeddings, we perform non-linear dimensionality reduction (McInnes et al., ), reducing each embedding to a 2D vector. For each example, we calculate the per-coordinate distance between the 2D embedding vectors of the original English text and the mixed-language-translated text. We then visualize these distance values and compare them to the baseline scenarios calculated in the same way, as shown in Figure 2.

Embeddings of English and mixed-language-translated text are similar. As shown, the embeddings of the original text and the mixed-translated text are quite close, with the difference vectors scattered around the origin. To further quantify this observation, we perform a two-sample statistical test on the following two distributions: (1) the cosine similarities between embeddings of original sentences and the embeddings of corresponding mixed-translated sentences, and (2) the cosine similarities between embeddings of original sentences and embeddings of corresponding sentences with random token replacement. The $p$-value of the test is smaller than $0.05$ for all models, suggesting that these two distributions are significantly different. In other words, replacing English words with translated words is significantly different from replacing English words with random tokens, which implies the explicit crosslingual capabilities of the multilingual LLMs.

Figure: Figure 2: The embeddings of the original English text and the mixed-language-translated text are closely aligned, unlike baselines with unrelated perturbations (e.g., random token replacement or dropout). The ellipses represent the covariance confidence intervals.
Refer to caption: x2.png

## 3 Crosslingual knowledge barrier in general and domain-specific knowledge

While multilingual LLMs have demonstrated impressive explicit crosslingual abilities, as we will show in this section, they also struggle to seamlessly bridge the language gap when faced with tasks demanding implicit crosslingual knowledge transfer. We term this phenomenon the *crosslingual knowledge barrier*. In the following, we demonstrate the presence of such barriers for both general knowledge (Section 3.1) and domain-specific knowledge (Section 3.2).

### 3.1 Crosslingual knowledge barrier in general knowledge

Monolingual evaluation is inadequate for assessing crosslingual abilities. Previous studies have evaluated open-domain Multiple Choice Question (MCQ) tasks on general knowledge in multilingual settings. For instance, Mistral series models (Mistral, ) were benchmarked on translated versions of the Massive Multitask Language Understanding (MMLU) (Hendrycks et al., ) dataset in languages such as French (fr), German (de), Spanish (es), and Italian (it), separately.
We call such monolingual evaluation setups as “full-translation” (i.e., the full English MCQ dataset is translated into another language).

While such results indicate *multilingual* proficiency, they are insufficient to show *crosslingual* proficiency. The core issues is that the relevant general knowledge might be present in each of the evaluated languages in the pretraining dataset, so the LLMs could answer the translated questions based on knowledge learned in each individual language without invoking any crosslingual capabilities. Such possibility is difficult to verify, as the pretraining datasets for most existing LLMs are undisclosed.

Figure: Figure 3: Monolingual evaluation of six LLMs on MMLU (fully translated for non-English languages), which is additionally split into four domains (STEM, Social Science, Humanities, Others) based on its subject categories. LLMs consistently perform better at answering multi-choice questions in English than in other languages.
Refer to caption: x3.png

Mixed-language evaluation. To directly evaluate crosslingual capabilities of LLMs on general knowledge MCQ tasks, we suggest adopting an inherent crosslingual interaction approach through mixed-language MCQ formats. Specifically, we propose the following formats purposefully designed to be novel compositions unlikely to have been encountered during pretraining (examples can be found in Figure 4):

- •
Mixup translation: translating the question and all options into 5 different languages, with the language assignments randomly determined from the set {en, fr, de, es, it}.
- •
Question translation: translating the question into a non-English language.
- •
Options translation: translating all options into a non-English language.
- •
Question+GT-option translation: translating both the question and the ground truth option into a non-English language, while keeping the remaining options in English.
- •
GT-option translation: translating the ground truth option into a non-English language, while keeping the question and the rest of the options in English.
- •
One-wrong-option translation: randomly selecting one incorrect option and translating it into a non-English language.

Figure: Figure 4: Examples of original, full-translated, and proposed mixed-language multiple choice question (MCQ) formats on MMLU.
Refer to caption: x10.png

In the above setups, even if a model has independently acquired knowledge in multiple languages, it must rely on crosslingual capabilities to select the correct answer. These tasks pose additional difficulty because, generally, the answer is expected to be in the same language as the questions. We use Google Translate API for all translations, and all derived datasets have the same size as the original dataset.

Open-source models are evaluated in the standard way by calculating the likelihood of each option token and using the maximum one as the model prediction (Touvron et al., ). For the close-soured models, we directly use the predicted best option (i.e., first token) by the model as answer.

Crosslingual barrier in MMLU knowledge. We focus on the MMLU benchmark for evaluating general knowledge, which comprises 4-option MCQs and includes $14k$ test samples from 4 domain categories (i.e., STEM, Social Science, Humanities, Others) across 57 subjects. The diversity of these domains enables us to draw general observations.
(1) The monolingual evaluation results in Figure 3 show that all LLMs consistently achieve higher accuracy when MCQs are presented in English compared to other languages. This is likely because the relevant general knowledge is more frequently presented in English within the pretraining corpus, and LLMs struggle to transfer this knowledge to other languages automatically.
Additionally, performance in German (de) is worse across all tasks and models, aligning with existing evaluations (Mistral, ), where Mistral and Llama models show lower accuracy in German than in other languages on commonsense reasoning benchmarks. Moreover, LLMs perform poorly in translation from English to German (Table 1), suggesting that the models may have inferior multilingual capabilities in German.
(2) The results in Figure 5 demonstrate a notable accuracy drop in the mixed-language settings, including question+GT-option, GT-option, and mixup translations, compared to monolingual settings (i.e., English and full-translation).
This suggests that LLMs struggle to understand the more difficult contexts in multiple languages and to relate the corresponding knowledge effectively to answer MCQs, highlighting a crosslingual knowledge barrier in the MMLU benchmark. We note such barrier exists even for the state-of-the-art models like GPT-4 (e.g., $81.82\xrightarrow{}68.61$ when comparing English to mixup-translated MMLU).
(3) The GT-option translation setting leads to the worst performance, indicating an inherent behavioral bias of LLMs that tends to avoid selecting a non-English option, even if it is the correct choice. This bias is further supported by the controlled comparisons in one-wrong-option translation settings, where LLMs achieve even higher accuracy than the English setting, as the model leverages the bias and avoids selecting the (incorrect) non-English option.
(4) LLMs obtain higher accuracy on question-translated and options-translated settings than full-translated settings, likely because the former two settings still have remaining context in English, which helps the models perform better.

Figure: Figure 5: Accuracy on MMLU variant benchmarks. The bars with * denotes the average accuracy across fr, de, es, and it. LLMs perform better at answering MCQs in English than in mixed-language settings, especially the ground truth option and mixup translation, indicating the existence of cross-lingual knowledge barriers. Due to budget constraints, GPT-3.5 and GPT-4 are evaluated only in the most challenging settings.
Refer to caption: x11.png

### 3.2 Crosslingual knowledge barrier in domain-specific knowledge

Harry Potter Quiz. We use the Harry Potter world for the domain-specific knowledge evaluations, as it revolves around a highly detailed and extensive fictional universe with its own unique characters, terminology, and concepts. We manually curate a multiple-choice question-answering dataset called the Harry Potter Quiz (HP-Quiz) by extracting information from the Harry Potter Wiki pages(^4^44[https://harrypotter.fandom.com/wiki/Main_Page](https://harrypotter.fandom.com/wiki/Main_Page)). Further details about the dataset are provided in Appendix A.

