Beyond English-Centric Training: How Reinforcement Learning Improves Cross-Lingual Reasoning in LLMs
Authors: Shulin Huang
Yiran Ding
Junshu Pan
Yue Zhang
Venue: ICLR 2026 Poster (2026)
Keywords: Reasoning
Generalization
Reinforcement Learning
Multilingual
Primary area: other topics in machine learning (i.e., none of the above)

Abstract: Enhancing the complex reasoning capabilities of Large Language Models (LLMs) attracts widespread attention. While reinforcement learning (RL) has shown superior performance for improving complex reasoning, its impact on cross-lingual generalization compared to Supervised Fine-Tuning (SFT) remains unexplored. We present the first systematic investigation into cross-lingual reasoning generalization of RL and SFT. Using Qwen2.5-3B-Base as our foundation model, we conduct experiments on diverse multilingual reasoning benchmarks, including math reasoning, commonsense reasoning, and scientific reasoning. Our investigation yields two significant findings: (1) Tuning with RL not only achieves higher accuracy but also demonstrates substantially stronger cross-lingual generalization capabilities compared to SFT. (2) RL training on non-English data yields better overall performance and generalization than training on English data, which is not observed with SFT. Furthermore, through comprehensive mechanistic analyses, we explore the underlying factors of RL's superiority and generalization across languages. Our results provide compelling evidence that RL enables the model with more robust reasoning strategies, offering crucial guidance for more equitable and effective multilingual reasoning.

Published as a conference paper at ICLR 2026
BEYOND ENGLISH-CENTRIE TRAINING: HOW REIN-
FORCEMENT LEARNING IMPROVES CROSS-LINGUAL REASONING IN LLMS
Shulin Huang" 12; Viran Junshu Pan1.2,, Yue Zhangat
"Zejiiang University, #Westlake University
/huangshulin, dingyiran, panjunshu, zhangyue)&westllake
ABSTRACT
Enhancing the complex reasoning capabilities of Large Language Models (LLMs) attracts widespread attention. While reinforcement learning (RL) has shown perior performance for improving complex reasoning, its impact on cross-lingual generalization compared Supervised Fine-Tuning (SFT) remains unexplored. We present the first systematic investigation into cross-lingual reasoning general- ization of RI. and SFT. Using Qwen2.5-3B Base as our foundation model, we con- duct experiments on diverse multilingual reasoning benchmarks, including math reasoning, commonsense reasoning, and scientific reasoning. Our investigation yields two significant findings: (1) Tuning with RL not only achieves higher ac- curacy but also demonstrates substantially stronger cross-lingual generalization capabilities compared to SFT. (2) RL training non-English data yields better overall performance and generalization than training on English data, which is not observed with SFT. Furthermore, through comprehensive mechanistic analyses, we explore the underlying factors of RL's superiority and generalization across languages. Our results provide compelling evidence that RL enables the model with more robust reasoning strategies, offering crucial guidance for more equi- table and effective multilingual reasoning.
INTRODUCTION
Accuracy Improvement
SFT Training
RL Training
60
60
Training on English
Training on English
50
Training Chinese
50
Training Chinese
Training on Germon
Training on German
+411
4137
30
30
:28
-24
123.7
+33.5
+23,
20
4133172
91
13.
10
10
-10
En
Zh
Fr
Es
Ja
De
En
Zh
Fr
Es Ja
De
Languages
Languages
Figure I: SFT and RL performance improvement using English, Chinese and German training data on the same base model, Owen2.553B--asse Performance improvements are measured relative to the base model. We report the performance improvement in six language settings.
Multilingualism plays significant role in human society and occupies critical position in the development of large language models (LLMs). With over 7,000 languages worldwide, each encap- sulates unique cultural contexts and expressive modalities (Campbell & Grondona, 2008). LLMs
indicates equal contribution.
Correspondence (zhangyue@ (rhangyne@wesslakec.ch) www.lake..ccc.c.cc

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Published as a conference paper at ICLR 2026
not only break down language barriers and facilitate cross-cultural communication, but also enable equitable global Artificial Intelligence benefits (Howard & Ruder
2018
Sharma et al. 2025
With advances in LLMs reasoning (Hao et al.
2023
Yue al.
2025).
cross-lingual reasoning
has received increasing attention (Wang et al. 2023). Multilingual reasoning requires models not only comprehend the semantic content of dif- ferent languages, but also to possess the ability to perform logical inference and problem-solving across diverse linguistic environments (Alam et al., 2024). Current research demonstrates that while large-scale pre-trained language models have achieved remarkable progress in English comprehen- sion and generation, significant performance gaps persist for other languages (Qiu al., 2024).
2024a Chai ct al.
2025
Payoungkhamdee et al,
Consequently, enhancing multilingual reasoning capabilities and achieving effective cross- lingual generalization has emerged as a significant challenge (Pham et al. 2024 Hu al. 2025).
Reinforcement Learning (RL) is considered a pivotal tool for enhancing reasoning capabili- ties (Wang et al.) 2024b] Guo et al.) (005)). Recent studies show that RL training exhibits supe-
rior performance on complex tasks such mathematical and logical reasoning (Xie et al.) (025).
Compared to Supervised Fine-tuning (SFT), Reinforcement Learning, through reward-guided mech- anisms, enables models with more robust and generalizable reasoning strategies (Huan et al. 2025)
Notably, researches reveal that RL not only significantly improves model performance, but also en- ables stronger cross-task generalization capabilities (Shao et al. 2024). In this work, we conduct the first investigation into whether RI. exhibits strong generalization capabilities across languages in reasoning. Experimentally, we compare the performance of RL and SFT on diverse languages, exploring their performance across various languages to examine their cross-lingual generalization abilities. To fully reflect reasoning capability, we evaluate performance on diverse multilingual reasoning benchmarks, including math reasoning, commonsense reasoning, and scientific reason- ing (Shi et al., She et al. 2024 Son et al. 2025 Xuan et al. 2025 Qi et al. 2025).
The empirical investigation yields two notable findings: (1) As illustrated in Figure I RL demon- strates superior performance improvements compared to SFT, with enhanced Pross-lingual general- ization capabilities. Our results indicate that models trained with RL. can more effectively transfer reasoning abilities learned in one language to another. This finding of cross-lingual reasoning consistent with existing findings for cross-task transfer (Korkmaz, 2024 Huan et al. 2025 Cheng (et al. 2025 Chu et al.)) (2) Given that the pre-training corpora of most existing LLMs are pre- dominantly English-centric (Morishita et al.) 2024 Rytting & Wingate, 2021 Singh et al. 2024), the conventional expectation is that RL training with English data would maximally leverage the model's potential (Yoon et al., 2024 She et al., 2024). However, shown in Figure/ 1, our find- ings surprisingly reveal a counter-intuitive phenomenon: RI. training using non-English data (such as Chinese and German) yields better cross-lingual reasoning performance and superior generaliza- tion than using English data. This contrasts with SFT, where no such phenomenon is observed, as performance remains comparable and, in some datasets, even shows an opposite trend.
To investigate underlying reasons for the findings, we conduct preliminary analyses: (1) First, we analyze whether the language used in reasoning is consistent with the language of input question. Our investigation reveals that language inconsistency serves as a potential factor of RL's cross- lingual generalization, and the superiority of the non-English data in RL. (2) Second, we examine the role of sampling mechanisms in RL's superior performance. We find that the sampling mechanism in RL explores sufficient and diverse solution paths, allowing models to learn more robust and generalizable strategies. (3) Third, we explore the semantic shift of the model after training. We find that the stability of the semantic space contributes to RL's superior cross-lingual generalization. Our preliminary explorations provide insights for future research in multilingual reasoning.
The main contributions of this work are as follows:
(1) We present the first systematic analysis of the differences between RL and SFT in cross-lingual reasoning generalization, filling an important gap in this research area.
(2) We reveal two significant findings: 1) RL excels over SFT in cross-lingual generalization. and 2) Counterintuitively. non- non-English data is superior to English data for RL training. To our knowledge, are the first to demonstrate that using non-Enge -ngglisish data for RL more effectively enhances perfor- mance and cross-lingual generalization, although most models are pre-trained mainly on English.
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Published as a conference paper at ICLR 2026
(3) Through comprehensive analyses, we explore three potential factors underlying RL's superiority: linguistic inconsistency in reasoning, sampling-drise driven policy optimization, and the semantic shift after training, which provides a crucial foundation for multilingual reasoning.
