x1: Learning to Think Adaptively Across Languages and Cultures

# x1: Learning to Think Adaptively Across Languages and Cultures
Source: [https://arxiv.org/html/2604.16917](https://arxiv.org/html/2604.16917)
Yangfan Ye1, Xiaocheng Feng1,2, Xiachong Feng3, Yichong Huang1, Zekun Yuan1, Lei Huang1Weitao Ma1, Qichen Hong4, Yunfei Lu4, Dandan Tu4, Bing Qin1,2 1Harbin Institute of Technology2Peng Cheng Laboratory 3The University of Hong Kong4Huawei Technologies Co\., Ltd \{yfye,xcfeng\}@ir\.hit\.edu\.cn

###### Abstract

Languages encode distinct abstractions and inductive priors, yet most large language models \(LLMs\) overlook this diversity by reasoning in a single dominant language\. In this work, we introducex1, a family of reasoning models that can*adaptively*reason in an advantageous language on a per\-instance basis\. To isolate the effect of reasoning\-language choice,x1is constructed without expanding the model’s knowledge boundaries and is trained by contrasting linguistically distinct reasoning trajectories for the same input\. Our extensive experiments demonstrate the benefits of adaptive multilingual reasoning in multilingual mathematical and culturally grounded tasks\. Moreover, our results challenge a simplistic view of scaling law: while scaling reduces cross\-lingual disparities in procedural domains such as math reasoning, it does not eliminate the advantages of reasoning in culture\-associated languages in cultural scenarios, as we empirically show that such reasoning enables more efficient and accurate cultural knowledge recall\. Overall, our findings establish language choice as a functional component of reasoning, with implications for building more generalist and globally competent reasoning models\.111[https://github\.com/YYF\-Tommy/x1\-adaptive\-multilingual\-reasoning](https://github.com/YYF-Tommy/x1-adaptive-multilingual-reasoning)

x1: Learning to Think Adaptively Across Languages and Cultures

Yangfan Ye1, Xiaocheng Feng1,2††thanks:Corresponding Author, Xiachong Feng3, Yichong Huang1, Zekun Yuan1,Lei Huang1Weitao Ma1, Qichen Hong4, Yunfei Lu4, Dandan Tu4, Bing Qin1,21Harbin Institute of Technology2Peng Cheng Laboratory3The University of Hong Kong4Huawei Technologies Co\., Ltd\{yfye,xcfeng\}@ir\.hit\.edu\.cn

## 1Introduction

“The limits of my language mean the limits of my world\.”

— Ludwig Wittgenstein, 1922\(wittgenstein2023tractatus\)

“Reasoning” endows large language models \(LLMs\) with the ability to go beyond surface\-level pattern matching and to tackle complex tasks such as competition\-level mathematics, logical reasoning, and multi\-hop question answering\(wei2022chain;snell2024scaling;brown2024large\)\. However, most existing LLMs, like OpenAI\-o1/o3\(jaech2024openai\)and Qwen3\(yang2025qwen3\), reason predominantly in high\-resource languages \(such as English, Chinese\)\. While reasoning in a dominant language is often effective, it implicitly assumes a single linguistic perspective to be universally optimal\. However, languages encode distinct abstractions, cultural priors, and modes of expression, which can subtly shape how problems are decomposed, interpreted, and solved\(goddard2003thinking;kovecses2006language\)\. Consequently, confining reasoning to a single language may underutilize this diversity, particularly in multilingual and culturally grounded scenarios\.

BnDeEsFrJaRuSwThZh020204040606080801001006\.43\.23\.64\.44\.88\.06\.87\.68\.859\.670\.470\.465\.269\.677\.69\.665\.676\.818\.013\.612\.417\.616\.810\.870\.816\.012\.416\.012\.813\.612\.88\.83\.612\.810\.82\.0Percentage \(%\)Non\-English Reasoning vs\. English Reasoning \(MGSM\)WinTie \(correct\)Tie \(incorrect\)LoseFigure 1:Win/tie/lose rates of non\-English vs\. English reasoning pathways forQwen3\-4BonMGSM\. Reasoning in contrast languages is enabled via Step 1 \(introduced in §[1](https://arxiv.org/html/2604.16917#S1)\)\. “Win”: cases where non\-English reasoning outperforms English reasoning; “Tie” \(correct/incorrect\): both reasoning pathways yield correct/incorrect answers; “Lose”: cases where English reasoning outperforms non\-English reasoning\.![Refer to caption](https://arxiv.org/html/2604.16917v1/x1.png)Figure 2:Overview of the construction process and inference usage ofx1models\.Recently,yong2025crosslingualconducted a detailed analysis of cross\-lingual reasoning and demonstrate that, in multilingual mathematics problems, English is not always the optimal language for reasoning\. In Figure[1](https://arxiv.org/html/2604.16917#S1.F1), we quantify the advantages of non\-English reasoning by measuring the win/tie/lose rates of non\-English reasoning compared to English reasoning, revealing that inMGSM\(shi2022language\), roughly 3%–9% \(varying across languages\) of instances can be solved by non\-English reasoning paths where English reasoning fails\. Beyond mathematical reasoning,yong2025crosslingualobserved that test\-time scaling of English reasoning \(i\.e\., extending the reasoning length\) does not necessarily improve performance in culture\-aware scenarios, where success may require more knowledge recall or culturally grounded reasoning\. This limitation further motivates our investigation into non\-English reasoning pathways, particularly for culturally situated reasoning, where the choice of thinking language may play a decisive role\.

In this paper, we take a step toward exploiting the diversity of reasoning perspectives offered by English and non\-English languages\. Building on existing open\-source reasoning models, we introducex1, a family of models that can*adaptively select*the more advantageous thinking language on a per\-instance basis\. Crucially, this is achieved*without expanding the model’s knowledge boundaries*, allowing us to isolate the effect of reasoning\-language choice in a controlled and comparable setting, rather than emphasizing absolute performance gains\. Specifically, we first equip the model with the ability to reason in a*specified language*across multiple languages through self\-supervised training, and then induce adaptive reasoning behavior by contrasting linguistically distinct reasoning trajectories for the same input\.

We investigate adaptive multilingual reasoning in two deeply language\-intertwined scenarios: multilingual mathematical reasoning and cultural reasoning\. Our findings suggest that reasoning in LLMs is not language\-agnostic, but shaped by the reasoning language choice\. By enabling adaptive multilingual reasoning, we show that linguistic diversity offers systematic benefits beyond reliance on a single language\. Importantly, our results challenge a simplistic view of scaling laws: while scaling reduces cross\-lingual disparities in procedural domains such as mathematical reasoning, it fails to eliminate the intrinsic advantages of reasoning in culture\-associated languages for culturally grounded tasks, which leads to more efficient and accurate cultural knowledge recall\. Together, these findings indicate that language choice is not merely a surface realization of thought, but a functional component of reasoning itself, with important implications for building truly generalist and globally competent reasoning models\.

## 2Constructingx1

To achieve reasoning in a advantageous language without expanding the model’s knowledge boundaries, we propose a two\-stage training strategy that leverages self\-generated contrastive signals to induce adaptive multilingual reasoning\.

### 2\.1Step 1: To be a Multilingual Reasoner

The first step aims to open up the model’s multilingual reasoning space, enabling it to deliberately reason in a specified language rather than being implicitly anchored to its default thinking language\.

To achieve this, we adopt a lightweight self\-supervised training strategy that teaches the model to perform reasoning in a required language while ensuring that the final answer remains consistent with the prompting language222For example, if the prompt is in English but the reasoning language is constrained to German, the final response should still be generated in English\.\. In practice, we first query the backbone modelℳ\\mathcal\{M\}with 200 seed questions sampled fromFlan\_v2\(wei2021finetuned\), collecting its generated reasoning traces\{ti\}i=1200\\\{\\operatorname\{t\}\_\{i\}\\\}\_\{i=1\}^\{200\}and final answers\{ai\}i=1200\\\{\\operatorname\{a\}\_\{i\}\\\}\_\{i=1\}^\{200\}\. We then instructℳ\\mathcal\{M\}itself to translate each reasoning trace into 30 different languages\{lj\}j=130\\\{l\_\{j\}\\\}\_\{j=1\}^\{30\}\(listed in Appendix[A\.1](https://arxiv.org/html/2604.16917#A1.SS1)\), yielding a multilingual set of reasoning traces\{tilj\}i=1200\\\{\\operatorname\{t\}\_\{i\}^\{l\_\{j\}\}\\\}\_\{i=1\}^\{200\}andj=1,…,30j=1,\\dots,30\. To ensure linguistic fidelity, we apply quality filtering using COMET333Unbabel/wmt23\-cometkiwi\-da\-xxl\(rei2023scaling\)scores and discard translations of evidently poor quality\.