Evaluation. Each multiple-choice question in the HP-Quiz dataset is available in five different languages: English (en), French (fr), German (de), Spanish (es), and Italian (it). To assess the crosslingual knowledge barrier, we consider both (1) the original model, and (2) the model fine-tuned on domain-specific corpora(^5^55Specifically, we preprocess the WikiText-103 dataset (Merity et al., ) and select documents highly relevant to the Harry Potter universe using a retriever (see Section B.3 for details).) presented only in English. For evaluation, we prompt the model with the multiple-choice question in each language, and report the accuracy of the model in selecting the correct answer in this multiple-choice task for each language.

Figure: Figure 6: Multiple-choice accuracy of various multilingual LLMs on the Harry Potter Quiz benchmark before (left) and after (right) fine-tuning the model on in-domain content presented in English (i.e., Harry Potter related documents selected from WikiText-103). Models consistently perform better at answering questions in English than other languages, indicating the presence of a crosslingual knowledge barrier. Notably, for Mistral, fine-tuning results in decreased performance on the HP-Quiz, potentially due to a mismatch between the fine-tuning data mixture and the pretraining data mixture, a phenomenon also observed by Xia et al. ().
Refer to caption: x18.png

Crosslingual barrier also exists for Harry Potter knowledge.
As shown in Figure 6, when presented with the same set of questions in 5 languages, the model consistently exhibits higher accuracy in answering correctly in English. This trend holds for both pretrained LLMs (left) and fine-tuned LLMs (right).
After fine-tuning on domain-specific English corpora, despite the increase in model accuracy in English (which is more evident for Llama2-7B and Llama3-8B), the crosslingual knowledge barrier persists. These observations provide compelling evidence that the crosslingual knowledge barrier extends beyond general knowledge into specific domains.

## 4 Overcoming crosslingual knowledge barriers

In this section, we explore potential methods to overcome the manifest crosslingual knowledge barrier that we identified in the existing multilingual LLMs. We consider two types of potential mitigation methods, including inference-time intervention (Section 4.1), including prompt engineering and few-shot demonstration, and training-time intervention (Section 4.2), including mixed-language fine-tuning on general and domain-specific corpora.

### 4.1 Inference-time mitigation falls short of overcoming crosslingual knowledge barriers

We evaluate inference-time mitigation methods to improve LLM performance on the mixup-translated MMLU, a challenging crosslingual setting evidenced by the low performance in Figure 5.

Prompt engineering. We evaluate the following prompting strategies: (1) Alternative option ID characters. We replace the default A/B/C/D with a/b/c/d or 1/2/3/4, motivated by recent evidence on selection bias in option IDs for MCQ tasks (Zheng et al., ) and to account for the possibility that the Arabic numerals are more invariant to languages.
(2) Multilingual awareness instruction: We add an explicit instruction before the MCQs (e.g., “Remember that the question and options can be in different languages”) to make models aware of the potential presence of other languages.

Few-shot demonstration.
Our evaluation mainly considers the 0-shot setting, which excludes any biases introduced by the few-shot demonstrations (Zhao et al., ), but we also conduct 5-shot experiments to further investigate crosslingual performance.
MMLU covers 57 subjects, and the few-shot demonstrations for each subject are derived from the corresponding development set and shared across all test samples within the same subject.
We employ several strategies to construct few-shot demonstrations:
(1) English demonstration: English MCQ and answer pairs.
(2) Same bias demonstration: mixup-translated MCQ and answer pairs, where each MCQ demonstration is constructed in the same way as the test sample.
(3) Translate-Then-Answer demonstration: For each mixup-translated MCQ, we prompt LLMs first to translate it into English before producing the final answer. To help LLMs follow the explicit translation instruction, we provide demonstrations where each includes a mixup-translated MCQ, the corresponding English MCQ, and its answer.
We provide the detailed prompt templates in Section B.2.

**Table 3: Effect of inference-time mitigation methods evaluated on MMLU benchmarks. The highest accuracy achieved under the 0-shot/5-shot setting is underlined. $\downarrow$ denotes the accuracy drop observed in mixup MMLU compared to English MMLU. Simple prompt engineering cannot address the cross-lingual knowledge barrier problem. Although few-shot demonstrations enhance accuracy compared to the 0-shot setting, the performance gap between mixup MMLU and English MMLU remains significant. For reference, GPT-4 achieves $81.82$ (0-shot) on English MMLU, and $68.61$ $\downarrow$$13.21$ (0-shot), $73.58$ $\downarrow$$8.24$ (5-shot english demonstrations), $77.71$ $\downarrow$$4.11$ (5-shot biased demonstrations) on mixup MMLU.**
| Eval setup | Prompt | Llama2-7B | Llama2-13B | Mistral-7B | Llama3-8B |
| --- | --- | --- | --- | --- | --- |
| English (0-shot) | A/B/C/D (default) | $41.53$ | $52.11$ | $60.21$ | $60.54$ |
| Mixup<br>(0-shot) | A/B/C/D (default) | $32.18$ $\downarrow$$9.35$ | $41.97$ $\downarrow$$10.14$ | $47.86$ $\downarrow$$12.35$ | $48.62$ $\downarrow$$11.92$ |
| a/b/c/d | $30.80$ | $41.68$ | $47.78$ | $44.10$ |  |
| 1/2/3/4 | $27.96$ | $38.39$ | $45.56$ | $44.63$ |  |
| Multilingual-Aware instruction 0 | $31.19$ | $41.01$ | $47.14$ | $48.13$ |  |
| Multilingual-Aware instruction 1 | $31.23$ | $41.35$ | $46.80$ | $47.89$ |  |
| Mixup<br>(5-shot) | English demonstrations | $35.23$ | $43.15$ | $49.46$ | $50.99$ |
| Same bias demonstrations | $36.92$ $\downarrow$$4.61$ | $44.32$ $\downarrow$$7.79$ | $51.07$ $\downarrow$$9.14$ | $51.65$ $\downarrow$$8.89$ |  |
| Translate-Then-Answer demonstrations | $30.02$ | $42.93$ | $42.27$ | $47.79$ |  |

From the results in Table 3, (1) regarding prompt engineering, we observe no improvement and even a performance drop compared to the default prompt. It suggests that the crosslingual knowledge barrier is an inherent failure of LLMs that cannot be effectively addressed by simple prompt engineering.
(2) 5-shot settings consistently improve performance compared to 0-shot settings on mixup MMLU because providing demonstrations in the corresponding subject helps LLMs generalize to knowledge-intensive tasks.
(3) Mixup demonstrations lead to better performance than English demonstrations because the mixed language pattern in the demonstrations matches that of the test examples. (4) Translate-Then-Answer demonstrations are not effective. We observe failure patterns where, after translating to English, sometimes LLMs merely continue generating text without outputting the desired answer for the MCQ task.
(5) Even under the best demonstration strategy, there still exhibits a substantial accuracy gap in mixup MMLU compared to English MMLU.
Consequently, we explore training-time intervention in Section 4.2 via mixed language fine-tuning methods.

### 4.2 Mixed-language fine-tuning effectively mitigates crosslingual knowledge barriers

Given the limited success of inference-time interventions, we turn our attention to training-based methods that aim to directly instill better crosslingual knowledge in the model itself. Specifically, we explore mixed-language fine-tuning, where we explicitly construct a fine-tuning dataset comprising examples from multiple languages. To ensure a balanced representation of different languages, we split the training data into smaller units and randomly select a target language for each unit, translating the unit into that language if necessary. This approach also ensures that the translated data is of similar size as the original English data, enabling a fair comparison. Note that this approach differs from using parallel corpora as each unit is only presented in a single language.