2 RELATED WORK
Multilingual Reasoning, Multilingual reasoning is challenging and representative task for evalu-
ating the intelligence of large language models (Ahn et al. 2024 She et al. 2024; Yoon et al. 2024] Chen et al. 2024). Shi et al.) establish the foundation for this field by translating English mathemar- ical problems from GSM8K (Cobbe et al., 2021) into multiple languages, creating the multilingual benchmark MGSM (Shi et al.). To enhance multilingual reasoning capabilities, existing work pri- marily employs prompting strategies. Qin et al. (2023) and Huung et al. (2023) propose a translate- then-solve approach that first translates non- -nnglsilhhhh questions into English before problem-solving achieving promising results on closed-source models like ChatGPT (Ouyang et al.) 2022). However, less attention has been paid to how different training paradigms affect the model's 's intrinsic cross- lingual generalization capabilities. Our work addresses this gap by comparing SFT and RL at the model's 's foundational level, demonstrating RL's unique advantage in learning reasoning strategies without relying on specific languages.
Supervised Fine-tuning For Reasoning. Supervised fine-tuning (SFT) effectively enhances LLM reasoning abilities by distilling expert-level chain-of-thought (CoT) examples (Huang et al., 2024). Synthetic data generation is a key strategy: Large teacher models are used to generate solutions for mathematical problems (Yue et al., 2023 Tang et al., 2024), enhancing the reasoning process. Additionally, recent research examines the impact of data quality factors on the model performance (Toshiiwal et al.] [025] Yu et al., 2023 Ye et al. 2025). Beyond mathematics, other works (Kim) ct al. 2023 Xu et al.) 2024) expand reasoning tasks to larger domains, broadening the scope and soolinnn in various fields. Although SFT is successful in enhancing rea- soning, its learning approach is fundamentally based on imitating and memorizing given "expert" trajectories (Ge et al., (023), leading to overfitting to the language and pattern in the training data. Our research differs from these works by focusing the limitations of SFT in cross-lingual sce- narios. By contrasting it with RL, we demonstrate that merely imitating high-quality CoT data is insufficient for achieving the robust tross-lingual generalization that RL provides.
complexity
Reinforcement Learning For Reasoning. Reinforcement learning (RL) has become a widely adopted technique for post-training large language models (LLMs) to better align their outputs with human preferences (Ouyang et al. 2022] Achiam et al. 2023). Recent studies extend its application to enhancing reasoning abilities, encouraging longer, structured CoT traces and occasional break- through moments (Jaech et al. 2024 Guo et al. 2025). These approaches treat chain-of-thought (CoT) reasoning as an RL problem, utilizing various reward mechanisms such as final-answer cor- rectness (Xie et al., [025]] Wen el al. 2025), verifier-based scoring (Gehring et al. 2025), and step- level rewards (Zhang et al.) (0225). While online RL approaches (Schulman et al.) 2017: Shao al.] 2024) are commonly used, high computational costs motivate the development of offline RL meth- ods (Zhang et al., 2024, Yuan et al. 2025). Existing work primarily relies on English-centric data in RI. In this work, we not only validate the effectiveness of RI. in multilingual setting but also innovatively uncover the unique advantages of non-English training data within the RL framework.
3 RL IMPROVES THE GENERALIZATION ACROSS LANGUAGES
3.1 EXPERIMENTAL SETUP
Base Model and Datasets. We adopt Owen2.5-3B-Bas YYang et al. 2024) as the base model to clearly explore the impact of RL and SFT. To further examine the generality of the observed phe- nomena, we also include SmoLLM333B-Booh
(Bakouch et al., 2025) and Awen2..57B-BB.
as the
additional base models for verification. The training datasets are translations of GSMSK (Cobbe) et al. 2021) and LUFFY (Yan et al. 2025). We use Qwen3 300---33--33-- 30B-A3B (Yang et al. 2025) to translate the training data into other languages and utilize the DeepSeek-V3 V3 (Liu et al. 22024's 's verification to further guarantee the quality of the translation. The base model trained on MGSM8K (8K sam-
ples per language) is tested on MGSM and the base model trained on LUFFY (45K samples per
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Table 1: Performance of base, SFT, and RL models on MGSM. "Base" denotes Qwen2.5-3B-BB "SFT (zh)" and "RL (zh)" indicate tuning on Chinese data. We report accuracy on 10 linguistic settings; (RL-SFT) denotes the performance gap. Each value averaged over six runs. "Avg" and "Gen" refer to the mean accuracy and generalization score, respectively.
Models
Ein
Zh
De
Es
Ja
Ru
Th
Sw
Bn
Avg
Gen
Base
63.4
48.3
33,5
57.7
38.9
19.5
30.3
17.6
7.3
1.2
31.8
0.0
SPT (En)
64.7
54.5
50.7
56,4
56.2
36.9
55,5
44.1
6.9
26.2
45.2
18.1
RI. (I.(Fn)
85.8
72.1
70.8
77.3
76.6
61.2
64,9
61.0
9.5
47.5
62,7
49.1
(RL-SFT)
+21.1
+17.6
+20.1
+20.9
+20.4
+24.3
+16.9
+2.6
+21.3
+17.5
+30.9
SFT
65.7
58.7
48.4
55.7
56.1
43.5
56.6
45.8
7.5
30.5
46,9
20.4
RL (Zh)
86.1
76.3
74,2
81.1
76.1
64.5
78.1
64,9
10.3
48.3
66.0
52.6
(RI-SFT)
+20.4
+17.6
+25.8
+25.4
+20.0
+21.0
+21.5
+19.1
+2.8
+17.8
+19.1
+32.3
SFT (De)
63,9
54.2
57.5
55.7
52.8
39.3
47.6
8.4
28.8
46.3
19.3
RI. (D))))
91.0
77.6
80.5
82.7
80.0
67.8
81.3
75.3
15.9
63.3
71.5
60.4
A (RL-SFT)
+27.1
+23.4
+23.0
+27.0
+27.2
+28.5
+26.2
+27.7
+7,5
+34.5
+25.2
+41.2
language) is tested on other datasets. To fully assess the reasoning ability, we evaluate the model on multilingual reasoning benchmarks from four kinds of reasoning: MGSM (Shi et al.), MMath550,, and MAIME2024 (Son et al.
2025) for mathematical reasoning. MMLU-ProX-Lite (Xuan et al.) 2025) for commonsense reasoning, and MGPQA-D (Qi et al. 2025) for scientific reasoning, Mul- tilingual LogiQA [Wang et al.
2024a) which emphasizes logical reasoning. Furthermore, M-ifEval (Dussolle et al. 2025 to test the multilingual eestruction-folloiiin capabilities.
Learning Algorithms and Evaluation Metries. We compare the performance of various tuning al- gorithms, including SFT and RL. Specifically, we use GRPO to explore the performance of RL. The final answer is explicitly distinguished and encapsulated with in \boxed }. To evaluate model performance, we calculate the accuracy of each reasoning dataset. We test times for MMath500 and MGSM, and 16 times for MAIME2024. This paper evaluates the reasoning capabilities of LLMs across ten languages: Bengali (Bn). Thai (Th), Swahili (Sw), Japanese (Ja), Chinese (Zh), German (De), French (Fr), Russian (Ru). Spanish (Es), and English (En). To measure the rela- tive improvement over the base model's potential, we introduce generalization score (Gen). This score is calculated by averaging the normalized gains across all test languages, which represents the model's 's ability to capitalize on the potential for improvement in each language. For given tuned model Muned the generalization score defined as:
1 [L]
Acc(Muned) 1) Acc(AcChaaaaa f I)
Gem (Mruned) =
1- Acc Mhase, !)
LEL
where L is the set of evaluation languages, Ac)(M, () is the accuracy of model M on language and Musee is the base model before tuning.
Implementation Details. All experiments utilize aall-parameter tuning during both the SFT and RL phases to enable a thorough evaluation of model capabilities. The SFT experiments are carried out within the LlamaFactory (Zheng al. 2024) framework, employing learning rate of 2 10 cosine learning rate scheduler, and batch size of 32. For RL, the verl (Sheng et al. (024) platform is used for implementation. To guarantee fair comparison among different RL approaches, uniform set of parameters is adopted: the learning rate is set to x 10 6 the rollout batch size to 512. and the sampling temperature to 1.0, along with a Ki--divereence coefficient of 0.001. Both SFT and RL experiments are conducted for 3 full epochs and then stop. Furthermore, we employ zero-shot setting to assess models' performance across various test datasets. To verify the robustness of our findings, we also provide 4-shots results in Table [6] which show consistent trends.