Using these translated reasoning traces, we finetune the backbone modelℳ\\mathcal\{M\}with a templated format that explicitly specifies a reasoning language as follows: \(see complete examples in Figure[6](https://arxiv.org/html/2604.16917#A1.F6)\)

// Example of reasoning inArabicInput:\{Questioni\\operatorname\{Question\}\_\{i\}\}Output: <think\>`\\`n<Arabic\_start\>`\\`n`\\`n\{tiAr\\\{\\operatorname\{t\}\_\{i\}^\{\\operatorname\{Ar\}\}\}`\\`n`\\`nOutput:<Arabic\_end\>`\\`n</think\>`\\`n`\\`n\{ai\\\{\\operatorname\{a\}\_\{i\}\}

The resulting “sibling” model,ℳsurface\\mathcal\{M\}\_\{\\operatorname\{surface\}\}, can be viewed as a*surface\-level multilingual reasoner*: it is capable of following simple templates to reason in a specified languageXXby appending a simple template “<think\>\\n<XX\_start\>” at inference time, while avoiding undesirable language drift\. Notably, this capability operates purely at the level of reasoning expression: it exposes alternative language\-conditioned reasoning paths and does not introduce any external knowledge or capability expansion \(such as Google Translation, external knowledge bases, or stronger auxiliary models\)\.

### 2\.2Step 2: To be an Adaptive Reasoner

The goal of Step 2 is to elevate multilingual reasoning from language following to adaptively choose the more advantageous reasoning language\.

Leveragingℳsurface\\mathcal\{M\}\_\{\\operatorname\{surface\}\}, we are able to generate paired reasoning trajectories in English and non\-English languages for each input444Ifℳ\\mathcal\{M\}naturally reasons in English, we requireℳsurface\\mathcal\{M\}\_\{\\operatorname\{surface\}\}to reason in a non\-English language; conversely, we requireℳsurface\\mathcal\{M\}\_\{\\operatorname\{surface\}\}to reason in English\.\. These paired trajectories can be viewed as*counterfactual reasoning paths*induced by different language choices, providing a basis for comparative learning\.

##### Training Data Source\.

We study adaptive reasoning in two language\-intertwined scenarios\.\(1\) Multilingual Math Problems\(DmathD\_\{\\operatorname\{math\}\}\): We use theMGSM8KInstructdataset\(chen2023breaking\), which contains math problems paired with their correct answers\. We sample 200 samples across 10 languages, resulting in 2,000 training instances\.\(2\) Culture\-related Problems\(DcultureD\_\{\\operatorname\{culture\}\}\): We use theCultureBankdataset\(shi2024culturebank\), which provides cultural questions along with their underlying cultural knowledge\. We sample 100\-200 samples from each of the 25 language groups \(depending on availability\), covering cultural questions from 45 countries/regions, resulting in 4,413 samples in total\. \(Detailed statistics are in Appendix[A\.2](https://arxiv.org/html/2604.16917#A1.SS2)\)

##### Advantageous Language Identification\.

For each question inDmathD\_\{\\operatorname\{math\}\}orDcultureD\_\{\\operatorname\{culture\}\}, we first obtain the paired reasoning trajectories in both English and non\-English withℳ\\mathcal\{M\}andℳsurface\\mathcal\{M\}\_\{\\operatorname\{surface\}\}[4](https://arxiv.org/html/2604.16917#footnote4)\. We identify the advantageous reasoning language based on the quality of the final answers, under the principle that stronger reasoning should manifest in superior outputs\. For multilingual math problems, answer quality is determined via exact numerical matching\. For culture\-related questions, we employLLM\-as\-a\-Judge\(zheng2023judging\)to score how well the response entails the relevant cultural knowledge\. The reasoning language associated with the higher\-scoring trajectory is then regarded as the advantageous thinking language for that instance\. \(Detailed implementations for comparison are provided in Appendix[A\.2](https://arxiv.org/html/2604.16917#A1.SS2)\.\)

ModelsMultilingual Math ReasoningCultural ReasoningMGSMMT\-AIMEFORKCulturalBenchNon\-ThinkThinkNon\-ThinkThinkNon\-ThinkThinkNon\-ThinkThinkTop\-tiered Reasoning Modelso4\-mini\-high–82\.32–75\.33–74\.46–82\.31DeepSeek\-V3\.279\.2476\.3253\.0085\.6772\.8378\.8084\.6089\.16Open\-sourced Reasoning ModelsQwen3\-4B70\.2176\.5912\.8921\.7874\.6473\.7368\.7670\.85Qwen3\-14B77\.6482\.5619\.3329\.2274\.4673\.9175\.5078\.24Qwen3\-32B80\.5283\.9821\.8333\.8978\.2681\.8878\.7681\.26DeepSeek\-R1\-Distill\-Qwen\-7B54\.7660\.058\.3325\.8340\.0455\.2529\.5838\.63DeepSeek\-R1\-Distill\-Llama\-8B38\.1740\.362\.6714\.4437\.8674\.0935\.0257\.19x1 Series Models\+ Math\+ Culturex1\-Qwen3\-4B70\.3077\.69 \(↑\\bm\{\\uparrow\}1\.10\)13\.5622\.83 \(↑\\bm\{\\uparrow\}1\.05\)75\.1878\.08 \(↑\\bm\{\\uparrow\}4\.35\)68\.4672\.74 \(↑\\bm\{\\uparrow\}1\.89\)x1\-Qwen3\-14B77\.3883\.64 \(↑\\bm\{\\uparrow\}1\.08\)19\.4433\.11 \(↑\\bm\{\\uparrow\}3\.89\)73\.1276\.81 \(↑\\bm\{\\uparrow\}2\.90\)76\.0781\.58 \(↑\\bm\{\\uparrow\}3\.34\)x1\-Qwen3\-32B80\.1284\.43 \(↑\\bm\{\\uparrow\}0\.45\)22\.1134\.50 \(↑\\bm\{\\uparrow\}0\.61\)79\.1782\.61 \(↑\\bm\{\\uparrow\}0\.73\)80\.4781\.99 \(↑\\bm\{\\uparrow\}0\.73\)x1\-DeepSeek\-R1\-Distill\-Qwen\-7B54\.5263\.24 \(↑\\bm\{\\uparrow\}3\.19\)9\.0027\.00 \(↑\\bm\{\\uparrow\}1\.17\)54\.8958\.70 \(↑\\bm\{\\uparrow\}3\.45\)44\.8249\.04 \(↑\\bm\{\\uparrow\}10\.4\)x1\-DeepSeek\-R1\-Distill\-Llama\-8B38\.0152\.17 \(↑\\bm\{\\uparrow\}11\.8\)2\.8917\.00 \(↑\\bm\{\\uparrow\}2\.56\)57\.0776\.27 \(↑\\bm\{\\uparrow\}2\.18\)51\.1360\.88 \(↑\\bm\{\\uparrow\}3\.69\)

Table 1:Mean@3 results that are the averages of the performance across all languages / cultures for each dataset\.
##### Training Data Construction\.

For each instance, we retain only the reasoning trace and answer corresponding to the advantageous language, and discard cases where English and non\-English reasoning receive tied scores, to enforces a sharper contrast between alternative reasoning pathways and provides a clear signal for language preference\.

We train the backbone modelℳ\\mathcal\{M\}using a templated format \(similar to Step 1\) that explicitly specifies the selected reasoning languageXX, implemented via parameter\-efficient LoRA finetuning\. For a given questionQQ, if languageXXis identified as the advantageous reasoning language, with corresponding reasoning traceTTand final answerAA, we construct the training instance as follows:

Input:\{Q\\operatorname\{Q\}\}Output: <think\>`\\`n<X\_start\>`\\`n`\\`n\{T\\\{\\operatorname\{T\}\}`\\`n`\\`n<X\_end\>`\\`nOutput:</think\>`\\`n`\\`n\{A\\\{\\operatorname\{A\}\}

Additionally, we introduce auxiliary self\-awareness data that externalizes the model’s language\-selection decision as an explicit prediction task\. This encourages the model to internalize reasoning\-language choice as a deliberate component of its reasoning strategy rather than as a fixed or implicit heuristic\. The data format is illustrated below \(see complete example in Figure[7](https://arxiv.org/html/2604.16917#A1.F7)\):

Input: …decide in which language you should internallyInput:think…for question\{Q\\operatorname\{Q\}\}`\\`n`\\`nThinking Language:Output: <think\>`\\`n`\\`n</think\>`\\`n`\\`n\{X\\\{\\mathit\{X\}\}

All training data in Step 2 are self\-generated by eitherℳ\\mathcal\{M\}orℳsurface\\mathcal\{M\}\_\{\\operatorname\{surface\}\}\. This stage relies on instance\-level comparisons between alternative reasoning\-language choices, enabling the backbone models to select and exploit its latent multilingual reasoning capabilities in an adaptive manner\.