We explore different choices for the smallest unit for translation, including the following settings:

- •
Full document translation: the entire document (example) is translated to a random language.
- •
Sentence-level translation: each document is split into units of sentences, using common English punctuation marks (Python regex r’(\s*[\.,;!?]\s+)’). Each sentence is then translated independently.
- •
$k$-word chunk-level translation: the document is split into chunks of $k$ words, where a “word” is any consecutive sequence of characters separated by one or more non-word characters defined by the Python regex r’(\W+)’. We found that the translation tool could be confused by $k$ words that span across sentence boundaries, so we did a little tweak by splitting into sentence first, and then split each sentence into $k$-word chunks.

Unless otherwise specified, for each translation unit, the target language is always randomly chosen uniformly from German, French, Italian, Spanish, and English (in this case the translation is a No-Op). We use a Google Translate API to perform all the translations.

Figure: Figure 7: Fine-tuning on a mixed-language general corpus (e.g., WikiText-2) enhances the model’s performance on domain-specific tasks (e.g., Harry Potter knowledge test) across multiple languages, including English. See Figure 9 for results on Mistral-7B and Llama2-13B.
Refer to caption: x21.png

**Table 4: Finetuning LLMs on the mixed-languages general corpus WikiText-103 can improve the performance on English and mixup MMLU benchmarks under 0-shot & 5-shot settings.**
| Model | Llama2-7B | Llama3-8B |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| En MMLU | Mixup MMLU | En MMLU | Mixup MMLU |  |  |  |
| Un-FTed | $41.53$ | $32.18$ | $60.54$ | $48.62$ |  |  |
| En FTed | $41.21$ | $31.46$ | $60.32$ | $47.83$ |  |  |
| Mixed language (sentence) FTed | $42.05$ | $34.08$ | $60.45$ | $51.75$ |  |  |
| Mixed language (words) FTed | $42.00$ | $34.06$ | $60.28$ | $50.88$ |  |  |
|  | (En demo) | (En demo | | Bias demo) | (En demo) | (En demo | | Bias demo) |
| Un-FTed + 5-shot | $45.88$ | $35.23$ | $36.92$ | $65.00$ | $50.99$ | $51.65$ |
| En FTed + 5-shot | $45.83$ | $35.43$ | $36.49$ | $64.97$ | $50.38$ | $50.88$ |
| Mixed language (sentence) FTed + 5-shot | $45.95$ | $36.80$ | $38.14$ | $65.06$ | $54.45$ | $54.57$ |
| Mixed language (words) FTed + 5-shot | $46.15$ | $37.35$ | $38.56$ | $64.91$ | $54.46$ | $54.64$ |

We explore mixed-language fine-tuning of the original model on two types of corpora: general knowledge where we use WikiText-2 or WikiText-103 (Merity et al., ), and domain-specific where we use a subset of WikiText-103 that is highly related to Harry Potter based on BM25 similarity ranking (the details are deferred to Section B.3).

Mixed-language fine-tuning on general corpus. We first experiment with fine-tuning LLMs on a general corpus, WikiText-2 (keyword searching suggests that WikiText-2 has no overlap with Harry Potter characters or spells), with different choices of translation units. Specifically, we fine-tune the model
for a single epoch, with a learning rate of $2\times 10^{-5}$ and a batch size of 32, and report the multiple-choice accuracy on the Harry Potter Quiz.
As shown in Figure 7, fine-tuning on the English general corpus alone does not improve performance on the Harry Potter task. However, fine-tuning on mixed translated general corpora enhances performance. This suggests that mixed-language fine-tuning could help LLMs recover crosslingual capabilities: By exposure to frequent language switch during fine-tuning, LLMs can better adapt to the setting when the same knowledge is asked in a different (and usually non-English) language. Interestingly, mixed-language fine-tuning also improves the performance in English.

Our second experiment is finetuning LLMs on WikiText-103, a general corpus that offers a larger size and a broader range of knowledge compared to WikiText-2, and reporting the accuracy on MMLU variant benchmarks.
(1) As shown in Table 4, finetuning on English WikiText-103 corpora hurts the performance, likely because it is an out-of-domain corpora for MMLU dataset. However, finetuning on mixed translated WikiText-103 corpora can lead to improvements, which are particularly noticeable on the mixup MMLU benchmarks but also evident on the English MMLU.
These results indicate that multiple language switches during fine-tuning enable LLMs to better understand and process multilingual input, become more robust to variations in language and phrasing, and perform better in knowledge-intensive crosslingual tasks.
(2) Combining training-time interventions with test-time interventions can further enhances performance. While adding 5-shot biased demonstrations to our fine-tuned models leads to the best performance on mixup MMLU, adding 5-shot English demonstrations is also effective. This indicates the general applicability of our fine-tuned models across different scenarios.
(3) Fine-tuning with both word-level and sentence-level mixed language WikiText-103 corpora effectively improves MMLU performance. Word-level mixing slightly outperforms in 5-shot settings, while sentence-level mixing is more effective in 0-shot settings.
We defer the evaluation results of fine-tuned models on more MMLU variant benchmarks to Appendix C.

Figure: Figure 8: Fine-tuning on a mixed-language domain-specific corpus (i.e., Harry Potter related documents from WikiText-103) enhances the model’s performance on the Harry Potter Quiz dataset across multiple languages, including English.
Refer to caption: x24.png

Mixed-language fine-tuning on domain-specific corpus. Similarly, we investigate the effectiveness of mixed-language fine-tuning for the domain-specific task. Specifically, we fine-tune the model on mixed-language versions of in-domain corpora (i.e., Harry Potter-related documents from WikiText-103) and evaluate performance on the Harry Potter Quiz benchmark. For an upper bound reference, we also report results from fine-tuning on a collection containing examples in all five languages (5$\times$ larger dataset size than our approach). As shown in Figure 8, mixed-language fine-tuning results in significant performance gains, especially when translation occurs at the sentence level. Notably, it also improves the model’s accuracy for both English and other languages.

## 5 Related work

#### Understanding and improving multilingual LMs.

Understanding language models’ performance in multilingual settings is an active area of research. Prior works have identified strong variations in the amount of knowledge across different languages, attributed to differences in training corpora sizes (Jiang et al., ; Kassner et al., ; Ryan et al., ). These observations have also been leveraged to improve models’ performance, especially in English. For instance, Ohmer et al. () propose using multilingual self-consistency of predictions to assess how well the model understands a given task. Wu et al. () suggest using a reward model in a different language during fine-tuning for alignment from human
feedback can yield better-aligned models than using one in the same language as the pre-trained model. Efforts have also been devoted to studying well-established tasks for monolingual models in crosslingual scenarios, such as crosslingual pretraining (Lample & Conneau, ; Abadji et al., ; Schioppa et al., ), information retrieval (Yu et al., ), knowledge editing (Wang et al., ; Xu et al., ; Beniwal et al., ; Xu et al., ), text summarization (Wang et al., ; Huang et al., ) and instruction tuning (Chirkova & Nikoulina, ; Zhang et al., ; Ranaldi et al., ; Zhu et al., ).

The closest work to ours is Qi et al. (), which proposes a metric to evaluate the consistency of a multilingual language model’s factual knowledge across languages. They find that while increasing model size generally leads to higher factual accuracy in most languages, it does not necessarily improve crosslingual knowledge consistency. One key difference is that their study does not account for different factors that could contribute to the crosslingual consistency (e.g., a model independently learns the knowledge in both languages during pretraining could lead to a high consistency); while we formulate a controlled setting of crosslingual knowledge barrier, measuring precisely the ability to transfer knowledge learned (only) in one language to another language. Furthermore, we also proposed mitigation methods that could effectively reduce the knowledge barrier.