3.2 FINDING RL EXIIBITS SUPERIOR CROSS-LINGUAL GENERALIZATION THAN SFT
Significant performance improvement. As shown in Table [ RL consistently outperforms SFT across ten languages. The improvements range from +9.4 points (evaluating Russian when trained in English) to +34.5 points (evaluating Bengali when trained in German), with an overall average improvement of +17.5 to +25.2 points depending on the training language. This establishes a strong baseline for RL's superiority. The complete results are provided in Appendix A.4.1
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Table Performance of base, SFT, and RL models on MMath500. We report the accuracy score on 6 linguistic settings.
Models
Zh
En
Ja
Avg
Gen
Base
38.9
27.2
49.1
16.3
17.4
36.6
30,9
0.0
SFT (Fi)
33.6
56.3
59.7
56.0
18.1
57.2
46.8
22.1
RL (En)
53.7
55.8
62.7
50.9
54.2
56.6
55.7
34.6
A (RL-SFT)
+20.1
-0.4
-5.1
+36.1
-0.6
+8.9
+12.5
SET (Zh)
41.9
38.4
48.4
35.0
37.2
38.1
39.8
11.3
RL (Zh)
61.3
61.2
63.3
61.2
58.5
62.1
61.3
42.5
A (RL-SFT)
+19.5
+22.8
+14.9
+26.2
+21.3
+24.0
+21.5
+31.2
SFT (De)
31.7
30.7
38.0
33.5
19.4
30.3
30.6
-2.6
RL (De)
61.4
61.5
62.8
60.7
62.1
42,6
(RL-SFT)
+29.7
+30.8
+24.8
+27.2
+40.7
+31.8
430.8
+45.3
Robustness in cross-lingual transfer. Notably, RL's advantage is most prominent cross-lingual transfer scenarios, suggesting it learns more robust reasoning strategies rather than optimizing for the training language. For instance, when trained on Chinese, RL not only excels on Chinese evaluation (+17.6 points SFT) but also generalizes significantly better to typologically distant languages like German (+25.8 points) and Spanish (+25.4 points). The consistency of these improvements +21.3 points) indicates that RL fosters the
across diverse language pairs (e.g.. development of multilingual reasoning capabilities.
Coherent validation. The validity of this conclusion is further strengthened by consistent results on the MMath500 dataset in Table 2 For example, when trained on Chinese data, the RL model achieves an average accuracy of 61.3%, substantially surpassing SFT's 39.8% +21.5 point im- provement). This cross-dataset corroboration confirms that the enhanced generalization ability of RL not an artifact of single benchmark.
Effective generalization across languages in other reasoning tasks. The superiority of RL ex- tends beyond multilingual mathematical reasoning challenging out-of-distribution tasks. As shown in Table 3 on benchmarks like MMI.U-roX-LLit and MGPQA-D, RI. consistently main- tains positive generalization scores, while SFT models often exhibit negative transfer. For instance, on MMMLU-PrX--LLE
an RL model trained on German data achieves generalization score (Gen) of 30.8, starkly contrasting with SFT's 8.0. This demonstrates that the robust reasoning represen- tations acquired via RL highly transferable across both linguistic and task boundaries. Notably, this advantage holds even under double-cross setting: when trained on mathematical data Ger- man (De) and evaluated point improvement over SFT.
commonsense reasoning task in Chinese (Zh), RL achieves +20.0
Comparison with Cold-Start.
To further validate the effectiveness of RL compared to the cold-start strategy, we conduct additional experiments using "SFT + RL." and "SFT (100 steps) + RI." settings. The detailed results are presented in Table 15 Surprisingly, we observe that directly applying RL generally yields performance superior to or comparable with the cold-start baselines. For instance, on MGSM, the average score for SFT+RL (De) 52.6%, whereas RL (De) achieves 71.5%. This suggests that SFT might cause the model to converge prematurely to specific language patterns or local optima, thereby limiting RL's capacity to explore better strategies for multilingual reasoning.
In summary, results from cross-lingual, cross-dataset, and cross-task evaluations robustly support that RL enables models with superior generalization in multilingual reasoning compared SFT.
3.3 FINDING2: RI USING NON-ENGL.ISH TRAINING DATA YIELDS SUPERIOR PERFORMANCE TO ENGLISH TRAINING DATA, WHILE SET DOES NOT
Superiority performance gains in non-English RL. Analyzing the average performance, RL train- ing on non- English data systematically surpasses the English baseline. Specifically, RL trained on German achieves the highest average performance at 71.5%, followed by French (70.7%) and Japanese (70.9%), shown in Table / in Appendix [A.4.]] all substantially exceeding English-based RL. training (62.7%), with the German advantage being significant +8.8 points.
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Table Performance comparison on MMLU-ProX-Lite and MGPQA-D. "Avg" denotes the average score across languages (En/Zh/De), and "Gen" represents the generalization score.
MIMLU-Pro--lae
MGPQA-D
Model
Zh
Avg
Gen
Zh
Avg
Gen
Base
21.1
20.6
SFT/En)
28.9
13.0
24.1
22.0
17.9
12.5
11.7
-13.7
RL(En)
40.6
31.6
25.6
32.6
29.1
30.0
23.5
25.2
26.2
7.0
A (RL-SFT)
+11.6
+18.6
+1.6
+10.6
+11.2
+17.4
+18.4
+13.5
+16.4
+20.7
SFT/Zb)
24.4
11.6
21.3
20.3
7.4
20.7
18.1
14.2
17.7
-3.7
RL(Zh)
40.8
35.0
34.4
36.7
33.4
25.0
27.3
28.3
26.9
7.8
(RL-SFT)
+16.3
+23.4
+13.1
+16.4
+19.8
+4.3
+9.2
+14.1
+9.2
+11.5
SFT(D))
15.8
7.3
15.0
12.7
8.0
7.2
12.8
8.8
9.6
-13.9
RL(De)
A (RL-SFT)
+24.1
+20.0
+20.5
+21.5
+22.8
+19.0
+14.4
+16.6
+16.7
+21.0
Further more, the superiority is also pronounced in cross-lingual scenarios. For example, RL trained on German only excels on German evaluation (80.5%) but also shows remarkable transfer to distant languages like Bengali (63.3% vs 47.5% for English, +15.8 pts) and Thai (75.3% vs 61.0% for English, +14.3 pts), indicating learning of transferable representations.
Similar phenomenon across diverse tasks. The pattern is consistently validated on diverse bench- marks. On MMLU-Pro-X Lite, from Table RL trained on Chinese achieves 36. 7%, outperforming RL trained on English (32.6%). On MGSM, RL trained on German attains generalization score of +41.2, significantly higher than RL trained on English (+30.9), confirming the robust and generaliz- able benefits of non-English RL training. Moreover, as shown in Table Table performance on M-ifEval and Multilingual LogiQA, which assess instruction following and logical reasoning, consistently demonstrates that non-English RI. yields superior cross-lingua generalization.
The Different Phenomenon observed in SFT. This phenomenon appears exclusively with RL. In contrast, SFT results exhibit minimal variation across training languages, with Avg scores ranging from 46.3% on German to 47.6% on Japanese (see Table 7 in Appendix [A.4.Ip. The performance differences remain within statistical noise, ruling out data quality as the sole explanation and high- lighting the critical role of the RL objective.
Comparison with Mixed- on mixed languages, we use a mixture of English, Chinese, and German training data (Mix), ensur- ing the total data volume remains consistent. Table [4] shows that while RL (Mix) achieves com- petitive results (Average 68.1
Training. To further investigate the performance of training
18.1%% 15), RL (De) still maintains the highest performance (Average 71.5%). This phenomenon indicates that some specific non-English languages can stimulate the model's generalization potential in RL training more effectively than even mixing multiple languages.
3.4 SAME PHENOMENON ON ANOTHER BASE MODEL
In Table we report the performance of SmolLM3-33 M--LLM3-3BBBBe under the same configuration of Qwen2.5-25 5-3B B-BB-----BB Base. We find that our observations are consistently.