## 3Experiments

### 3\.1Setup

##### Models\.

We perform training on five representative reasoning models\. Qwen3\-series models\(yang2025qwen3\): \(1\)Qwen3\-4B, \(2\)Qwen3\-14B, \(3\)Qwen3\-32Band DeepSeek\-R1\-distilled models\(guo2025deepseek\): \(4\)DeepSeek\-R1\-Distill\-Qwen\-7Band \(5\)DeepSeek\-R1\-Distill\-Llama\-8B\.

##### Training\.

Our training processes are conducted on8×\\timesA800\-SXM4\-80GBGPUs\. In step\-1 self\-supervised training, we perform full\-parameter finetuning\(ouyang2022training\)for all models to ensure effective acquisition of the designed templates, except forQwen3\-32B, for which we adopt LoRA\(hu2022lora\)training due to its large model size\. In step\-2, we apply LoRA training separately for multilingual math and cultural reasoning scenarios, aiming to minimally modify the backbone models while enabling lightweight and flexible scenario adaptation\. More training details and hyperparameters are provided in Appendix[A](https://arxiv.org/html/2604.16917#A1)\.

##### Evaluations\.

We conduct experiments on four benchmarks, which can be categorized into:

- •Multilingual Math Reasoning:\(1\)MGSM\(shi2022language\), the multilingual version of grade\-school math problems translated by human annotators and \(2\)MT\-AIME\(son2025linguistic\), the multilingual version of challenging mathematical problems from American Invitational Mathematics Examination \(AIME\)\. For multilingual math reasoning, our main experiments cover 10 languages:Bn, De, En, Es, Fr, Ja, Ru, Sw, Th, Zh\.
- •Cultural Reasoning:\(1\)FORK\(palta\-rudinger\-2023\-fork\), a manually\-curated set of English questions for probing cultural biases present in commonsense reasoning, with a specific focus on food\-related customs, covering 10 global regions and \(2\)CulturalBench\(chiu\-etal\-2025\-culturalbench\), a set of 1,696 human written and human\-verified English questions to assess LMs’ cultural knowledge, covering 45 global regions\.

We follow the default official sampling parameters for each model and we report the Mean@3 \(average results of three runs\) performance in our main experiments\. We set the maximum number of new tokens to 32,768 to ensure sufficient output length\. To prevent meaningless repetitive reasoning during inference, we adopt a repetition\-detection truncation mechanism to reduce unnecessary token generation and computational overhead\. The implementations are provided in the Appendix[A\.3](https://arxiv.org/html/2604.16917#A1.SS3)\.

### 3\.2Overall Performance

The average Mean@3 results over different languages / cultures are presented in Table[1](https://arxiv.org/html/2604.16917#S2.T1)\. The results for each language are in §[A\.4](https://arxiv.org/html/2604.16917#A1.SS4)Table[9](https://arxiv.org/html/2604.16917#A5.T9)\. We also compare and anaylze the performance ofvanilla finetuningandmajority votingin Appendix §[A\.5](https://arxiv.org/html/2604.16917#A1.SS5)\.

Data Format: \(Thinking Phase \| Answer Phase \| Both Phases\)Language Compliance Rate \(%\) on MGSMQuery LanguageBnDeEnEsFrJaRuSwThZhQwen3\-4B– \| 95\.6 \| –– \| 96\.8 \| –– \| 100 \| –– \| 98\.0 \| –– \| 99\.2 \| –– \| 96\.8 \| –– \| 99\.6 \| –– \| 26\.4 \| –– \| 92\.4 \| –– \| 100 \| –x1\-Qwen3\-4B95\.6 \| 97\.6 \| 93\.2100 \| 99\.2 \| 99\.2100 \| 100 \| 10099\.6 \| 99\.2 \| 98\.899\.2 \| 99\.6 \| 98\.8100 \| 99\.6 \| 99\.699\.6 \| 100 \| 99\.699\.6 \| 24\.0 \| 23\.698\.0 \| 95\.6 \| 94\.0100 \| 99\.6 \| 99\.6Qwen3\-14B– \| 97\.6 \| –– \| 97\.2 \| –– \| 100 \| –– \| 92\.0 \| –– \| 89\.6 \| –– \| 99\.6 \| –– \| 99\.6 \| –– \| 49\.6 \| –– \| 99\.2 \| –– \| 99\.6 \| –x1\-Qwen3\-14B99\.6 \| 70\.8 \| 70\.4099\.2 \| 93\.6 \| 92\.8100 \| 99\.6 \| 99\.6100 \| 92\.0 \| 92\.099\.2 \| 92\.4 \| 91\.6100 \| 97\.2 \| 97\.292\.0 \| 96\.0 \| 88\.0100 \| 54\.4 \| 54\.498\.8 \| 94\.0 \| 92\.8100 \| 100 \| 100Qwen3\-32B– \| 93\.6 \| –– \| 94\.8 \| –– \| 100 \| –– \| 93\.6 \| –– \| 96\.0 \| –– \| 91\.2 \| –– \| 99\.6 \| –– \| 64\.0 \| –– \| 92\.4 \| –– \| 100 \| –x1\-Qwen3\-32B98\.8 \| 90\.0 \| 89\.293\.2 \| 93\.2 \| 86\.4100 \| 100 \| 100100 \| 90\.8 \| 90\.8100 \| 96\.0 \| 96\.0100 \| 90\.0 \| 90\.098\.8 \| 93\.6 \| 92\.499\.6 \| 64\.8 \| 64\.898\.8 \| 86\.8 \| 86\.499\.6 \| 100 \| 99\.6

Table 2:Language compliance results ofx1models and their backbones onMGSMacross different languages\.##### \(1\) Evidence of Decoupling in Math and Cultural Reasoning\.

We observe a decoupling between a model’s proficiency in math reasoning and culturally situated tasks\. For instance,DS\-R1\-Distill\-Qwen\-7Bsubstantially outperformsDS\-R1\-Distill\-Llama\-8BonMGSM\(\+19\.69%\+19\.69\\%\) andMT\-AIME\(\+11\.39%\+11\.39\\%\), yet trails significantly in cultural reasoning \(−18\.84%\-18\.84\\%onFORK;−18\.56%\-18\.56\\%onCulturalBench\)\. Besides,o4\-mini\-highleadsDeepSeek\-V3\.2onMGSMbut exhibits worse performance in cultural reasoning\. This pattern suggests that the underlying reasoning mechanisms leveraged for structured, procedural calculation \(Math\) are distinct from those required for contextual, knowledge\-intensive reasoning \(Culture\)\.

##### \(2\)x1Models Exhibit Better Overall Reasoning Performance\.

Our results show thatx1systematically outperforms their backbone models in both multilingual and cultural scenarios\. The improvements validate the efficacy of adaptive multilingual reasoning that leverages linguistic diversity in reasoning\. Notably, the gains are more pronounced in cultural tasks, suggesting a closer connection between cultural knowledge and linguistic expression of reasoning\. Moreover, despite utilizing onlyThinkmode data formats for self\-generated training,x1models show no noticeable performance degradation in theNon\-Thinkmode and even exhibit improvements in cultural scenarios\.

##### \(3\) Greater Relative Improvements on Smaller and Weaker Backbones\.

We find that performance gains are inversely correlated with backbone strength\. Smaller and lower\-performing models, such asQwen3\-4Band theDS\-R1\-Distillseries, achieve substantially larger relative improvements, whereas the gap betweenx1\-Qwen3\-32B and its backbone is the smallest within the Qwen family\. This trend suggests that as model scale and capability increase, multilingual and multi\-domain reasoning becomes more internally integrated, leaving less "room" for improvement through thinking\-language switching \(We conduct a further discussion in Section[4\.2\.2](https://arxiv.org/html/2604.16917#S4.SS2.SSS2)\)\.