#### Machine translation ability of LLMs.

The off-the-shelf pretrained LLMs show promise in machine translation but still lag behind the commercial translation system, especially in low-resource languages. Previous studies have sought to enhance LLM translation capabilities through various prompting and finetuning methods.
Zhu et al. () introduce crosslingual translation in-context examples, while He et al. () employ advanced prompt engineering that induces translation-related knowledge (e.g., keywords, topics) from the given source sentence to guide the final translation process. Xu et al. () propose a two-stage fine-tuning approach, first enhancing proficiency in non-English languages by fine-tuning on non-English monolingual data, and then fine-tuning on high-quality parallel data for translation task.
Our work has a different goal of comprehensively examining LLMs’ crosslingual capabilities, beyond the translation task. We show that even though LLMs are very competitive at explicit translation tasks, they could struggle in more demanding tasks that requires implicit knowledge transfer across language boundaries.

#### Crosslingual transfer of multilingual LMs.

Crosslingual transfer refers to transfer learning that fine-tunes the model on a target task in one language (e.g., English), and then makes predictions for this task in another, typically more low-resource language. It addresses the challenges of limited training data in the target language for a target task.
It has been broadly studied for natural language understanding (Schioppa et al., ; Artetxe et al., ; Pires et al., ; Wu & Dredze, ; Li et al., ) and generation tasks (Chirkova & Nikoulina, ; Bapna & Firat, ; Vu et al., ; Maurya et al., ; Li & Murray, ; Tanwar et al., ) for multilingual models such as mBART, mT5, NLLB family. For instance, Chirkova & Nikoulina () demonstrated that fine-tuning the full model with a small learning rate yields the best crosslingual language generation performance, outperforming other methods such as adapter (Bapna & Firat, ), prompt-tuning (Vu et al., )) and hyperparameter tuning (Chirkova & Nikoulina, ). Additionally, several studies have improved crosslingual generalization by mixing auxiliary unsupervised data from additional languages during fine-tuning. For example, sampling target language examples with probability (e.g., 1%) when forming the mini-batch (Chirkova & Nikoulina, ; Vu et al., ).

Our study focuses on more recent autoregressive LLMs (e.g., Llama series, Mistral, GPT-3.5, GPT-4) that acquire multilingual capabilities from their internet-scale pretraining corpora. While several works have explored approaches to enhancing LLMs’ crosslingual transfer abilities such as finetuning with adapter merging (Zhao et al., ), our work differs in its primary focus.
We aim to provide a comprehensive understanding of the crosslingual capabilities of pretrained LLMs on tasks requiring explicit (e.g., translation tasks) and implicit crosslingual transfer (e.g., question-answering tasks involving general or domain-specific knowledge).
Furthermore, to improve crosslingual transfer ability of LLMs in general, our study employs fine-tuning on (out-of-domain) general corpora and proposes a principled approach to processing mixed language data at different levels of granularity, including word, sentence, and document levels.

#### Compositional generalization.

We also acknowledge that the crosslingual knowledge barrier can be viewed as an instance of the broader challenge of compositional generalization (Lake et al., ; Kim & Linzen, ; Hupkes et al., ; Xu et al., ; Yu et al., ) — the ability to systematically combine different skills to understand and produce novel compositions not directly trained on. In the case of crosslingual knowledge understanding, models must compose the skills of question answering and knowledge translation. However, this specific combination of crosslingual knowledge consistency warrants dedicated study due to its strong practical implications, as ensuring consistent feedback across languages is crucial for deploying trustworthy and effective multilingual AI assistants to a global user base.

#### Behavioral bias of LLMs.

Recent research also studies various behaviors and biases in LLMs that are different from human reasoning, such as reversal curse (Berglund et al., ; Grosse et al., ), order and position bias  (Wang et al., ; Pezeshkpour & Hruschka, ), option ID bias in multiple-choice question tasks (Zheng et al., ), premise order bias (Chen et al., ), susceptibility to distraction by irrelevant context (Shi et al., ). These studies provide a deeper understanding of LLMs and suggest various ways to improve those models. Our paper contributes to this important line of research from the perspective of crosslingual behaviors.

## 6 Conclusion and future work

In this work, we observed that multilingual LLMs without explicit training on parallel corpora demonstrate crosslingual capabilities. However, despite competitive performance in explicit crosslingual tasks such as translation, those models fail to transfer learned knowledge across the language boundary, a phenomenon we termed as the crosslingual knowledge barrier. Through comprehensive evaluations on both general and domain-specific knowledge, we confirmed a systematic presence of such barriers across all 6 models and the five languages that those models know. Finally, we evaluated both test-time and training-time mitigation and proposed a simple and effective mixed-language fine-tuning procedure to reduce the knowledge barrier in those models.

Limitations and future work. One important question that is not answered in this paper is how these models develop such strong crosslingual capabilities (despite the existence of crosslingual knowledge barriers). This is intriguing because unlike humans exposed to multiple lingual environments, LLMs do not have grounding in the physical world to help them establish connections between different words that refer to the same thing in the real world. While there is some preliminary work on grounding LLMs with the physical world (e.g., Zhang et al., ; Wang et al., ; Gao et al., ; Cheng et al., ), the majority of the models nowadays are still trained without interaction with the physical world. Therefore, an interesting future direction is to understand the mechanisms that allow the LLMs to develop crosslingual capabilities.

Another interesting observation is that mixed-language fine-tuning (on out-of-domain data) can improve the question-answering performance not only in low-resource languages but also in English in many of our evaluations. Previous studies (e.g., Abutalebi et al., ; Bialystok et al., ; Marian & Shook, ) have shown that multilingualism could have a positive effect on human cognitive abilities. But how does better crosslingual capabilities impact LLMs’ reasoning abilities (in English) remains to be fully understood.

## Acknowledgements

We thank Zheng-Xin Yong, Mengzhou Xia, John Yang, and Alexandre Sablayrolles for providing helpful suggestions and feedback. Yangsibo Huang acknowledges the support of the Wallace Memorial Fellowship.

The icon in Figure 1 uses images from [https://www.freepik.com/](https://www.freepik.com/).

## Appendix

## Appendix A The Harry Potter Quiz Dataset

We use Harry Potter as a setting to mimic domain-specific knowledge, as it revolves around a highly detailed and extensive fictional universe with its own unique characters, terminology, and concepts. We manually curate an English-only dataset named Harry Potter Quiz (or HP-Quiz in short) by collecting information about characters and magic spells(^6^66In Harry Potter, the magic spell is a magical action used by witches and wizards to perform magic.) from the Harry Potter Wiki pages(^7^77[https://harrypotter.fandom.com/wiki/Main_Page](https://harrypotter.fandom.com/wiki/Main_Page)). For characters, we gather attributes such as gender, hair color, house(^8^88Hogwarts, the fictional boarding school of magic in the Harry Potter book series, is divided into four houses: Gryffindor, Slytherin, Ravenclaw, and Hufflepuff.), and relationships with other characters. Regarding magic spells, we collected data on the types of spells they belong to. We then curate multiple-choice questions and answers based on the collected information. Specifically, the dataset consists of 300 questions in total, 157 questions about characters and 143 questions about magic spells. We format these questions as multiple choice questions.