Finding RL exhibits superior cross-lingual generalization than SFT. Across all training lan- guages, RL consistently and significantly outperforms SFT. The improvements are substantial, rang- ing from 1.7 points (evaluating Swedish when trained on German) to +34.7 points (evaluating Chinese when trained on German).
Finding 2: RL using non-English training data yields superior performance English training data, while SFT does not. Similar to the trend observed on Owen2.553B--ass. RL trained on non- English data surpasses RL trained on English. RL (De) reaches the highest average accuracy at 69.9 and the strongest generalization score at 64.9. In contrast, SFT models remain far behind.
To ensure the robustness of our findings across model scales, we further verify our conclusions on As shown in Table 13] 7B model exhibits trend highly consistent with the 3B model: (1) RL achieves significantly higher performance gains compared to SFT. (2) RL training on non-English data (e.g., German, Chinese) continues to demonstrate stronger cross-lingual general-
Qwen2.5-7B-Ba.

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Table 4: Performance of base model, SFT, and RL tuning models on MGSM. Base denotes the original MmolLM3-3B-Baal model. We report the accuracy score on 10 linguistic settings.
Models
En
Zh
De
Es
Fr
Ru
Th
Sw
Bn
Avg
Gen
Base
29.3
24.3
27.3
26.9
13.0
19.0
SET (En)
40.7
49.3
48.0
32.8
47.7
10.0
38.6
25.3
RL (En)
87.3
70.8
78.3
81.0
81.3
62.2
79.7
67.3
16.5
22.2
64.6
58.6
A (RL-SFT)
+27.1
+30.1
+28.9
+29.2
+33.3
+29.4
+32.0
+29.5
+9.1
+12.2
+26.1
+33.3
SFT (Zh)
58.9
51.5
50.5
54.9
54.9
39.3
48.7
43.7
9.2
11.7
42.3
30,0
RL (Zh)
88.6
77.1
79.3
82,5
80,9
71.1
82.4
76.2
20.1
28.5
68.7
63.4
A (RL-SFT)
+29.7
+25.6
+28.7
+27.6
+26.0
+31.8
+33.7
+32.5
+10.9
+16.9
+26.3
+33.4
SET (De)
60.1
43.5
53.9
56.1
52,1
38.3
51.8
43.3
9.0
9.7
41.8
29.4
RL (De)
85.1
78.2
81.7
85.6
84.1
69.1
85.8
77.2
20.7
31.3
69.9
64.9
(RL-SPT)
+24.9
+34.7
+27.7
+29.5
+31.9
+30.8
+34.0
+33.9
+11.7
+21.7
+28.1
+35.5
ization capabilities than RL on English data. This provides compelling evidence that the superiority of non-English RL specific to small models but holds at larger parameter scales.
MECHANICS ANALYSIS OF RL's
GENERALIZATION
To investigate why RL exhibits stronger generalization than SFT, and why RL training on non- English data outperforms that on English, we present an abbreviated set of responses generated by RL-trained models on the test set in Table[3] The complete responses are provided Appendix Our analysis reveals that when models are trained using German instructions during RL training, the resulting models do not strictly adhere to German when generating thinking and responses. Instead, they employ non- German mixed languages for reasoning processes. This observation attracts our attention and leads us to propose hypothesis: could this inconsistent language usage in reasoning contribute the enhanced generalization observed in RL training?
4.1 EXPLORATION OF LANGUAGE CONSISTENCY IN RL
To empirically validate this hypothesis, we conduct comparative experiments using two distinct approaches: (1) employing prompts that strictly constrain language usage, and (2) incorporating the language consistency reward that encourages the model to adhere to the language of the question into the RL training process. The details are as follows:
Toverall 0.5racc + 0.5l consistency 0.5
The language consistency reward rconsistency is designed to explicitly encourage the model's output language to match the input instruction's language. We implement this using langid (Lui & Baldwin) as a language identifier to detect the primary language of the generated response. A positive reward given for match, and penalty applied otherwise.
We investigate the impact of language consistency by forcing the model to use specific language during inference and observing performance changes. The results are presented in Figure and Table 6 with a specific case study provided in Table
We observe two key aspects: (a) Language inconsistency serves a potential source of cross-lingual generalization capability, and (b) Building upon this mechanism, RL (De) exhibits greater language inconsistency than RL (En), resulting superior cross-lingual performance. These observations suggest that the degree of flexibility in deviating from training language constraints may determine the extent of cross-lingual generalization achieved by RI-trained models.
Language inconsistency enhances cross-lingual generalization. Enforcing language consistency significantly degrades performance. As demonstrated in Figure both RL (Zh) and RL (De) models achieve strong baseline performance (61.3% and 61.4%, respectively). However, when constrained to use their training languages through prompting, performance drops substantially- RRL (Zh) falls to 53.7% and RL (De) to 60.5%. The degradation becomes more pronounced when language consistency rewards are applied, with RL (De) plummeting to 52.0%. This pattern strongly indicates that enforced language consistency impairs cross-lingual reasoning capabilities.

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Table Case study of on MMath500. We present case of German question.
Ein Matheclub veranstaltet einen Kuchenverkauf Spendenaktion, um Geld für eine bevorstehende Reise sammeln. Sie verkaufen Kekse zu drei für S1S, und $205 Cupcakes S25 pro Stück, und S355 Brownies zu S1$ pro Stück. Wenn es den Mutheclub S155 gekostet hat, diese Artikel zu backen, wie hoch war ihr Gewinn?
Question:
Answer: 78
Base:
Da Kekse zu drei für $1 verkaufen werden, müssen wir zahlenweise Kekse zählen. Es gibt Kekse zu backen, und joder Kuchen besteht aus drei Keksen. Also haben 54/3 Kuchen backen. Da fiir die Backzeit 15 Dollar ausgehen, hahen sie für den Verkauf
146 $131 eingenommen. Daber haben einen Gewinn
Reinforcement Learning (with German Data):
1. Calculate the revenue from Kekse: They sold 54 Kekse at rate of 3 Kekse for $1, The number sets Kekse in 54 is 54 18. Revenue from Kekse 18 x 1 18 dollars.
5. Calculate the profit: Cost to make the items $15. Profit Total revenue Cost to make the items Profit= = 93 15 dollars.
Therefore, the profit 78
Reinforcement Learning (with German Data and with Consistency Reward);
Zuerst berechmen wir den Einnahmen von den Keksen. Da sie drei Kekse für 81 verkaufen, Da es ihnen $15 gekostet hat, um die Artikel zu backen, erhalten sie: 91 15 76 Dollar Die Gewinnsumme beträgt 76
erhalten sie: 54 + 3 18 Doppelsätze,
MMATH150
Busc
30.9
Table 6: Language consistency of models on MMath500. We test 6 times and report the erage percentage of language consistency.
(L.(tn)) [tms]
$5.7
(21)
It (20 Conminees
$3.7
Models
En (%)
Zh (%)
De (%)
XL (20 lnceiistosss
Pooapt and Rowad
Pooppe and Rowasl
S3M
59.5
SFT (Ea)
Base
98.6
99.4
91.4
99.3
94.5
83.7
(D
RL (En)
99.9
89.0
96.2
IL (D) i Conmannee
(2h)
99.7
Proege
RL (Zh)
99.8
0.0
0.0
mtano Concerecy
Consistency Promps
99.3
99.6
97.3
fnveniiiiones and Reward
400
Inconsistenicy Prompt and Reward
Consistency Prompe and
99.7
99.9
99.8
0.0
98.9
8.1
30
50
(De)
85.5
99.1
Rl.(De)
99.7
4.8
0.0
Figure 2: Scores on MMath500. The chart com-
Consistency Promps
99.8
52.4
0.0
Consistency Prompt and Reward
99.8
99.8
99.9
pares the average accuracy of different models. "RL (Zh)" indicates training Chinese data.
Inconsistaacy Prompt and Reward
99.6
0.0
0.0
Table 6 reveals that unconstrained RL. models show low consistency in their training lan- guages-bott RL (Zh) and RL (De) achieve 0.0% consistency, indicating they spontaneously adopt other languages during reasoning. Conversely, constrained models exhibit high consistency rates (up to 99.9% for RL (De) with consistency rewards), but the cost of reduced performance. This neg- ative correlation between language consistency and performance suggests that linguistic flexibility enables models to leverage more powerful, multilingual reasoning modules.