![Refer to caption](https://arxiv.org/html/2604.16917v1/x2.png)Figure 3:Distribution of thinking languages frequency byx1models along with the performance of their backbones across different languages/cultures subsets\. All statistics and results are averaged overQwen3\-4B,14Band32B\.

## 4Further Analysis

### 4\.1Language Compliance inx1

We defineLanguage Complianceas the model’s ability to satisfy the following requirements: \(1\)Thinking Phase: perform reasoning in a specified language\. \(2\)Answer Phase: generate the final answer in the prompting language given the context, without being influenced by the reasoning language\. \(3\)Both Phases: meet above two requirements simultaneously\. The language compliance results onMGSMdataset are shown in Table[2](https://arxiv.org/html/2604.16917#S3.T2)\.

The results indicate thatx1models generally demonstrate great language compliance\. However, a critical observation is the high correlation between the language compliance ofx1models and their backbone models\. Sincex1models are trained on self\-generated data from their backbones, pre\-existing compliance deficiencies are not fully mitigated\. This dependency is most pronounced in low\-resource languages like Swahili, where the compliance rates for the Qwen3 backbones \(4B:26\.4%26\.4\\%, 14B:49\.6%49\.6\\%, 32B:64\.0%64\.0\\%\) andx1models \(4B:23\.6%23\.6\\%, 14B:54\.4%54\.4\\%, 32B:64\.8%64\.8\\%\) remain low \(We exclude the responses ofx1\-Qwen3\-14BonBnfrom subsequent analysis due to insufficient language compliance\)\.

### 4\.2Thinking\-Language Switching inx1

#### 4\.2\.1Thinking\-Language Frequency

Figure[3](https://arxiv.org/html/2604.16917#S3.F3)illustrates the distribution of the chosen thinking language byx1models and the vanilla performance of backbone models across various languages/cultures\. We observe a key pattern:x1demonstrate an increased frequency of “Native Thinking” on language/culture subsets where backbone models originally perform worse\.

This pattern holds consistently across both multilingual math and cultural tasks, with the exception that Qwen3 backbone models naturally reason in Russian and Chinese for the corresponding math problems, leadingx1to retain a high proportion of native thinking for these languages\. For other languages/cultures, native\-thinking frequency is inversely correlated with the backbone’s original performance \(e\.g\., in low\-resource languages like Bengali, Swahili, Thai in Figure[3](https://arxiv.org/html/2604.16917#S3.F3)\(a\)\(b\), or low\-performing cultural subsets circled in Figure[3](https://arxiv.org/html/2604.16917#S3.F3)\(c\)\)\. This trend suggests that when the dominant English reasoning pathway becomes unreliable, the model increases thinking\-language switching as a recovery mechanism, attempting to exploit language\-specific knowledge or alternative reasoning pathways encoded in non\-English representations\.

#### 4\.2\.2Net Benefits of Language Switching

To assess the true utility ofx1’s adaptive thinking mechanism, we focus on the subset of samples where a thinking\-language switch occurred\. We define theBenefit Rateas the proportion of cases where the backbone fails butx1succeeds after switching \(computed over all samples\), and theHarm Rateas the opposite case\. Their difference reflects thenet benefitof adaptive switching\. As shown in Figure[4](https://arxiv.org/html/2604.16917#S4.F4), the benefit consistently outweighs the harm, providing clear evidence for the effectiveness of thinking\-language switching\. Besides, the analysis further reveals several insights:

##### \(1\) Larger Cross\-Lingual Disparity Leads to Greater Net Benefits from Thinking\-Language Switching\.

From Figure[4](https://arxiv.org/html/2604.16917#S4.F4)\(a\), we observe that inMGSM\(grade school level\), the net benefit of thinking\-language switching decreases steadily as model size scales\. But for the more challenging benchmarkMT\-AIMEshown in \(b\), the net benefits remains low and nearly unchanged\.

This trend aligns with the standard deviation \(Std\) statistics in §[B](https://arxiv.org/html/2604.16917#A2)Table[6](https://arxiv.org/html/2604.16917#A1.T6), where a largerStdindicates greater cross\-lingual performance disparity\. We find a clear positive correlation: the greater this disparity, the larger the net benefit of switching\.

ForMGSM, the Qwen3 backbone becomes increasingly balanced across languages as model size grows \(Std: 4B\-16\.9616\.96, 14B\-7\.4467\.446, 32B\-4\.6654\.665\), naturally reducing the benefit of switching\. Intuitively, if performance were identical across all languages, switching would offer no gain\. ForMT\-AIME, although overall accuracy improves with scale, the performance imbalances remains low and stable \(Std: 4B\-6\.5766\.576, 14B\-8\.3088\.308, 32B\-7\.4957\.495\), explaining the consistently small and almost scale\-invariant net benefit observed in Figure[4](https://arxiv.org/html/2604.16917#S4.F4)\(b\)\.

![Refer to caption](https://arxiv.org/html/2604.16917v1/x3.png)Figure 4:Benefit and harm rates of thinking\-language switching onMGSM,MT\-AIME,FORKandCulturalBenchdatasets acrossQwen3\-4B,14Band32B\. The shaded area \(benefit rate minus harm rate\) represents the net benefits\.
##### \(2\) Thinking in Culture\-associated Language Offers Inherent and Persistent Advantages\.

Figure[4](https://arxiv.org/html/2604.16917#S4.F4)\(c\)\(d\) shows that the net benefit of reasoning in culture\-associated language remains stable across model scales, and is consistently larger than that observed in multilingual math reasoning\. This indicates that the advantage of reasoning in culture\-associated language is not a transient effect of limited model capacity, but instead reflects a deeper entanglement between language and culture\.

This persistence also reveals a fundamental challenge to “Scaling Law”: cultural knowledge is tightly intertwined with the linguistic forms through which it is acquired, represented, and invoked\. Consequently, reasoning in English cannot fully substitute for reasoning in the culture\-associated language, even as model size and overall capability continue to increase\. This points to an intrinsic upper bound on English\-centric reasoning in cultural contexts—one that is difficult to overcome through scaling alone\.

ModelsAvg\. Cultural KnowledgeRecall Count per Thought\(Efficiency\)Avg\. Cultural KnowledgeRecall Accuracy \(%\)\(Accuracy\)Qwen3\-4B3\.36647\.699x1\-Qwen3\-4B2\.662 \(↓\\bm\{\\downarrow\}0\.704\)53\.439 \(↑\\bm\{\\uparrow\}5\.740\)Qwen3\-14B3\.35349\.123x1\-Qwen3\-14B2\.765 \(↓\\bm\{\\downarrow\}0\.588\)55\.319 \(↑\\bm\{\\uparrow\}6\.196\)Qwen3\-32B3\.56145\.813x1\-Qwen3\-32B3\.000 \(↓\\bm\{\\downarrow\}0\.561\)56\.725 \(↑\\bm\{\\uparrow\}7\.902\)

Table 3:Statistics of cultural knowledge recall frequency and accuracy on theCulturalBenchdataset\.

### 4\.3Cultural Knowledge Recall Behavior

Section[4\.2\.2](https://arxiv.org/html/2604.16917#S4.SS2.SSS2)demonstrates the persistent advantages of thinking in culture\-associated language\. But what underlies this advantage? As illustrated in Appendix §[C](https://arxiv.org/html/2604.16917#A3)Figure[8](https://arxiv.org/html/2604.16917#A1.F8), both backbone andx1models exhibit explicit*cultural knowledge recall*during cultural reasoning, actively retrieving relevant cultural facts or norms as part of their reasoning process\. While such recall alone does not guarantee correctness, it plays a critical role in shaping the final answer\. Motivated by this observation, we compare the cultural knowledge recall behavior ofx1and its backbone models\. Specifically, we employGPT\-5\-minito identify recalled cultural knowledge that supports or justifies the golden answer and to verify its correctness \(implementations are in Appendix §[C](https://arxiv.org/html/2604.16917#A3)\)\. The results are summarized in Table[3](https://arxiv.org/html/2604.16917#S4.T3), leading to the following finding:

##### Thinking in Culture\-associated Language Enables More Efficient and Accurate Cultural Knowledge Recall\.

As shown in Table[3](https://arxiv.org/html/2604.16917#S4.T3), across all model scales,x1consistently recalls fewer but more accurate cultural knowledge instances compared to its backbone model\.x1reduces the average recall count per thought by0\.560\.56\-0\.700\.70, while improving recall accuracy by5\.74%5\.74\\%\-7\.90%7\.90\\%\. This indicates that reasoning in culture\-associated languages promotes more targeted and relevant knowledge retrieval, rather than broader but noisier recall, providing a concrete mechanistic explanation for the persistent gains observed in cultural tasks\.