Below is the full list of characters and spells included in HP-Quiz:

Aberforth Dumbledore, Albus Potter, Ariana Dumbledore, Arthur Weasley, Astoria Malfoy, Cedric Diggory, Charles Weasley, Cho Chang, Draco Malfoy, Dudley Dursley, Euphemia Potter, Fleamont Potter, Harry Potter, Hermione Granger, James Potter I, Kendra Dumbledore, Lily J. Potter, Lucius Malfoy, Narcissa Malfoy, Percival Dumbledore, Petunia Dursley, Roger Davies, Ron Weasley, Scorpius Malfoy, William Weasley

Aberto, Accio, Age Line, Alarte Ascendare, Alohomora, Anti-Cheating Spell, Anti-Apparition Charm, Anti-Disapparition Jinx, Anti-intruder jinx, Aparecium, Appare Vestigium, Apparition, Aqua Eructo, Arania Exumai, Arresto Momentum, Arrow-shooting spell, Ascendio, Avada Kedavra, Avifors, Avenseguim, Babbling Curse, Badgering, Bat-Bogey Hex, Bedazzling Hex, Bewitched Snowballs, Bluebell Flames, Blue sparks, Bombarda, Bombarda Maxima, Bravery Charm, Bridge-conjuring spell, Broom jinx, Bubble-Head Charm, Bubble Spell, Calvorio, Cantis, Capacious extremis, Carpe Retractum, Cascading Jinx, Caterwauling Charm, Cave inimicum, Celescere, Cheering Charm, Circumrota, Cistem Aperio, Colloportus, Colloshoo, Colovaria, Confringo, Confundo, Conjunctivitis Curse, Cracker Jinx, Cribbing Spell, Crinus Muto, Crucio, Defodio, Deletrius, Densaugeo, Deprimo, Depulso, Descendo, Deterioration Hex, Diffindo, Diminuendo, Dissendium, Disillusionment Charm, Draconifors, Drought Charm, Duro, Ear-shrivelling Curse, Ebublio, Engorgio, Entrail-Expelling Curse, Epoximise, Erecto, Evanesce, Evanesco, Everte Statum, Expecto Patronum, Expelliarmus, Expulso, Extinguishing Spell, Feather-light charm, Fianto Duri, Fidelius Charm, Fiendfyre, Finestra, Finite Incantatem, Finger-removing jinx, Firestorm, Flagrante Curse, Flagrate, Flame-Freezing Charm, Flask-conjuring spell, Flintifors, Flipendo, Flipendo Duo, Flipendo Maxima, Flipendo Tria, Flying charm, Fracto Strata, Fumos, Fumos Duo, Furnunculus, Fur spell, Geminio, Glacius, Glacius Duo, Glacius Tria, Glisseo, Gripping Charm, Hair-thickening Charm, Herbifors, Herbivicus, Homenum Revelio, Homonculous Charm, Hurling Hex, Impedimenta, Imperio, Inanimatus Conjurus, Incarcerous, Inflatus, Jelly-Brain Jinx, Jelly-Fingers Curse, Knee-reversal hex, Langlock, Lapifors, Leek Jinx, Levicorpus, Liberacorpus, Locomotor Mortis, Melofors, Meteolojinx recanto, Mimblewimble, Multicorfors, Obscuro, Oppugno, Orbis, Orchideous, Pepper Breath, Petrificus Totalus, Piscifors, Point Me

## Appendix B Experimental details

### B.1 Evaluated models

Table 5 provides the details of the models evaluated in our study.

**Table 5: HuggingFace links or endpoint specifications for evaluated models.**
| Model | Link |
| --- | --- |
| Llama2-7B | [https://huggingface.co/meta-llama/Llama-2-7b-hf](https://huggingface.co/meta-llama/Llama-2-7b-hf) |
| Llama2-13B | [https://huggingface.co/meta-llama/Llama-2-13b-hf](https://huggingface.co/meta-llama/Llama-2-13b-hf) |
| Mistral-7B | [https://huggingface.co/mistralai/Mistral-7B-v0.1](https://huggingface.co/mistralai/Mistral-7B-v0.1) |
| Llama3-8B | [https://huggingface.co/meta-llama/Meta-Llama-3-8B](https://huggingface.co/meta-llama/Meta-Llama-3-8B) |
| GPT-3.5 | [https://platform.openai.com/docs/models/gpt-3-5-turbo](https://platform.openai.com/docs/models/gpt-3-5-turbo), gpt-3.5-turbo-0125 endpoint |
| GPT-4 | [https://platform.openai.com/docs/models/gpt-4-turbo-and-gpt-4](https://platform.openai.com/docs/models/gpt-4-turbo-and-gpt-4), gpt-4-0613 endpoint |

**Table 6: Prompt templates for inference-time mitigation methods in mixup-translated MMLU evaluation. The templates are consistent across different evaluation setups, varying only in the language pattern of multiple-choice questions.**
| Setting | Type | Prompt |
| --- | --- | --- |
| 0-shot | Default prompt | The following are multiple choice questions (with answers) about $\{\mathrm{subject}\}$. |
|  | $\{\mathrm{Mixup_MultiChoiceQuestion}\}$ |  |
|  | Answer: |  |
| Multilingual-Aware<br>instruction 0 | The following are multiple choice questions (with answers) about $\{\mathrm{subject}\}$. Keep in mind that the question and options may be presented in various languages. |  |
| $\{\mathrm{Mixup_MultiChoiceQuestion}\}$ |  |  |
|  | Answer: |  |
| Multilingual-Aware<br>instruction 1 | The following are multiple choice questions (with answers) about $\{\mathrm{subject}\}$. Remember that the question and options can be in different languages. |  |
| $\{\mathrm{Mixup_MultiChoiceQuestion}\}$ |  |  |
|  | Answer: |  |
| few-shot | English<br>demonstrations | The following are multiple choice questions (with answers) about $\{\mathrm{subject}\}$. |
| $\{\mathrm{En_MultiChoiceQuestion_Demo1}\}$ |  |  |
| Answer: $\{\mathrm{Answer_Demo1}\}$ |  |  |
|  | …. |  |
|  | $\{\mathrm{Mixup_MultiChoiceQuestion}\}$ |  |
|  | Answer: |  |
| Same bias<br>demonstrations | The following are multiple choice questions (with answers) about $\{\mathrm{subject}\}$. |  |
| $\{\mathrm{Mixup_MultiChoiceQuestion_Demo1}\}$ |  |  |
| Answer: $\{\mathrm{Answer_Demo1}\}$ |  |  |
|  | …. |  |
|  | $\{\mathrm{Mixup_MultiChoiceQuestion}\}$ |  |
|  | Answer: |  |
| Translate-Then-Answer<br>demonstrations | The following are multiple choice questions (with answers) about $\{\mathrm{subject}\}$. Remember that the question and options can be in different languages. First translate them all to English. Then output the answer. |  |
| Question: $\{\mathrm{Mixup_MultiChoiceQuestion_Demo1}\}$ |  |  |
| Answer: |  |  |
|  | Translate the question and options into English, and then answer. |  |
|  | Question: $\{\mathrm{En_MultiChoiceQuestion_Demo1}\}$ |  |
|  | Answer: $\{\mathrm{Answer_Demo1}\}$ |  |
|  | …. |  |
|  | Question: $\{\mathrm{Mixup_MultiChoiceQuestion}\}$ |  |
|  |  | Translate the question and options into English, and then answer. |
|  |  | Question: |

### B.2 Evaluation and training details

#### LLM Evaluation

For MMLU evaluation, we follow the templates in its official codebase(^9^99[https://github.com/hendrycks/test](https://github.com/hendrycks/test)) to construct the prompts for 0-shot and 5-shot settings. We employ a temperature of 0 for GPT-3.5 and GPT4, and we select the choice with the highest logits score as the predicted answer for open-source models.
We provide the prompt templates for inference-time mitigation methods in Table 6.