Case analysis of the language inconsistency. As shown in Table When solving German question, the unconstrained model (RL (De)) employs mixed English and German reasoning and reaches cor- rect solutions, while the monsistency-constaili flawed logical steps and wrong answers. This demonstrates that constraining models to specific lan- guages may inhibit access to more robust reasoning patterns established during pre-training.
model, despite only reasoning in German, produces
Language inconsistency in non-English RL. The performance comparison in Figure 2 shows that RL (De) achieves 61.4% average accuracy compared to RL (En)'s 55.7%. More importantly, RL (De) maintains strong performance across different target languages, while RL (En) shows more pronounced degradation in non non-English tasks. This suggests that German-based training may pro- vide advantages for cross-lingual generalization.
Different source languages yield distinct generalization patterns. The superior performance of RL (De) may stem from German's 's grammatical complexity and its linguistic distance from other lan- guages, potentially encouraging the development of more multilingual reasoning strategies. In
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Amrary
08
07
06
05
04
03
Eifish
Bengat
Chiiose
Gemaon
Sporidh
Frand
Japarese
Rumdon
Thei
Languggs
Figure 3: Model performance comparisons among the Base, SFT, RFT, and RL models MGSM. We use German data in LUFFY SFT, RI., RFT for training.
trast, English-based training might lead more language-specific reasoning patterns that transfer less effectively across languages.
Language consistency in SFT. Unlike RL models, SFT models exhibit high language consistency SF. (Zh) maintains 99.7% consistency) due to their imitation based training paradigm. While this consistency appears desirable, actually constrains generalization by trapping models within language-specific thought patterns established during training, leading to impaired cross-lingual per- formance when facing problems in other languages.
SFT
Furthermore, results in Figure 2 show that while encouraging inconsistency (RL + Inconsistency Prompt and Reward) yields better performance than enforcing consistency (RL + Consistency Prompt and Reward), allowing the RL model to autonomously select the language (RL) still achieves the best results. This suggests that while language inconsistency is a key factor in the superiority of RL, freely exploring reasoning paths without forced constraints is also crucial.
4.2 EXPLORATION OF SAMPLING IN RL
To further investigate the source of RL's advantage over SFT, we analyze the role of sampling in performance enhancement, We introduce Rejection Sampling Fine- Fine-Tuning (RFT) (Touvron et al.) 2023) as an intermediate baseline between SFT and full RL. The RFT we use involves sampling multiple times from the model after RL training. It then fine-tunes the model using only the samples that yield the correct answer. This represents a more on-policy exploration mechanism than SFT.
As shown in Figure 3 across all languages, accuracy increases progressively from the Base model to SFT, RFT, and finally to the RL-tuned model. Specifically, SFT achieves 46.3% average accuracy, RFT improves to 66.8% and RL reaches 71.5%. This trend underscores the importance of the model's 's exploration of solution paths in enhancing its reasoning abilities.
Better Performance with Data Aligned to the Model's Distribution. Although SFT follows completely correct off-policy solution path, RFT data, more aligned with the model's distribution, enables the model explore reasoning chains better suited its own configuration through sam- pling. This alignment helps the model capture reasoning patterns and optimization trajectories more effectively, allowing to generalize beyond memorized solutions.
The Importance of Online Optimization in RL. Compared to RFT, RL (GRPO in our experiments) continuously performs more on-policy sampling with both positive and negative examples during training. This not only further aligns the data with the model but also goes beyond mere imitation learning. As shown in F RI. consistently outperforms the other methods across all languages, demonstrating that the online policy optimization process in RL is more effective at enhancing the model's s generalizable reasoning than RFT.
Exploration. To further investigate why RL training Genman data yields superior transferability, we analyze the sampling diversity. We employ the base model generate six responses for each question across different languages via sampling. We then calculate the Perplexity (PPL) and Self-Similarity (measured by BLEU scores among sampled re- sponses for each question) of the base model's outputs across different languages. As shown in
Uncertainty Promotes

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Festure
PC2
0 PCT Differnce
10
IC1 Decterenee
PC1 Defereacce
Figure 4: Feature of LLM's hidden state of last layer, in training (dataset LUFFY) configuration of (a)RL-De, Prompp, and DeeRR---++Poopt-Reee prompts, and "+Reward"" adds a language consistency reward.
"+Prompt" adds language control
German questions exhibit higher PPL (1.414) and and the lowest Self-Similarity (0.425). This indicates that the model faces higher uncertainty when processing German questions. In the ex- ploration phase of RL, this uncertainty potentially prompts the model step out of single-language constraints and explore reasoning paths in mixed languages or its dominant language (English). This process inadvertently activates stronger cross-lingual generalization capabilities. In contrast, the low perplexity in English questions limits this diversity during sampling. Furthermore, SFT tends to closely fit the language distribution, also limiting such exploration.
Table 11
4.3 EXPLORATION OF MODEL SEMANTIC FEATURE SHIFT
To investigate why RL training with different languages yields varying generalization capabilities, analyze the semantic feature shifts in learned representations.
Methodology. We extract final layer hidden states from base and RL-trained models when process- ing MMath500 test data across six languages. These representations projected to 2D space using PCA, and we compute difference vectors: haiff = h h Base-
Results. Figure 4 reveals distinct shift patterns across training configurations. RL-De exhibits the most concentrated distribution around the origin, indicating minimal deviation from base represen- tations, while RL-En displays more scattered distributions. This ordering directly correlates with cross-lingual performance in Table 2 Similarly. language consistency interventions in RL-De pro- gressively increase representational scatter: baseline RL-De maintains compact distributions, while RL-De+Proomtt-Rewal shows greater dispersion, mirroring the performance degradation pattern.
Interpretation. These findings suggest that pre-training establishes multilingual reasoning struc- tures crucial for cross-lingual transfer (Hua et al. 2024, Merchant et al. (2020). Models preserving these structures through minimal representational drift maintain stronger generalization capabili-
ties. Conversely, larger shifts disrupt universal reasoning mechanisms (Luo et al. (2025), explaining why RL's linguistic inconsistency paradoxically enhances cross-lingual performance by preserving pre-trained reasoning structures (Lai et al. 2025
CONCLUSION
We systematically investigated the differences between Reinforcement Learning and Supervised Fine-Tuning for enhancing cross-lingual reasoning and the generalization across languages. Multi- ple experiments demonstrate that RL not only achieves substantially higher accuracy than SFT but also exhibits superior lioss-lingual generalization. Contrary to conventional cognition, we find that RL training on non-English data yields superior performance, challenging English-centric training. Our preliminary mechanistic analysis investigates the potential reasons for the superior tross-lingual generalization of RL from three perspectives: the linguistic inconsistency during the reasoning pro- cess, the unique explore-and and-oppiiizzee sampling strategy, and the semantic shift after training. The understanding of these potential factors not only provides crucial insights into understanding RL's advantages in multilingual reasoning but also establishes a foundation for effectively enhancing cross-lingual reasoning in the future.
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ACKNOWLEDGMENTS
This work has been financially supported by the National Key R&D program of China No. 2022FFE020490 and the National Natural Science Foundation of China (NSFC) Key Project under Grant Number 62336006.
ETHICS STATEMENT
This study acknowledges several ethical implications of investigation into cross-lingual reason- ing in LLMs. Data and faimess concerns arise from potential biases in multilingual benchmarks, which may introduce performance disparities across languages. Our evaluations incorporate diverse linguistic settings and different multilingual reasoning tasks mitigate such biases, though future work must further scrutinize cultural and linguistic influences on model behavior.
Beyond technical limitations, societal impact requires careful consideration. While improved mul- tilingual reasoning could enhance accessibility for non-English speakers, reducing barriers edu- cation and professional settings, it also risks misuse-such automated disinformation generation or harmful content propagation across languages. We advocate for responsible deployment, empha- sizing robust safeguards, human oversight, and ongoing risk assessments to balance innovation with ethical constraints.
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A APPENDIX
A.1
USE OF LLM
During the preparation of this work, large language models (e.g., ChatGPT) were used for English writing refinement and minor assistance in code debugging. All ideas, experiments, and analyses are solely by the authors.
A.2 EXPERIMENTAL SETTINGS
A.2.1 RFT SETTINGS
In the RFT experiments, we sample from the RL-trained model on the training set with temperature of 1.0 and top-p of 0.95. For each prompt, we sample 10 times and filter for responses with correct answers for fine-tuning. We strictly controll the RFT training data volume be consistent with SFT.