### 4\.4Language\-Mixing inx1

In multilingual reasoning, models often interleave multiple languages within a single reasoning trajectory, a phenomenon commonly known aslanguage mixing\(yong2025crosslingual\)\(we present a example in Figure[9](https://arxiv.org/html/2604.16917#A1.F9)\)\. Unlike explicit thinking\-language switching, which operates at the context level, language mixing captures a finer\-grained, sentence\-level adaptation that can occur without explicit switching\. To isolate this effect, we focus on samples wherex1does not perform explicit thinking\-language switching\. For these samples, we measure the change in sentence\-level language\-mixing strength ofx1’s responses relative to its backbone and analyze its correlation with the resulting net benefits aggregated over all samples\.

##### Increased Language Mixing Is Associated with Positive Outcomes in Multilingual Reasoning\.

As we do not introduce any design about language mixing, we observe that on bothMGSMandMT\-AIME, the proportions of samples with increased and decreased language mixing rates are broadly balanced\. However, those with increased language mixing rates consistently yield higher net benefits than those with decreased mixing \(0\.26%0\.26\\%vs\.0\.21%0\.21\\%onMGSM,0\.85%0\.85\\%vs\.0\.11%0\.11\\%onMT\-AIME\)\.

These results indicate that the gains ofx1cannot be fully attributed to explicit language switching\. Even in the absence of such switching, higher sentence\-level language mixing rates is positively correlated with improved performance\. Language mixing thus appears to act as a fine\-grained mechanism that integrates complementary linguistic representations within a single reasoning trajectory, and may further provide a useful guidance signal for model optimization \(e\.g\., in reward design\)\.

![Refer to caption](https://arxiv.org/html/2604.16917v1/x4.png)Figure 5:Proportions of samples with changed language mixing strength inx1’s responses relative to its backbone, and the correlation with the resulting net benefits\.

### 4\.5Preference Optimization with DPO

The instance\-level contrastive signals naturally induce implicit preferences between alternative reasoning\-language choices\. In this subsection, we further apply Direct Preference Optimization \(DPO\)\(rafailov2023direct\)as an auxiliary enhancement, treating reasoning trajectories in the advantageous language as preferred samples and those in the less advantageous language as dispreferred ones555Reusing the same data produced in Section[2](https://arxiv.org/html/2604.16917#S2)Step 2\.\. The results are shown in Appendix §[E](https://arxiv.org/html/2604.16917#A5)Table[8](https://arxiv.org/html/2604.16917#A5.T8), where we observe that DPO further improves the performance ofx1models, achieving a second jump in multilingual math reasoning\.

## 5Related Work

##### Multi\- & Cross\-lingual Reasoning\.

Recent studies examined how LLMs perform reasoning across languages\. Some approaches utilize response alignment, latent connection and language separability to bridge the gap between languages\(zhu2024power;ye\-etal\-2025\-cc;ye2025langgps\)\. Besides,ko2025understandanchor reasoning in English to minimize the gaps, whereas SLAM\(fan2025slam\)maintains reasoning capabilities with lower computational costs\. Further refinement is achieved through reasoning\-focused tuning like mCoT\(lai\-nissim\-2024\-mcot\), preference\-based alignment\(she\-etal\-2024\-mapo\), and process reward modeling\(wang2025demystifying\)\. Some previous works focus on prompting strategies\(qin2023cross\)\. Researchers proposed𝒳\\mathcal\{X\}Transplant for cross\-lingual complementarity\(ye2024exploring\), dictionary insertion prompting\(lu2024dictionary\)that embeds key English terms into native prompts and program\-based demonstrations\(ranaldi2025natural\)for structured logic transfer\. Recently,yong2025crosslingualconducted a detailed analysis, revealing the potentials and limitations of cross\-lingual test\-time scaling\.

##### Cultural Reasoning\.

Early efforts primarily focused on constructing culturally grounded knowledge bases, such as CANDLE\(nguyen2023extracting\)for normative assertions, CultureBank\(shi2024culturebank\)for community\-driven cultural descriptors, MAPS\(liu2024multilingual\)for figurative expressions, and GlobeSumm\(ye\-etal\-2024\-globesumm\)for global perspectives on international news\. From a methodological perspective, existing work explores how to elicit or control cultural perspectives in LLMs\(kovavc2023large\), enhance cultural reasoning by explicitly recognizing cultural context in prompts\(wang\-etal\-2024\-countries\), integrate moral reasoning across normative ethics frameworks\(rao\-etal\-2023\-ethical\), and complement English reasoning with non\-English cultural features via cross\-lingual transplantation\(ye2024exploring\)\.

Rather than enforcing consistency across languages, we investigate whether different languages inherently provide complementary reasoning advantages for different instances\. By framing reasoning\-language choice as a self\-aware decision process, our method bridges multilingual and cultural reasoning from a unified perspective, positioning language as an active component of reasoning rather than a passive carrier of content\.

## 6Conclusion

In this work, we presentedx1models that enable adaptive multilingual reasoning\. By constructingx1without expanding the model’s knowledge boundaries, we isolated the effect of reasoning\-language choice and demonstrated that linguistic diversity can be systematically leveraged to improve both multilingual mathematical reasoning and culturally grounded reasoning\. Beyond empirical gains, our findings challenge a simplistic interpretation of scaling laws, revealing that even as models grow larger and more capable, the advantages of reasoning in culture\-associated languages persist rather than vanish\. This highlights reasoning\-language choice as a functional component of reasoning rather than a superficial artifact of generation\. We hope this work encourages future research to move beyond monolithic reasoning paradigms toward building LLMs that are more globally and culturally competent\.

## Limitations

This work exhibits several limitations worth noting\. First, to enable a clean comparison between alternative reasoning pathways, for each instance, we intentionally restrict the candidate thinking languages to English and one non\-English language \(which is determined by the query language or cultural background\)\. Although this design choice facilitates controlled analysis, it limits the exploration of richer multilingual combinations and linguistic diversity\. Extending adaptive reasoning to a larger pool of languages can be a further exploration\. Second, while our analysis reveals the potential positive impact of “language mixing” for reasoning, we do not pursue this direction further due to space constraints\. Exploring principled ways to incorporate mixed\-language reasoning, for example as a training signal or an optimization objective can be great future work\. Thirdly, for culture\-related tasks, we employ an LLM\-as\-a\-Judge framework to assess response quality\. Although this approach enables scalable evaluation, it may inherit the biases and limitations of the evaluator model\. We mitigate this risk by using evaluation only for relative comparison between reasoning\-language choices, rather than for absolute or normative judgments\.

## Acknowledgements

Xiaocheng Feng is the corresponding author of this work\. We thank the anonymous reviewers for their insightful comments\. This work was supported by the National Natural Science Foundation of China \(NSFC\) \(grant 62522603, 62276078\), the Key R&D Program of Heilongjiang via grant 2022ZX01A32, the Fundamental Research Funds for the Central Universities \( XNJKKGYDJ2024013 \) \.

## Ethical Considerations

This work studies multilingual and culturally grounded reasoning in large language models\. All model outputs, especially those related to cultural knowledge or perspectives, are generated by the models themselves and do not represent the views or opinions of the authors\. Our method does not introduce new knowledge sources or external supervision, and therefore does not increase the risk of generating sensitive or private information beyond the capabilities of the backbone models\. While reasoning in culture\-associated languages may surface different cultural expressions or viewpoints, such outputs should not be interpreted as authoritative or normative cultural judgments\. In this paper, we use Gemini to correct grammatical errors\.

## References

## Appendix AExperiment Details

### A\.1Step 1: To be a Multilingual Reasoner

##### Language List\.

The 31 languages \(English included\) involved in step 1 training are as follows:

\["Arabic","Bulgarian","Bengali","German","Greek",

"English","Spanish","Finnish","French","Hebrew",

"Hindi","Hungarian","Indonesian","Italian",

"Japanese","Korean","Malay","Dutch","Polish",

"Portuguese","Romanian","Russian","Swedish",

"Swahili","Thai","Tagalog","Turkish","Ukrainian",

"Urdu","Vietnamese","Chinese"\]

##### Quality Filtering\.

To ensure linguistic fidelity, we apply quality filtering using COMET \(Unbabel/wmt23\-cometkiwi\-da\-xxl\) scores and discard translations of evidently poor quality \(whose scores fall below 0\.4\)\.