For the Harry Potter evaluation, we use the following prompt template, with an example shown below:

The following are multiple choice questions (with answers) about Harry Potter.
Which house is Harry Potter belong to?
A.Ravenclaw
B.Slytherin
C.Gryffindor
D.Hufflepuff

After querying the model, we select the choice with the highest logical score as the predicted answer.

#### LLM Finetuning

(1) For WikiText-103 fine-tuning, we finetune Llama3-8B for 200 steps, and Llama2-7B for 400 steps, with a learning rate of $2\times 10^{-5}$ and a batch size of 32.
(2) For fine-tuning on WikiText-2 or Harry Potter related documents from WikiText-103, we finetune the models for one epoch with the same set of hyperparameters. We use AdamW (Loshchilov & Hutter, ) as the optimizer.

#### Computation Resources

All fine-tuning experiments are conducted on 2 NVIDIA A100 GPU cards, each with 80GB of memory. For the fine-tuning experiments, each training step takes 5.2 seconds for the Llama2-7B model and 6.1 seconds for the Llama3-8B model, with a batch size of 32. All LLM evaluation experiments can be conducted on one NVIDIA RTX A6000 GPU card with 48 GB of memory.

**Table 7: Top three most relevant documents to the Harry Potter universe in WikiText-103 based on BM25 document ranking. Keywords related to Harry Potter universe are bolded.**
| 1 | In Philosopher’s Stone, Harry re @-@ enters the wizarding world at age 11 and enrols in Hogwarts School of Witchcraft and Wizardry. He makes friends with fellow students Ron Weasley and Hermione Granger, and is mentored by the school’s headmaster, Albus Dumbledore. He also meets Professor Severus Snape, who intensely dislikes and bullies him. Harry fights Voldemort several times while at school, as the wizard tries to regain a physical form. In Goblet of Fire, Harry is mysteriously entered in a dangerous magical competition called the Triwizard Tournament, which he discovers is a trap designed to allow the return of Lord Voldemort to full strength. During Order of the Phoenix, Harry and several of his friends face off against Voldemort’s Death Eaters, a group of Dark witches and wizards, and narrowly defeat them. In Half @-@ Blood Prince, Harry learns that Voldemort has divided his soul into several parts, creating " horcruxes " from various unknown objects to contain them; in this way he has ensured his immortality as long as at least one of the horcruxes still exists. Two of these had already been destroyed, one a diary destroyed by Harry in the events of Chamber of Secrets and one a ring destroyed by Dumbledore shortly before the events of Half @-@ Blood Prince. Dumbledore takes Harry along in the attempt to destroy a third horcrux contained in a locket. However the horcrux has been taken by an unknown wizard, and upon their return Dumbledore is ambushed and disarmed by Draco Malfoy who cannot bring himself to kill him, then killed by Snape. |
| --- | --- |
| 2 | Luna, Ron, Ginny, and Neville join them in the forest and all six fly to the Ministry on , expecting to find and rescue Sirius. Once in the Department of Mysteries, Harry realises that his vision was falsely planted by Voldemort; however, he finds a glass sphere that bears his and the Dark Lord’s names. Death Eaters led by Lucius Malfoy attack in order to capture the sphere, which is a recording of a prophecy concerning Harry and Lord Voldemort, which is revealed to be the object Voldemort has been trying to obtain for the whole year, the Dark Lord believing that there was something he missed when he first heard the prophecy. Lucius explains that only the subjects of the prophecies, in this case Harry or Voldemort, can safely remove them from the shelves. Harry and his friends, soon joined by members of the Order, enter a battle with the Death Eaters. Amidst the chaos, Bellatrix Lestrange kills Sirius and Harry faces Voldemort. Voldemort attempts to kill Harry, but Dumbledore prevents him and fights the Dark Lord to a stalemate. In the midst of the duel, Voldemort unsuccessfully tries to possess Harry in an attempt to get Dumbledore to kill the boy. Dumbledore does not do so and Voldemort escapes just as Cornelius Fudge appears, finally faced with first @-@ hand evidence that Voldemort has truly returned. |
| 3 | During another summer with his Aunt Petunia and Uncle Vernon, Harry Potter and Dudley are attacked. After using magic to save Dudley and himself, Harry is expelled from Hogwarts, but the decision is later rescinded. Harry is whisked off by a group of wizards to Number 12, Grimmauld Place, the home of his godfather, Sirius Black. The house also serves as the headquarters of the Order of the Phoenix, of which Mr. and Mrs. Weasley, Remus Lupin, Mad @-@ Eye Moody, and Sirius are members. Ron Weasley and Hermione Granger explain that the Order of the Phoenix is a secret organisation led by Hogwarts headmaster Albus Dumbledore, dedicated to fighting Lord Voldemort and his followers, the Death Eaters. From the members of the Order, Harry and the others learn that Voldemort is seeking an object that he did not have prior to his first defeat, and assume this object to be a weapon of some sort. Harry learns that the Ministry of Magic, led by Cornelius Fudge, is refusing to acknowledge Voldemort’s return because of the trouble that doing so would cause, and has been running a smear campaign against him and Dumbledore. |

### B.3 WikiText-103 subset: Harry Potter-related documents

Table: Table 8: The top $k$ retrieved documents containing the Harry potter keywords.

We employ the BM25 algorithm (Trotman et al., ) (BM stands for best matching) for document ranking(^10^1010[https://pypi.org/project/rank-bm25/](https://pypi.org/project/rank-bm25/)), which is a bag-of-words retrieval function that ranks documents based on the presence of query terms in each document. The WikiText-103 corpus comprises $M=1,165,029$ documents $d_{i},i\in[M]$. We concatenate the passages crawled from Harry Potter Wiki pages into a single document to use as a query $q$. We then calculate the similarity score between the query and each document in WikiText-103, denoted as $s_{i}=\texttt{Sim}(d_{i},q)$. The top $k=3$ relevant documents are listed in Table 7.

Additionally, we use the list of Harry Potter character names and spell names(^11^1111The spell name “None” is excluded due to its generic nature.) as keywords to evaluate the quality of the retrieved documents and to identify additional relevant documents. Table 8 illustrates the trend that as $k$ increases, more documents containing the keywords are retrieved.
Note that keyword matching is not a golden retrieval method and it only serves as reference because:
(1) documents may not contain the full name of characters or spells (e.g., “Harry” instead of “Harry Potter”);
(2) some spell names are generic and have multiple meanings (e.g., “Pack”, “Avis”).

Therefore, we combine the top documents retrieved by BM25 with keyword matching to create our final dataset. The final dataset contains 4,348 documents (0.37% of WikiText-103), comprising: (1) the top $k=2000$ documents retrieved by BM25. Of these, 106 documents contain at least one exact keyword. (2) An additional 2,358 documents that contain the keywords.

## Appendix C Additional experimental results

#### HP Quiz evaluation results of LLMs fine-tuned on WikiText-2

Figure 7 in the main paper presents the Harry Potter Quiz evaluation results on Llama2-7B and Llama3-8B models fine-tuned on general knowledge corpora (i.e., WikiText-2). Figure 9 presents additional results for the Llama2-13B (left) and Mistral 7B (right) models. (1) The trends are consistent with those observed for Llama2-7B and Llama3-8B, where fine-tuning on a mixed-language general corpus, WikiText-2, enhances the models’ performance on the domain-specific HP Quiz task across multiple languages, including English. (2) Word-level language mixing is generally most effective for Llama2-13B, whereas sentence-level mixing is more effective for Mistral-7B.