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A.2.2 PROMPTS FOR GENERATING TRANSLATED GSM8K TRAINING DATASETS
Here the prompts for generating translated GSM8K training datasets.
TRANSLATION PROMPT TEMPLATE = """You are professional math translation assistant. Please translate the following English math problem into [target language), maintaining the mathematical expressions and formatting.
Requircments:
1. Maintain the format of the mathematical calculation process
(e.g.r <<48/2-24>>>
2. Maintain the format of the final answer (e.g., #### 72)
3. The translation should pe accurate and natural.
4. Keep the numbers and mathematical symbols unchanged.
Original question:
Original answer:
Please translate the question and separately, using the following format:
{f
"translated_question"" "Translated question",
"translated_ "Translated answer"
)
Please return the result in JSON format, using the (target Laargat__anguagel language, and do not add any additicnal text. u*.
A.2.3 PROMPTS FOR GENERATING TRANSLATED LUFFY TRAINING DATASETS
Here is the prompts for generating translated LUFFY training datasets.
TRANSLATION_PRORET TEMPLATE """You are professional math translation assistant. Please translate the following content into (target__anguage) preserving mathematical expressions, LaTex formulas, and special formatting.
Requirements:
1. Keep all mathenatical formulas and LaTeX expressions intact (e.g., $24 Amathrrm ( ("km) 18, (boxed[11). etc.)
2. Keep the <think> and </think> tags intact
3. The translation should accurate and natural.
4. Keep numbers and mathematical symbols intact.
Original content:
(content)
Please return the translated Baarget_Langugee content directly in the format
{{
"translated_conten
"Translated content"
)
Do not add any additional explanatory text.
A.3 TRANSLATION DETAILS
To ensure high translation quality, we implement automated verification mechanism during the translation process. Instances that fail this verification re-generated until they met the quality standards.
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To further verify translation quality, we sample translation examples from each language and use DeepSeek- V3.2 (Liu 2024), Deepsoek-RI (Guo (025), and GPT-4o (Achiam et (023) as judges conduct a mead-to-heace quality comparison between our translations and the validated (GGSM8K-Instrur datasct (Chen ct al. (202)). We utilize the first 20 strictly aligned examples from MGSM8K Instrrcct (20 per language) to conduct a direct comparison with our corresponding translated data. The results are shown in Table T2 Our translation data has win rate comparable to MGSM8K-Instrue (Average Wins: Ours 47.2% vs MGSM8K 45.0%) demonstrating the high quality of our training data, which is comparable the high-quality MGSM8K- Instruct dataset.
A.4 RESULTS DETAILS
A.4.1 LANGUAGE USAGE STATISTICS
To further understand the model's hehavior, we also analyze the language usage statistics detailed in Table T9 We conduct detailed language analysis on MMath500 hy randomly sampling 100 questions for each language (En, Zh, De, Fs, Fr, Ja). For each question, we sample 6 responses and calculate the rank score of language usage to analyze the distribution. We report scores rank scores across different models. Specifically, for each response, we use DeepSeek-v3.2 (Liu et al.) 2024
the primary languages (En, De. Es. Fr, Ja)
to annotate the primary languages used, identifying up to 3 languages per response. The scoring rules are as follows: (1) Rank 1 language receives a score of 1. (2) Rank 2 language receives a score of 1/2. (3) Rank 3 language receives score of 1/3. (4) If only one primary language identified, receives score of 1. Results show that the Base Model's language usage is relatively balanced. After SFT and RL training, the usage of English significantly increases. RL-trained models (especially RL-Zh and RL-De) show a significant increase in the usage of English (or English-mixed language) when answering non-English questions. The RL training process enables the model adaptively learn and select suitable languages for complex reasoning, rather than passively adhering to input language. With the Inconsistency Analysis, this diversity and adaptive selection capability confer better performance to RL, facilitating more effective Cross-Lingun Transfer.
Table 7: Performance of base model, SFT, and RL tuning models on MGSM. Base denotes the original Qwen2.5-3B Base model. SFT (zh) and RL (zh) mean we tune the base model in Chinese data through SFT and RL, respectively. We report the accuracy score on 10 linguistic settings. A (RL-SFT) represents the performance difference between RL and the corresponding SFT score. Each score represents the average accuracy over six measurements. Avg represents the average of the scores of 10 language settings and Gen represents the generalization score.
Models
En
Zh
De
Ja
Ru
Th
Bn
Avg
Gen
Base
63.4
48.3
33.5
$7.7
38.9
19.5
30.3
17.6
7.3
1.2
31.8
0.0
SFT (En)
64.7
54.5
50.7
56.4
56.2
36.9
55.5
44.1
6,9
26.2
45.2
18.1
RL (En)
85,8
72.1
70.8
77.3
76.6
61.2
64.9
61.0
9,5
47.5
62,7
49.1
(RI-SFT)
+21.1
+17.6
+20.1
+20.9
+20.4
+24.3
+9.4
+16.9
+2.6
+21.3
+17.5
+30.9
SFT (Zh)
65.7
58.7
48.4
55.7
56.1
43.5
56.6
45.8
7.5
30.5
46.9
20.4
RI. (/h)
86.1
76.3
74.2
81.1
76.1
64.5
78.1
64.9
10.3
48.3
66.0
52.6
A (RL-SFT)
+20.4
+17.6
+25.8
+25.4
+20.0
+21.0
+21.5
+19.1
+2.8
+17.8
+19.1
+32.3
SET (De)
63.9
54.2
57.5
55.7
52.8
39.3
55.1
47.6
8.4
28.8
46.3
19.3
RL (De)
77.6
80.5
82.7
75.3
63.3
71.5
60.4
A (RL-SFT)
+27.1
+23.4
+23.0
+27.0
+27.2
+28.5
+26.2
+27.7
+7.5
+34.5
+25.2
+41.2
SFT (Es)
63,9
54.7
54.3
62.7
54,0
41.1
58.1
46.5
9,5
31.1
47.6
21.6
(I.(F)
89.3
77.8
78.0
82.1
77.3
68.9
80.3
72.7
13.4
53.7
69.4
$7.5
(RL-SFT)
+25.4
+23.1
+23.7
+19.4
+23.3
+27.8
+22.2
+26.2
+22.6
+21.8
+35.9
SFT (Pr)
64.8
53.7
51.3
58.8
57.9
40.9
57.1
46.5
8.9
29.9
47.0
20.6
RL (F))
89.3
78.9
77.5
82,3
81.1
70.9
81.1
73.1
13.3
59.1
70.7
59.3
(RL-SFT)
+24.5
+25.2
+26.2
+23.5
+23.2
+30.0
+24.0
+26.6
+4.4
+29.2
+23.7
+38.7
SFT (Ja)
64.4
56.5
50.5
58.2
53.6
51.3
45.6
8.1
33.7
47.6
21.1
RI. (Ja)
88.1
79.1
78.8
81.5
79.3
72.7
81.7
72.4
14.1
61.7
70.9
59.2
A (RL-SFT)
+23.7
+22.6
+28.3
+23.3
+25.7
+21.4
+27.4
+26.8
+6.0
+28.0
+23.3
+38.1
SET (Ru)
64.8
54.9
53.5
56.7
55.1
39.5
57.3
44.9
10.4
29.8
46.7
20.0
RL
87.5
76.6
78.5
79.9
78.8
80.3
73.5
12.5
$7.8
69.5
$7.1
A (RL-SFT)
+22.7
+21.7
+25.0
+23.2
+23.7
+30.1
+23.0
+28.6
+2.1
+28.0
+22.8
+37.1
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Table Performance of base model, SFT, and RL tuning models on MAIME2024. Base denotes the original Qwen2.5-3B-Ban data through SFT and RL, respectively. We report the Pass @ 16 score on 10 linguistic settings. A (RL-SFT) represents the performance difference between RL and the corresponding SFT score.
model. SFT (zh) and RL (zh) mean we the base model in Chinese
Models
Zh
Fr
En
Ja
Es
Th
Bn
Sw
Average
Base
6.7
6.7
16.7
10.0
10.0
13.3
3.3
10.0
3.3
0.0
8.0
SFT (Zh)
20.0
6.7
13.3
6.7
10.0
13.3
10.0
20.0
6.7
3.3
11.0
RL (Zh)
26.7
30.0
23.3
26.7
26.7
23.3
23.3
26.7
20.0
10.0
23.7
A (RI--FT)
+6.7
+23.3
+10.0
+20.0
+16.7
+10.0
+13.3
+6.7
+13.3
+6.7
+12.7
SFT (De)
13.3
13.3
16.7
13.3
0.0
6.7
10.0
3.3
6.7
6.7
9.0
(De)
26.7
20.0
23.3
13.3
30.0
26.7
20.0
13.3
21.0
A (RI--SFT)
+13.4
+10.0
+13.3
+23.3
+16.7
+16.7
+10.0
+12.0
Amuayy
08
Base
SFT
RFT
RL
Q7
Q6
05
04
02
01
000
Spuetihh
Jagunee Langaggs
(a) A comparison of performance MMath500.