##### Data Format\.

We adopt the official training templates provided by the corresponding backbone models\. For instance, when trainingQwen3\-4B,14B, and32B, we use the official“Qwen3”template to ensure consistency with the original training and inference protocols\. Beyond the official templates, we introduce a customized template tailored for multilingual reasoning control\. This template explicitly specifies the language used in the reasoning process while keeping the final answer aligned with the prompt language\. Real examples are shown in Figure[6](https://arxiv.org/html/2604.16917#A1.F6)\. Note that, due to the diversity ofXXand to preserve the generality of the template, we do not register “<XX\_start\>” series as special tokens in the tokenizer\.

![Refer to caption](https://arxiv.org/html/2604.16917v1/x5.png)Figure 6:Examples of Step 1 constructed training data \(reasoning in Arabic, Spanish and Chinese\)\.
##### Training Hyperparameters\.

We perform full\-parameter finetuning for all models, except forQwen3\-32B, for which we adopt LoRA training due to its large model size\.

per\_device\_train\_batch\_size:1

gradient\_accumulation\_steps:16

learning\_rate:1\.0e\-5

num\_train\_epochs:3\.0

bf16:true

lora\_rank:8

lora\_target:all

per\_device\_train\_batch\_size:1

gradient\_accumulation\_steps:16

learning\_rate:1\.0e\-4

num\_train\_epochs:3\.0

bf16:true

### A\.2Step 2: To be an Adaptive Reasoner

##### Training Data Statistics\.

- •\(1\) Multilingual Math Problems: We use theMGSM8KInstructdataset\(chen2023breaking\), which contains math problems paired with their correct answers\. We sample 200 questions across 10 languages, resulting in 2,000 training instances\. Detailed statistics are as follows: \{//language:samplesize "Bengali":200, "German":200, "English":200, "Spanish":200, "French":200, "Japanese":200, "Russian":200, "Swahili":200, "Thai":200, "Chinese":200 \} //Total:2000
- •\(2\) Culture\-related Problems: We use theCultureBankdataset\(shi2024culturebank\), which provides cultural questions along with the underlying cultural knowledge they reflect\. We sample 100\-200 questions from each of the 25 language groups \(depending on availability\), covering cultural questions from 45 countries/regions, resulting in 4,413 samples in total\. Detailed statistics are as follows: \{//languagegroup:samplesize "Arabic":200, "Danish":122 "German":200, "Greek":100, "English":200, "Spanish":200, "Finnish":142, "French":200, "Irish":157, "Scottish␣Gaelic":125, "Hindi":200, "Indonesian":200, "Italian":200, "Japanese":200, "Korean":200, "Maori":141, "Malay":130, "Dutch":200, "Norwegian":173, "Polish":123, "Portuguese":200, "Russian":200, "Swedish":200, "Tagalog":200, "Chinese":200 \} //Total:4413 Each language group is associated with a list of countries/regions: \{//languagegroup:listofcountries/regions "Arabic":\["Algeria","Arab","Egypt","Iraq", "Lebanon","Syria","Morocco","Tunisia","Jordan"\], "Danish":\["Denmark"\], "German":\["Germany","Austria","Switzerland"\], "Greek":\["Greece","Cyprus"\], "English":\["United␣States"\], "Spanish":\["Argentina","Spain","Cuba", "Chile","Colombia","Dominican␣Republic", "Mexico","Peru"\], "Finnish":\["Finland"\], "French":\["France"\], "Irish":\["Ireland"\], "Scottish␣Gaelic":\["Scotland"\], "Hindi":\["India"\], "Indonesian":\["Indonesia"\], "Italian":\["Italy"\], "Japanese":\["Japan"\], "Korean":\["Korea"\], "Maori":\["New␣Zealand"\], "Malay":\["Malaysia"\], "Dutch":\["Netherlands","Belgium"\] "Norwegian":\["Norway"\], "Polish":\["Poland"\], "Portuguese":\["Brazil","Portugal"\], "Russian":\["Russia"\], "Swedish":\["Sweden"\], "Tagalog":\["Philippines"\], "Chinese":\["China"\] \}

##### Advantageous Language Identification\.

For each question inDmathD\_\{\\operatorname\{math\}\}orDcultureD\_\{\\operatorname\{culture\}\}, we first obtain the paired reasoning trajectories in both English and non\-English withℳ\\mathcal\{M\}andℳsurface\\mathcal\{M\}\_\{\\operatorname\{surface\}\}[4](https://arxiv.org/html/2604.16917#footnote4)\. We identify the advantageous reasoning language based on the quality of the final answers, under the principle that stronger reasoning should manifest in superior outputs\. For multilingual math problems, answer quality is determined via numerical matching\.

s​c​o​r​emath​\(y^,y\)=\{10,if​y^​matches​y,0,otherwise,score\_\{\\text\{math\}\}\(\\hat\{y\},y\)=\\begin\{cases\}10,&\\text\{if \}\\hat\{y\}\\text\{ matches \}y,\\\\ 0,&\\text\{otherwise\},\\end\{cases\}\(1\)wherey^\\hat\{y\}denotes the model\-predicted numerical answer andyyis the ground\-truth answer\.

For culture\-related questions, we employGPT\-5\-minito score how well the response entails the relevant cultural knowledge\.

s​c​o​r​eculture​\(y^,n\)=Entailment​\(Q,y^,n,L​L​M\)\\displaystyle score\_\{\\text\{culture\}\}\(\\hat\{y\},n\)=\\text\{Entailment\}\(Q,\\hat\{y\},n,LLM\)\(2\)∈\[0,10\]\\displaystyle\\hskip 73\.97733pt\\in\[0,0\]whereQQdenotes the culture\-related question,y^\\hat\{y\}denotes the model\-predicted response andnnrepresents the relevant cultural knowledge or norm that the model is expected to comply with\. The prompt for scoring is shown in Table[4](https://arxiv.org/html/2604.16917#A1.T4)\.

Prompt for Scoring Cultural Knowledge EntailmentYou will be given a culture\-related question, a related cultural knowledge and a response from an agent\.Your task is to provide a ’total rating’ scoring how well the response from an agent answers the culture\-related question and entails the related cultural knowledge\.Give your answer as a float on a scale of 0 to 10, where 0 means that the response from agent is not helpful at all, and 10 means that the answer completely and helpfully addresses the question\.Your output should be a float score only\.Question:\{question\}Cultural Knowledge:\{cultural knowledge description\}Response:\{model response\}Total rating \(a float on a scale of 0 to 10\):

Table 4:Prompts designed for scoring cultural knowledge entailment\.The reasoning language associated with the higher\-scoring trajectory is then regarded as the advantageous thinking language for that instance\.

##### Data Format\.

Besides the data format introduced in Figure[6](https://arxiv.org/html/2604.16917#A1.F6), we also construct self\-awareness data that externalizes the model’s language\-selection decision as an explicit prediction task and the format is shown in Figure[7](https://arxiv.org/html/2604.16917#A1.F7)\.

![Refer to caption](https://arxiv.org/html/2604.16917v1/x6.png)Figure 7:Example of self\-awareness data, where “Arabic” is the advantageous reasoning language\.
##### Training Hyperparameters\.

We apply LoRA training separately for the multilingual math and cultural reasoning scenarios\. ForMGSM8KInstruct, we set the LoRA rank to 4, as we empirically observe that using a larger rank leads to unexpected and substantial drops in performance\.

lora\_rank:4

lora\_target:all

per\_device\_train\_batch\_size:1

gradient\_accumulation\_steps:16

learning\_rate:1\.0e\-4

bf16:true

lora\_rank:16

lora\_target:all

per\_device\_train\_batch\_size:1

gradient\_accumulation\_steps:16

learning\_rate:1\.0e\-4

bf16:true

### A\.3Repetition\-Detection Truncation Mechanism

To prevent the model from producing meaningless repetitive reasoning during inference, we implement a repetition\-detection truncation mechanism based on a customStoppingCriteria\. The method monitors the generated text in fixed\-size blocks and terminates decoding if a newly generated block has appeared earlier in the output, indicating repetitive looping behavior\.