Figure: Figure 9: Fine-tuning on a mixed-language general corpus (e.g., WikiText-2) enhances the model’s performance on domain-specific task (e.g., Harry Potter knowledge test) across multiple languages, including English.
Refer to caption: x21.png

Figure: Figure 10: Performance of Llama2-7B models on MMLU variant benchmarks. Fine-tuning on mixed language WikiText-103 generally outperforms fine-tuning on English WikiText-103 or using the un-finetuned model.
Refer to caption: x28.png

Figure: Figure 11: Performance of Llama3-8B models on MMLU variant benchmarks. Fine-tuning on mixed language WikiText-103 generally outperforms fine-tuning on English WikiText-103 or using the un-finetuned model.
Refer to caption: x46.png

#### MMLU evaluation results of LLMs fine-tuned on WikiText-103

Table 4 in the main paper presents the English MMLU and mixup MMLU evaluation results on Llama2-7B and Llama3-8B models fine-tuned on general knowledge corpora (i.e., WikiText-103).
Here we present additional results for Llama2-7B (Figure 10) and Llama3-8B (Figure 11) on more MMLU variant benchmarks, including full translation, question translation, options transition, and ground-truth option translation.
We report the average accuracy (with *) across four non-English languages {fr, de, es, and it } for those settings.

(1) As shown in Figure 10 and Figure 11, models fine-tuned on mixed language WikiText-103 (whether at the word level or sentence level) generally achieve better performance than those fine-tuned on the original English WikiText-103 or the un-finetuned models, especially in the GT-option translated and mixup translated MMLU setups.
These two evaluation setups originally had the lowest performance for the un-finetuned model, and thus the cross-lingual ability gains after fine-tuning are more apparent.
These results suggest that multiple language switches during fine-tuning enable LLMs to better understand and process multilingual input and leverage cross-lingual knowledge for commonsense reasoning tasks.
(2) An exception to this trend is observed with the GT-option translated MMLU under the 5-shot biased demonstrations setting for Llama3-8B, where performance drops. This drop is likely due to the un-finetuned Llama3-8B’s stronger tendency to follow biased demonstrations, using a shortcut to select the non-English option as the answer.
(3) Fine-tuning models on a mixed-languages corpus performs better than other models across different 0-shot and few-shot scenarios, particularly in the 0-shot setting and 5-shot English demonstrations setting. While 5-shot biased demonstrations lead to the best performance, they are less applicable than English demonstrations in real-world scenarios, as we cannot know in advance the language mixing pattern of user queries.

## Peer Reviews

confidence: 4
contribution: 3
initial_rating: 8
presentation: 3
questions: In Footnote 1 you say "This criterion allows the case when a small amount of parallel texts accidentally crawled from the web are mixed in the pretraining dataset, as it is nearly impossible to verify. We believe such presence, if it exists at all, would have negligible impact on the model given the size of the rest of the pretraining data."

A) How do you know that GPT 3.5 and 4 don't use parallel data explicitly during training?

B) While the parallel data might be small in comparison to the rest of the data, does that really mean it has a negligible impact on the model, considering the vast amount of parameters that could allow for quite a high degree of memorisation? Can you substantiate your claim a bit better (references or otherwise)?
soundness: 3
strengths: - well written paper
- interesting outcomes. Not entirely surprising but still nice to see.
- solid methodological evaluation (but see my comment regarding choice of language below)
summary: This paper investigates how multilingual LLMs perform for actual cross-lingual tasks. This covers a wide range of tasks including machine translation but also several variations of multilingual tasks where different parts of the input (text, multiple choice options, questions) are translated into different languages. The authors show a consistent drop in performance when considering actual mixed language tasks and suggest simple fine-tuning strategies to remedy this drop.
weaknesses: - the languages considered are rather few and still relatively similar to each other: 2 germanic languages (English and German) and three romance languages (French, Italian, Spanish). In addition all languages are most likely very high resource (albeit not as high as English of course) during training of the different models. It would have been good to see languages that are rather different from the rest (Arabic or Chinese) maybe even low-resource (Bengali or Amharic). 

- while multilingual have been used it would have been interesting to also consider models that do explicitly use cross-lingual supervision during training such as ALMA or Tower.

---

confidence: 4
contribution: 1
initial_rating: 5
presentation: 3
questions: 1. It would be very beneficial if the authors of the paper would use different languages, such as Chinese, Hebrew, Russian or Hindi, since these languages have a much lower amount of shared tokens with English, which is selected as the most highly resourced language in the training mix of all selected models. This would give us insight into how the applied methodology translates into languages, which the model has a harder time training due to lesser overlap between dictionaries.

2. Please, repeat your evaluations using a different set of models, such as Mistral-Nemo-12B, Qwen-2.5-7B, Command-R and LLaMA-3.1-8B which are multilingual by design. Claims of multilinguality of these models are supported by extensive multilingual evaluations both by model authors and community members.

3. Perhaps designing another evaluation dataset for domain specific knowledge, based on something like some local company guidelines or university campus rules and translating it into different languages would make a much stronger point to support the claims, since it would not exhibit translation artifacts.
soundness: 1
strengths: 1. Experiments with embeddings of the models are interesting and give some insight into how models encode meaning of partially translated sentences.

2. Experiments with general purpose knowledge can be used to better understand multilingual capabilities of trained models. 

3. Mixup-version of MMLU, when provided, will be useful to do better multilingual evaluations, since the language perturbations can successfully combat the test leakage.

4. The text is clear and understandable.
summary: Authors study multilingual abilities and extent of crosslingual transfer of decoder transformer language models, using three different methodologies: embedding-based, MMLU based and domain-specific. In embedding part authors collect embeddings of sentences in English, sentences, in which some of the input tokens were corrupted by masking the attention or randomly replacing them with different tokens from vocabulary of the model and sentences, in which words were randomly translated into a different language and calculate distances between English, corrupted and partially translated languages. General knowledge based evaluation is conducted by translating parts of the questions or answers from MMLU dataset into a different language. In domain-specific evaluation authors ask questions about Harry Potter series and apply same translation techniques as in general knowledge evaluation. First evaluation show that models have close embeddings after per token translations. Second evaluation shows that models are doing much worse on MMLU after partial translations of the answers. Third evaluation shows that applying translation to parts of the questions or answers from Harry Potter trivia the crosslingual barrier still exists. In later parts of the paper authors test different methodologies of overcoming this barrier, either by prompt engineering and doing few-shot prompting which has limited success and by finetuning selected models on WikiText-2 for general text knowledge and WikiText-103 for domain specific trivia, which improves the performance on both MMLU and HP-Quiz.
weaknesses: 1. Models, selected on line 100, are not multilingual. Llama-3-8B was explicitly stated as a monolingual model, focusing only on English, with usage in other languages described as out-of-scope use. Multilinguality was only stated in 3.1’s model card. Same can be said about Llama-2-7B and Llama-2-13B. Mistral-7B is not explicitly stated to be multilingual, either. Given both multilingual evaluations and community reports, it is safe to say that these models do not exhibit strong multilingual capabilities. Authors additionally evaluate Mixtral 8x7B and Aya-23-8b, which are explicitly stated to be multilingual models and have some knowledge in selected languages (en, fr, de, es, it), but they are mostly ignored in the main part of paper, instead focusing on Llama-2 and Llama-3. To my mind this is a big misstep, since bad performance of the selected models could be incorrectly generalized to truly multilingual models.