Acuwacy
03.
0.1
Feefss
Versyai
Chieee
Gemmes
Spandoh
Prneah
Japueane
The
Sheebill
Langages
(b) A comparison of performance on MAIME2024.
Figure 5: Model performance comparisons among the Base, SFT, RFT, and RL models. We German data in LUFFY in SFT, RL, RFT for training.
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Table 9: Performance of models on MMath500. "RL (zh)" denotes the model trained with Rein- forcement Learning on Chinese data. "+ Consistency Prompt" indicates the addition of language control prompts during both the training and the inference. "+ Consistency Prompt and Reward" further incorporates language consistency reward into the training objective. "+ Inconsistency Prompt and Reward" incorporates the inconsistency prompt and inconsistency reward into the train- ing objective. We report the accuracy score on 6 linguistic settings, We test 6 times and report the average accuracy scores and pass@ k scores.
Models
Zh
Fr
En
De
Ja
Es
Average
Average Scores
Base
38.9
49.1
16.3
17.4
36.6
RI. (Fn)
53.7
55.8
62.7
50.9
54.2
56.6
55.7
RL (Zh)
61.3
61.2
63.3
61.2
58.5
62.1
61.3
Consistency Prompt
53.3
54.9
59.7
42.2
55.1
56.8
53.7
Consistency Prompt Reward
56.2
62.9
45.5
48.2
56.4
53.9
+nconsistency Prompt Reward
59.9
56.
61.6
57.6
57.7
58.2
58.5
RL (De)
61.4
61.5
62.8
60.7
60.1
62.1
61.4
Consistency Prompt
56.0
63.8
60.8
59.0
61.9
60.5
Consistency Prompt Reward
52.1
62.4
49.3
41.6
54.6
$2.0
+Inconsistency Prompt Reward
60.1
62.4
60.1
57.5
60.9
Pass@6 6 Scores
Base
67.9
60.9
75.8
48.1
44.9
69.3
61.2
RL (En)
74.7
77.2
78.8
73.9
75.4
77.6
76.3
RL (Zh)
78.4
76.2
81.4
78.0
75.2
77.8
77.8
Consistency Prompt
73.9
76.8
77.0
72.7
74.5
77.2
75.4
Consistency Prompt and Reward
74.1
73.7
81.4
72.7
70.9
76.2
74.8
Inconsistency Prompt and Reward
77.8
76.6
78.8
76.8
77.2
76.2
77.2
RL (De)
78.4
78.8
79.0
76.4
77.8
78.8
78.2
Consistency Prompt
77.8
79.4
80.4
77.8
77.8
79.2
78.7
Consistency Prompt and Reward
74.1
73.9
79.0
72.9
65.3
76.2
73.6
Inconsistency Prompt and Reward
78.6
77.6
80.4
78.4
76.8
77.8
78.3
To complement Figure Table 10 reports the quantitative measurements of representational movement under different RL configurations. Specifically, "Model Center Distance" denotes the distance between each model's representation center and the base model center, while "Model Shift Distance" denotes the distance between the model's shift center and the zero point. These measurements provide quantitative evidence supporting the representational patterns illustrated in the ligure.
Table 10: Numerical results corresponding to Figure reporting the model center distance and shift
distance under different RL configurations.
Config
Model Center Distance
Model Shift Distance
RL-En
2.255
41.332
RL-Zh
1.815
41.294
RL-De
1.753
41.241
RL-De+Prompt
1.891
41.286
RL-De+-rompt-RRwward
1.908
41.652
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Table 11: Sampling of the Base Model different language questions. We calculate the average Perplexity of responses, and Self-Similarity among responses for each question of six sampling times.
En
Zh
De
Fr
Ja
Es
Perplexity
1.186
1.248
1.414
1.332
1.440
1.267
Self-Similarity
0.621
0,505
0.425
0.448
0.433
0.534
Table 12: The translation quality comparison between and MGSM8K-Instrrct.
Languages
Ours Wins Ratio (%)
(NGSM8K-Instruc Wins Ratio (%)
Ties Ratio (%)
Fleiss' Kappa
Zh
63.3
33.3
3.3
0.726
De
46.7
48.3
5.0
0.817
40.0
50.0
10.0
0.885
48.3
46.7
0.756
36.7
16.7
0.731
48.3
45.0
6.7
0.762
Average
47.2
45.0
7.8
0.779
Table 13: Performance of base model, SFT, and RL tuning models on MGSM. Base denotes the
original Qwen2.5-7BB Bren2.5--B-Bass model.
Models
En
Zh
Es
Fr
Ja
Ru
Sw
Avg
Gen
Base
75.9
50.9
56.6
68.2
62.9
50.2
64.5
48.1
39.7
52.2
SET (En)
71.8
63.5
51.1
68.3
58.4
13.1
45.2
RL (En)
90.9
82.2
84.1
84.9
82.1
73.8
85.1
79.3
19.2
68.3
75.0
52.2
A (RL-SFF)
+19.1
+18.7
+21.6
+18.6
+18.8
+22.7
+16.8
+20.9
+6.1
+23.1
+18.6
+45.4
SFT (Zb)
70.7
64.7
62.1
63.5
59.8
52.5
61.7
54.7
13.0
41.8
54.4
1.8
(Zh)
92.7
83.9
75.1
83.9
78.1
A (RL-SFT)
+22.0
+19.2
+19.9
+21.6
+23.9
+22.6
+22.2
+23.4
+6.3
+26.3
+20.8
+51.2
SFT (De)
67.5
59.9
62.7
64.0
57.7
48.9
61.5
54.6
13.9
41.5
53.2
-1.6
RL (De)
92.3
83.7
84.2
86.3
83.5
76.3
88.5
82.8
20.9
71.1
77.0
56.7
(RI-SSF
+24.8
+23.8
+27.0
+28.2
+7.0
Table 14: Performance of base model, SFT, and RL tuning models MGSM. Base denotes the original Qwen2.5-3B-B model. Mix means using the mixture of English, Chinese and German data tune the base model.
Models
En
Zh
De
Es
Fr
Ja
Ru
Th
Sw
Bn
Avg
Gen
Base
63.4
48.3
33.5
57.7
38.9
19.5
30.3
17.6
7.3
31.8
0.0
SFT (En)
64.7
54.5
50.7
56.4
56.2
36.9
55.5
44.1
6,9
26.2
45.2
18.1
RL (En)
85.8
72.1
70.8
77.3
76.6
61.2
64.9
61.0
9.5
47.5
62.7
49.1
SFT (7h)
65.7
58.7
48.4
55.7
56.
43.5
56.6
45.8
7.5
30.5
46.9
RL (Zh)
86.1
76.3
74.2
81.1
76.1
64.5
78.1
64.9
10.3
48.3
66.0
52.6
SFT (De)
63.9
54.2
57.5
55.7
52.8
39.3
55.1
47.6
8.4
28.8
46.3
19.3
RL (De)
91.0
77.6
80.5
82.7
80.0
67.8
81.3
75.3
15.9
63.3
71.5
60.4
SFT (Mix)
65.3
55.9
52.9
56.3
53.0
42.9
53.2
47.1
7.6
29.8
46.4
19.6
RL (Mix)
87.9
75.4
77.1
79.0
79.3
64.1
78.2
69.7
12.6
57.7
68.1
55.2
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Table 15: The performance the base model, SFT, RL, and cold-start tuning models on MGSM. "Base" denotes the original Qwen2.5-3B-Base model. "SFT RL" refers first fine-tuning the base model with SFT, followed by reinforcement learning (RL) tuning using the same dataset. "SFT (100 steps) RL" indicates that the base model is first fine-tuned with SFT for 100 steps, and then further tuned with RL.