Algorithm 1Repetition\-Detection Truncation Mechanism1:Tokenizer

𝒯\\mathcal\{T\}, prompt length

LL, block size

BB, model

ℳ\\mathcal\{M\}
2:Initialize generated sequence

X←X\\leftarrowmodel prompt

3:flag

←\\leftarrowFalse

4:whilenot flagdo

5:

x←ℳx\\leftarrow\\mathcal\{M\}\.generate\_next\( \)

6:Append

xxto

XX
7:

T←𝒯\.decode\(X\[L:\]\)T\\leftarrow\\mathcal\{T\}\.\\texttt\{decode\}\(X\[L:\]\)⊳\\trianglerightdecode newly generated text

8:if

\|T\|<2​B\|T\|<2Bthen

9:continue⊳\\trianglerightinsufficient text length

10:endif

11:last\_block

←T\[\|T\|−B:\|T\|\]\\leftarrow T\[\|T\|\-B:\|T\|\]
12:prefix

←T\[0:\|T\|−B\]\\leftarrow T\[0:\|T\|\-B\]
13:iflast\_block

∈\\inprefixthen

14:flag

←\\leftarrowTrue⊳\\trianglerightrepetition detected

15:break

16:endif

17:endwhile

18:return

XX

ModelsMultilingual Math ReasoningMGSMMT\-AIMENon\-ThinkThinkNon\-ThinkThinkBackbone ModelsQwen3\-4B70\.2176\.5912\.8921\.78Qwen3\-14B77\.6482\.5619\.3329\.22Qwen3\-32B80\.5283\.9821\.8333\.89\+ Vanilla FinetuningQwen3\-4B50\.801\.667Qwen3\-14B64\.242\.000Qwen3\-32B72\.680\.333Backbone \+ Majority VotingQwen3\-4B87\.4692\.0016\.6735\.56Qwen3\-14B89\.3392\.9328\.8947\.78Qwen3\-32B89\.2093\.0734\.4450\.00x1 Series Modelsx1\-Qwen3\-4B70\.3077\.6913\.5622\.83x1\-Qwen3\-14B77\.3883\.6419\.4433\.11x1\-Qwen3\-32B80\.1284\.4322\.1134\.50x1 Series Models \+ Majority Votingx1\-Qwen3\-4B88\.8093\.3320\.0035\.56x1\-Qwen3\-14B90\.2793\.7331\.1148\.89x1\-Qwen3\-32B90\.0093\.2036\.6750\.00

Table 5:Supplementary experimental Mean@3 results that are the averages of the performance across all languages / cultures involved for each dataset\.ModelsMean@3 Performance on MGSMBnDeEnEsFrJaRuSwThZhAverageStandard DeviationQwen3\-4B75\.3382\.5387\.6084\.6781\.678\.6784\.6726\.8079\.3384\.6776\.5916\.96Qwen3\-14B83\.6085\.6086\.6084\.6082\.8082\.2087\.0060\.8086\.0086\.4082\.567\.446Qwen3\-32B84\.0086\.6089\.2084\.2083\.2082\.8086\.8071\.8084\.2087\.0083\.984\.665ModelsMean@3 Performance on MT\-AIMEBnDeEnEsFrJaRuSwThZhAverageStandard DeviationQwen3\-4B22\.2225\.5625\.5624\.4423\.3322\.2217\.786\.6725\.5624\.4421\.786\.576Qwen3\-14B26\.6726\.6732\.2225\.5634\.4424\.4434\.4418\.8923\.3345\.5629\.228\.308Qwen3\-32B28\.8928\.8926\.6743\.3331\.1131\.1138\.8927\.7835\.5646\.6733\.897\.495

Table 6:Performance of backbone models onMGSMandMT\-AIMEalong with the average and standard deviation\. The larger the standard deviation, the greater the cross\-lingual performance disparity\.
### A\.4Results For Each Subset

We present the results for each language subset forMGSMandMT\-AIMEin Table[9](https://arxiv.org/html/2604.16917#A5.T9)\.

### A\.5Supplementary Experimental Results

We present the supplementary experimental results of \(1\)vanilla finetuningand \(2\)majority votingin Table[5](https://arxiv.org/html/2604.16917#A1.T5)\. Since theCultureBankdataset lacks reference answers for supervised training, andFORKandCulturalBenchare not designed to support multilingual evaluation, we restrict the analysis to multilingual mathematical reasoning tasks\.

- •Vanilla Finetuning:We perform vanilla finetuning \(lora\) for the backbone models withMGSM8KInstructdataset\.
- •Majority Voting:For each math problem, we query the model using 10 parallel versions of the same question in different languages and aggregate the resulting answers via majority voting, taking the most frequent answer as the final prediction\. In this setting, we ignore constraints on response\-language consistency and the voting outcome serves as an approximate indicator of the potential gains from linguistic diversity\.

We observe that continuous finetuning on already strongQwen3\-series models leads to a noticeable degradation in performance\. This degradation is likely due to the limited difficulty and suboptimal quality of the reasoning traces inMGSM8KInstruct, which can substantially disrupt the models’ existing reasoning capabilities\.

By contrasting “Backbone \+ Majority Voting” with “x1 \+ Majority Voting”, we find that the upper bound afforded by linguistic diversity remains remarkably high: aggregating predictions across 10 languages substantially surpasses the models’ original performance\. Moreover, thex1series consistently exhibits a higher majority\-voting upper bound than their backbone models, suggesting thatx1more effectively integrates and aligns reasoning signals across languages, thereby enabling linguistic diversity to be exploited more coherently\.

![Refer to caption](https://arxiv.org/html/2604.16917v1/x7.png)Figure 8:Examples of cultural knowledge recall behavior\.Prompt for Identifying Cultural Knowledge Recall Behaviors\(Input:\)Given the following QA pair, I will provide you with my reasoning process\.Your task is to determine whether my reasoning includes any recall of cultural norms that directly support or justify the Golden Answer\.If such culturally relevant recall exists, extract only the portions that are directly tied to the Golden Answer and return them in a Python list\.Question:\{question\}Golden Answer:\{answer\}Reasoning Process:\{reasoning\}\(Output:\)\{Response of Extracted Cultural Knowledge Recalls\}Prompt for Verifying Cultural Knowledge Recall Behaviors\(Input:\)Given the following QA pair, I will provide you with a cultural statement\.Your task is to determine whether this statement provides a decisive and indispensable contribution to arriving at the Golden Answer\.Mere relevance or weak association does not count\.Return only True or False\.Question:\{question\}Golden Answer:\{answer\}Cultural Statement:\{norm\}\(Output:\)\{True or False\}

Table 7:Prompts for identifying and verifying cultural knowledge recall behaviors\.![Refer to caption](https://arxiv.org/html/2604.16917v1/x8.png)Figure 9:Example of language mixing behavior\.

## Appendix BPerformance Standard Deviation Across Languages

The statistics of performance standard deviation \(Std\) across languages for backbone models inMGSMandMT\-AIMEis presented in Table[6](https://arxiv.org/html/2604.16917#A1.T6)\. LargerStdindicates greater cross\-lingual performance disparity\. The statistics provides important support for the analysis in Section[4\.2\.2](https://arxiv.org/html/2604.16917#S4.SS2.SSS2)\(1\)\.

## Appendix CCultural Knowledge Recall Analysis

We observe that both backbone andx1models exhibit explicit*cultural knowledge recall*behavior during cultural reasoning, actively retrieving relevant cultural facts or norms as part of their reasoning process\. While such recall alone does not guarantee correctness, it plays a critical role in shaping the final answer\. As illustrated in Figure[8](https://arxiv.org/html/2604.16917#A1.F8), we present a pair of examples of cultural knowledge recall behavior produced byQwen3\-32B\(thinking in English\) andx1\-Qwen3\-32B\(thinking in Chinese\) on a question fromCulturalBenchdataset\. We use high\-light to highlight the cultural knowledge recall behavior, where the green parts are the key recall behaviors that directly lead to the model’s correct answer\.

Motivated by this observation and to further analyze such behavior, we employGPT\-5\-minito identify recalled cultural knowledge that supports or justifies the golden answer and to verify its correctness\. The designed prompts are presented in Table[7](https://arxiv.org/html/2604.16917#A1.T7)\.

As shown in Table[3](https://arxiv.org/html/2604.16917#S4.T3), across all model scales,x1consistently recalls fewer but more accurate cultural knowledge instances compared to its backbone model\.x1reduces the average recall count per thought by0\.560\.56\-0\.700\.70, while improving recall accuracy by5\.74%5\.74\\%\-7\.90%7\.90\\%\. This indicates that reasoning in culture\-associated languages promotes more targeted and relevant knowledge retrieval, rather than broader but noisier recall, providing a concrete mechanistic explanation for the persistent gains observed in cultural tasks\.

## Appendix DLanguage Mixing Behavior

We present a example of language mixing behavior in Figure[9](https://arxiv.org/html/2604.16917#A1.F9), where the default reasoning in English is interleaved with reasoning in Japanese\.