2. Domain specific evaluations are being done on the Harry Potter series of books, which was translated to different languages with varying quality. This raises the question of how well the terms described in the books are translated: for instance, tha name of Neville Longbottom is translated to Italian as Neville Paciock, which retains the connotation of clumsiness, but does not sound similarly and does not preserve the meaning of long bottom with the English version, to Chinese as Nàwēi Lóngbādùn, which does not retain the connotation since it’s a simple transliteration and to Russian as Nevil Dolgopups, which both does not retain the clumsiness connotation, meaning or common sound/tokens. This raises concerns if the arguments presented in the paper (e.g. knowledge learned in one language can be translated to other languages) can be checked via Harry Potter trivia.

3. All of the selected models almost certainly have seen the original books, dumps from HP Wiki or Wikipedia and blog posts about Harry Potter in non-English languages, so it may have leaked into the training data for all of the languages.

4. It is common knowledge that both instruction and preference tuning causes catastrophic forgetting, which leads to models being better at instruction following, safety and answer formatting, but worse at parametric knowledge. From the list of the described models we can see that only Llama-2, Llama-3, Mixtral-8x7b, Zamba-7b and Mistral-7b models are available as base models, with GPT-3.5, GPT-4, Aya-23 being instruction tuned models. It is not explicitly stated, which versions of the models are used – pretrained or finetuned, Thus, some clarification is required, since it directly influences the amount of multilingual capability of the models. If these are instruction tuned models, further finetune of them on Harry Potter dataset could lead to catastrophic forgetting, thus perturbating the models’ scores and if these are base models, direct comparison between Aya-23 and llamas, for instance, presents a potential inconsistency in methodology.

5. The phenomenon of crosslingual knowledge barrier (e.g. limited multilinguality capabilities of the model) is well known, so the main contribution of the paper lacks originality.

---

confidence: 4
contribution: 1
initial_rating: 3
presentation: 2
questions: See weaknesses part especially L137, L134-142, L158-159, L199-200.
soundness: 2
strengths: - The paper demonstrates that a cross-lingual knowledge barrier exists for four non-English languages through experiments evaluating how much benchmark scores vary when the benchmarks are translated under different scenarios.

- The authors assess well-established methods to improve the multilinguality score and propose constructing a fine-tuning dataset that comprises examples from multiple languages, particularly at the sentence level, to achieve better scores in multilinguality.
summary: The paper claims to investigate the cross-lingual knowledge barrier for four high-resource non-English languages by examining benchmark score variability under different translation scenarios for six LLMs. However, it suffers from several weaknesses, including:

- A lack of detail regarding how sentence embeddings are obtained to demonstrate explicit cross-lingual capabilities. And no justification for the chosen probability settings.
- Uncontrolled experiments that do not sufficiently prove that the results are due to the cross-lingual knowledge barrier rather than the performance of the languages in non-knowledge related tasks.

In the rest of the paper, the authors evaluate well-established methods to improve the multilinguality score. Their proposal to construct a fine-tuning dataset comprising examples from multiple languages, particularly at the sentence level, aims to achieve better scores compared to English fine-tuning. However, I believe this outcome is completely expected and does not represent a significant contribution.
weaknesses: - L26-36: The first figure presents a poor example. Why couldn't it simply be the same question in both English and French? Additionally, why is there a need to create a knowledge that does not exist, so it can not be tested out as an example?

- L104: The authors state, “such presence, if it exists at all,” regarding parallel sentences on the web. It would be interesting to know how papers that mine billions of parallel texts from the web feel about this statement (e.g., https://arxiv.org/abs/1911.04944).

- L137: The paper mentions obtaining sentence embeddings from the LLM; however, it does not detail how this is done. Since these are decoder-only models with causal attention, how are the embeddings of the tokens aggregated? Is it the last token, or are they weighted? (see section 3.1 of https://arxiv.org/pdf/2410.05873 for a background on the different techniques)

- L134-142: There are many variables concerning probabilities, yet there is no explanation for why these specific values were chosen.

- L158-159: The statement “This underscores the explicit cross-lingual capabilities of multilingual LLMs” lacks clarity regarding the rationale and conclusions drawn. With a lower probability (0.16 vs. 0.8), tokens were randomly selected from the vocabulary. Now, the distribution of these two (cosine similarities between the original and mixed translated sentence embeddings versus the original and random token-replaced sentence embeddings) varies significantly. Many variables are involved here: do the random tokens from the vocabulary come only from all writing systems or just Latin? How are the embeddings computed, and why were these probabilities chosen? Although I acknowledge the existence of cross-lingual capabilities, I am not convinced by the authors' experiment.

- L199-200: There is no experiment/evaluation/audit demonstrating how valid these translations are.

- L247: Conclusion 1 does not necessarily indicate a knowledge transfer problem. In English-centric LLMs, it is expected that performance will be better in English. Simply stating that English performs better in an English-centric LLM does not imply that knowledge cannot be transferred; rather, it suggests that performance in the secondary language may be low, even in language understanding tasks. The authors selected languages where LLMs typically perform better (but is it on the level of English?), so it is not surprising that they cannot fully grasp the knowledge of English. If the authors had chosen low-resource languages, we might observe even lower performance, which could indicate that the LLM lacks substantial knowledge of those languages to begin with than other knowledges.

For the rest of the paper, the authors evaluate well-established methods to improve the multilinguality score. Their proposal to construct a fine-tuning dataset comprising examples from multiple languages, particularly at the sentence level and achieve better scores compared to English fine-tuning. However, I believe this outcome is completely expected and does not represent a significant contribution.

Meta-review: The paper investigates the cross-lingual knowledge barrier for large language models (LLMs) by evaluating their performance on mixed-language tasks, general knowledge benchmarks (MMLU), and domain-specific evaluations (Harry Potter quiz). The paper observes that while LLMs demonstrate surface-level cross-lingual capabilities, they struggle with deeper cross-lingual transfer and propose fine-tuning on mixed-language datasets as a mitigation strategy. While the study raises an important topic of cross-lingual knowledge transfer, there are significant concerns regarding the methodology, experimental design, and overall contribution. 

The strengths of the paper include its attempt to examine cross-lingual reasoning systematically and its clear writing. The expanded evaluation to include more languages and multilingual models is commendable. However, the weaknesses of the paper outweigh these strengths. First, the paper does not convincingly isolate the cross-lingual barrier phenomenon due to insufficiently controlled experiments and unclear disentanglement of confounding factors such as model multilinguality, token overlap, and pretraining data leakage. Many of the selected models, such as the Llama series, are not explicitly multilingual, raising concerns about whether their performance can be generalized. Second, the domain-specific evaluation setup using the Harry Potter dataset is problematic. Translation artifacts, inconsistent naming conventions, and the likelihood of pretraining data contamination undermine the reliability of the findings. Some reviewers argue that results from this dataset may reflect memorization rather than cross-lingual reasoning. Third, the proposed fine-tuning method to address the barrier lacks novelty. Techniques like mixed-language fine-tuning or code-switching have been previously explored, particularly for encoder-based models, and the improvements reported here are therefore incremental and expected. The paper also lacks discussion on the trade-offs of such fine-tuning. Finally, some aspects of the experimental presentation remains unclear. 

Despite the authors' efforts to address these issues in the rebuttal, fundamental concerns about the experimental rigor and the novelty of the contribution persist. While the topic is relevant, the current version of the paper does not provide sufficiently strong evidence or a significant advancement in understanding or mitigating cross-lingual barriers in LLMs. For these reasons, I recommend rejection.

Decision: Reject