## Appendix EFurther Enhancement with Direct Preference Optimization

In our main experiments, our trainining strategy only leverages the signals from the advantageous language\. However, the instance\-level contrastive signals between the advantageous and less advantageous languages naturally induce implicit preferences between alternative reasoning\-language choices\. In this subsection, we further apply Direct Preference Optimization \(DPO\) as an auxiliary enhancement, treating reasoning trajectories in the advantageous language as preferred samples and those in the less advantageous language as dispreferred ones\. The results are shown in Table[8](https://arxiv.org/html/2604.16917#A5.T8)\.

ModelsMultilingual Math ReasoningCultural ReasoningMGSMMT\-AIMEFORKCulturalBenchThinkThinkThinkThinkOpen\-sourced Reasoning ModelsQwen3\-4B76\.5921\.7873\.7370\.85Qwen3\-14B82\.5629\.2273\.9178\.24Qwen3\-32B83\.9833\.8981\.8881\.26x1 Series Models\+ Math\+ Culturex1\-Qwen3\-4B77\.6922\.8378\.0872\.74x1\-Qwen3\-14B83\.6433\.1176\.8181\.58x1\-Qwen3\-32B84\.4334\.5082\.6181\.99x1 Series Models \+ DPO\+ Math\+ Culturex1\-Qwen3\-4B78\.2322\.0077\.7272\.51x1\-Qwen3\-14B83\.5633\.3377\.9081\.34x1\-Qwen3\-32B84\.5638\.6783\.7081\.05

Table 8:Results after applying DPO tox1models\.MGSMBnDeEnEsFrJaRuSwThZhAverageBackbone ModelsQwen3\-4B \(non\-think\)68\.6776\.2783\.8775\.7374\.4073\.0781\.2015\.8774\.0079\.0770\.21Qwen3\-4B \(think\)75\.3382\.5387\.6084\.6781\.6078\.6784\.6726\.8079\.3384\.6776\.59Qwen3\-14B \(non\-think\)80\.2081\.2086\.0080\.6078\.4078\.6082\.8043\.8081\.6083\.2077\.64Qwen3\-14B \(think\)83\.6085\.6086\.6084\.6082\.8082\.2087\.0060\.8086\.0086\.4082\.56Qwen3\-32B \(non\-think\)80\.880\.885\.68277\.680\.884\.465\.283\.684\.480\.52Qwen3\-32B \(think\)84\.0086\.6089\.2084\.2083\.2082\.8086\.8071\.8084\.2087\.0083\.98DeepSeek\-R1\-Distill\-Qwen\-7B \(non\-think\)46\.0061\.0080\.4069\.0063\.4045\.6059\.205\.0044\.2073\.8054\.76DeepSeek\-R1\-Distill\-Qwen\-7B \(think\)50\.4067\.0780\.0071\.0768\.8051\.8771\.877\.0752\.1380\.2760\.05DeepSeek\-R1\-Distill\-Llama\-8B \(non\-think\)12\.1346\.0065\.7349\.6045\.6035\.3347\.333\.7319\.8756\.4038\.17DeepSeek\-R1\-Distill\-Llama\-8B \(think\)11\.7345\.0766\.4051\.8747\.0733\.8744\.935\.0725\.4772\.1340\.36x1 Series Modelsx1\-Qwen3\-4B \(non\-think\)66\.2076\.4084\.8078\.0075\.6071\.4078\.8017\.8076\.6077\.4070\.30x1\-Qwen3\-4B \(think\)77\.4784\.5391\.0785\.4781\.8778\.9385\.4727\.3380\.1384\.6777\.69x1\-Qwen3\-14B \(non\-think\)78\.0079\.2086\.4079\.0077\.4080\.0083\.0044\.4084\.4082\.0077\.38x1\-Qwen3\-14B \(think\)82\.0086\.0088\.8086\.2084\.0083\.0087\.6061\.2088\.4089\.2083\.64x1\-Qwen3\-32B \(non\-think\)82\.0082\.4087\.6082\.4076\.8080\.0084\.8062\.0078\.4084\.8080\.12x1\-Qwen3\-32B \(think\)85\.4784\.8089\.8785\.0783\.0784\.4087\.3373\.3384\.2786\.6784\.43x1\-DeepSeek\-R1\-Distill\-Qwen\-7B \(non\-think\)50\.0057\.2080\.4068\.0060\.8050\.8060\.404\.8043\.6069\.2054\.52x1\-DeepSeek\-R1\-Distill\-Qwen\-7B \(think\)57\.6071\.4080\.2072\.4067\.8060\.4074\.009\.8059\.0079\.8063\.24x1\-DeepSeek\-R1\-Distill\-Llama\-8B \(non\-think\)10\.6746\.0065\.6049\.6045\.6035\.3347\.333\.7319\.8756\.4038\.01x1\-DeepSeek\-R1\-Distill\-Llama\-8B \(think\)26\.4060\.5376\.5362\.8062\.6749\.7364\.9312\.9337\.2068\.0052\.17MT\-AIMEBnDeEnEsFrJaRuSwThZhAverageBackbone ModelsQwen3\-4B \(non\-think\)6\.6716\.6717\.7812\.2223\.337\.7815\.564\.447\.7816\.6712\.89Qwen3\-4B \(think\)22\.2225\.5625\.5624\.4423\.3322\.2217\.786\.6725\.5624\.4421\.78Qwen3\-14B \(non\-think\)16\.6726\.6725\.0025\.0021\.6718\.3321\.675\.0013\.3320\.0019\.33Qwen3\-14B \(think\)26\.6726\.6732\.2225\.5634\.4424\.4434\.4418\.8923\.3345\.5629\.22Qwen3\-32B \(non\-think\)23\.3321\.6726\.6721\.6721\.6725\.0026\.6710\.0021\.6720\.0021\.83Qwen3\-32B \(think\)28\.8928\.8926\.6743\.3331\.1131\.1138\.8927\.7835\.5646\.6733\.89DeepSeek\-R1\-Distill\-Qwen\-7B \(non\-think\)2\.226\.6716\.6711\.117\.783\.3310\.003\.336\.6715\.568\.33DeepSeek\-R1\-Distill\-Qwen\-7B \(think\)23\.3331\.6733\.3325\.0030\.0028\.3326\.678\.3320\.0031\.6725\.83DeepSeek\-R1\-Distill\-Llama\-8B \(non\-think\)1\.112\.221\.114\.443\.331\.113\.330\.004\.445\.562\.67DeepSeek\-R1\-Distill\-Llama\-8B \(think\)11\.1116\.6715\.5618\.8917\.7812\.2215\.565\.5611\.1120\.0014\.44x1 Series Modelsx1\-Qwen3\-4B \(non\-think\)6\.6718\.8923\.3315\.5616\.678\.8915\.565\.567\.7816\.6713\.56x1\-Qwen3\-4B \(think\)16\.6725\.0025\.0025\.0023\.3321\.6723\.3310\.0025\.0033\.3322\.83x1\-Qwen3\-14B \(non\-think\)14\.4421\.1123\.3323\.3324\.4417\.7827\.787\.7818\.8915\.5619\.44x1\-Qwen3\-14B \(think\)20\.0034\.4438\.8935\.5627\.7836\.6732\.2220\.0033\.3352\.2233\.11x1\-Qwen3\-32B \(non\-think\)18\.8921\.1124\.4425\.5616\.6723\.3322\.2218\.8925\.5624\.4422\.11x1\-Qwen3\-32B \(think\)31\.6735\.0035\.0033\.3336\.6740\.0035\.0023\.3330\.0045\.0034\.50x1\-DeepSeek\-R1\-Distill\-Qwen\-7B \(non\-think\)7\.788\.8912\.2211\.117\.784\.4410\.006\.6710\.0011\.119\.00x1\-DeepSeek\-R1\-Distill\-Qwen\-7B \(think\)23\.3326\.6723\.3326\.6730\.0023\.3326\.6723\.3333\.3333\.3327\.00x1\-DeepSeek\-R1\-Distill\-Llama\-8B \(non\-think\)2\.223\.333\.332\.222\.223\.332\.220\.002\.227\.782\.89x1\-DeepSeek\-R1\-Distill\-Llama\-8B \(think\)3\.3323\.3323\.3320\.0023\.3320\.0016\.673\.3316\.6720\.0017\.00

Table 9:Results for each subsets inMGSMandMT\-AIMEacross different languages\.