Models
En
Zh
De
Es
Fr
Ja
Ru
Th
Sw
Bn
Avg
Gen
Basc
63
48.3
33.5
57.7
38.9
19.5
30.3
17.6
7.3
1.2
31.8
0.0
SFT (En)
64.7
54.5
50.7
56.4
56.2
36,9
55.5
44.1
6.9
26.2
45.2
18.1
RL (Ea)
85.8
72.1
70.8
77.3
76.6
61.2
64.9
61.0
9.5
47.5
62.7
49.1
SFT + (En)
63.1
55.8
56.3
55.3
57.5
42.7
53.0
45.8
7.0
30.3
46.7
19.7
SPT (100 steps) (En)
59.3
50.5
44.9
50.1
47.3
28.1
48.9
37.2
6.8
20.7
39.4
8.7
SFT (100 steps) RL (En)
49.3
58.9
37.9
23.9
20.5
51.1
23.3
21.7
6.8
33.1
32.7
-5.5
SFT (Zh)
65.7
58.7
48.4
55.7
56.1
43.5
56.6
45.8
7.5
30.5
46.9
20.4
RL (Zh)
86.1
76.3
74.2
81.1
76.1
64.5
78.1
64.9
10.3
48.3
66.0
52.6
SFT + RL (2h)
76.3
67.8
61.7
65.9
64.0
55.4
63.1
53.1
8.3
34.5
55.0
34.5
SFT (100 steps) (Zh)
60.5
48.9
43.3
49.3
47.2
32.8
48.8
37.0
5.8
18.2
39.2
8.4
SPT (100 steps) RL (Zh)
84.1
70.5
70.7
74.3
70.6
62.2
72.1
61.5
10.2
45.8
62.2
46.1
(De)
57.5
39.3
28.8
46.3
RL (De)
91.0
77.6
80.5
82.7
80.0
67.8
81.3
75.3
15.9
63.3
71.5
60.4
SFT + RL (De)
53.5
66.0
62.7
60.6
51.0
61.9
53.5
9.9
38.9
52.6
28.8
SFT (100 steps) (De)
61.1
50.4
49.6
52.6
49.7
34.7
49.0
41.1
6.9
22.7
41.8
12.3
SFT (100 steps) RL (De)
82.1
73.5
74.3
74.7
73.8
58.8
74.2
62.3
12.5
47.3
63.4
47.7
Table 16: Performance of base model, SFT, and RL tuning models on MGSM in the 4-shots setting. Base denotes the original Qwen2.5-3B B-Bac model.
Models
En
Zh
De
Es
Fr
Ja
Ru
Avg
Gen
Base
69.3
58.7
26.5
54.8
38.4
34.3
41.5
46.2
0.0
SFT (En)
64.9
52.6
51.2
53.5
53.6
37.6
53.9
52.5
7.5
RL (En)
85.5
69.9
73.9
76.4
75.9
59.9
72.0
73.4
49.2
(RL-SFT)
+20.6
+17.3
+22.7
+22.9
+22.3
+22.3
+18.1
+20.9
+41.7
SFT (Zh)
58.0
58.6
47.3
54.6
51.0
41.2
51.7
51.8
5.6
RL (Zh)
86.8
75.0
70.6
79.8
75.5
62.1
79.3
75.6
54.1
A (RL-SFT)
+28.8
+16.4
+23.3
+25.2
+24.5
+20.9
+27.6
+23.8
+48.5
SET (De)
64.2
56.9
54.4
$4.0
48.3
38.7
52.1
52.7
8.0
RL (De)
90.5
76.8
80.1
82.9
80.5
68.9
80.7
80.1
62,3
A (RL-SFT)
+26.3
+19.9
+25.7
+28.9
+32.2
+30.2
+28.5
+27.4
+54.3
Table 17: Performance base model, SFT, and RL tuning models on M-ifeval under strict scores. Base denotes the orginal Qwen2.5-3B--Bae model.
Models
En
Es
Fr
Ja
Avg
Gen
Base
40.1
46.0
40.6
23.9
37.6
0.0
SET (En)
34.2
44.5
40.9
21.2
35.2
-3.9
RL (En)
40.1
46.0
41.5
23.5
37.7
0.2
A (RL-SFT)
+5.9
+1.5
+0.6
+2.2
+2.5
+4.1
SFT (Zh)
36.9
40.9
35.7
21.2
33.7
-6.6
RL (Zh)
40.8
44.5
43.2
31.0
39.9
3.0
(RL-SFT)
+3.8
+3.6
+7.5
+9.7
+6.2
+9.7
SET (De)
32.7
37.2
29.0
23.5
30.6
-12.1
RL (De)
41.4
39.4
44.9
29.7
38.8
1.2
A (RL-SFT)
+8.6
+2.2
+15.9
+6.2
+8.2
+13.4
21

---

Published as a conference paper at ICLR 2026
Table 18: Performance of base, SFT, and RL models multilingual LogiQA. Language codes: En = English, Zh = Chinese, Es = Spanish, Vi Vietnamese, Id Indonesian, Ms = Malay, Fil
Filipino.
Model
En
Zh
Es
Fil
Id
Ms
Vi
Avg
Gen
Base
35.2
27.8
35.2
1.1
3.4
4.0
15.9
17.5
0.00
SFT (En)
42.0
38.6
35.2
24.4
38.6
31.3
34.1
34.9
19.4
RL (En)
48.9
52.3
42.0
35.2
47.2
38.6
42.6
43.8
30.4
A (RL-SFT)
+6.8
+13.6
+6.8
+10.8
+8.5
+7.4
+8.5
+8.9
+11.1
SFT (Zh)
47.7
43.8
43.8
28.4
44.9
37.5
23.3
38.5
24.1
RL (Zh)
55.1
59.1
46.0
31.3
41.5
39.8
44.3
45.3
33.1
A (RL-SFT)
+7.4
+15.3
+2.3
+2.8
-3.4
+2.3
+21.0
+6.8
+9.0
SFT (De)
45.5
27.8
35.2
14.2
21.6
25.6
11.4
25.9
9.3
RL (De)
52.3
61.4
44.3
35.8
44.9
46.0
48.3
47.6
35.3
A (RL-SFT)
+6.8
+33.5
+9.1
+21.6
+23.3
+20.5
+36.9
+21.7
+26.0
Table 19: Language usage scores on MMath500. We randomly sample 100 questions per language from MMath500 and analyze 6 sampled responses for each question. The scores are calculated based on the rank of language usage within the responses. We report results for the primary languages (En, Zh, De, Es, Ja) across different models.
Model
En
Zh
De
Es
Fr
Ja
Base
0.228
0.163
0.160
0.161
0.141
0.190
SFT (En)
0.668
0.175
0.001
0.000
0.000
0.297
RL (En)
0.294
0.230
0.161
0.159
0.153
0.196
SFT (Zh)
0.309
0.420
0.077
0.092
0.097
0.350
RL (Zh)
0.873
0.090
0.040
0.015
0.076
0.020
SET (De)
0.533
0.150
0.336
0.068
0.062
0.234
RL (De)
0.819
0.112
0.073
0.010
0.021
0.096
22

---

Published as a conference paper at ICLR 2026
A.5
CASE STUDY
Table 20: Case study on MMath500. We select the German question to show the case.
Ein Matheclub veranstaltet einen Kuchenverkauf als Spendenaktion, um Geld für eine bevorstchende Reise zu sammeln. Sie verkaufen 54 Kekse drei für $1S, und $205 Cupcakes zu $2S pro Stück, und $35$ Brownies zu $1$ pro Stück, Wenn es den Matheclub $15$ gekostct hat, diese Artikel zu backen, wie hoch war ihr Gewinn?
Question:
Answer: 78
Base:
Da Kekse zu drei für $1 verkaufen werden, müssen wir zahlenweise Kekse zählen. Es gibt 54 Kekse backen, und jeder Kuchen besteht drei Keksen. Also haben sie 54/3 18 Kuchen backen. Zudem hahen sie 20 Cupeakes Matheclub hat also insgesamt 18 + - 35 73 Artikel zu backen. Sind sie zu backen, es ihnen 73 2 = $146 gekostet. Da sie für die Backzeit 15 Dollar ausgeben, haben sie für den
backen und 35 Brownies backen. Die
Verkauf
$131 eingenommen. Daher haben einen Gewinn von 131
Reinforcement Learning (with German Data):
Calculate revenue from Kekse: They sold Kekse at rate 3 Kekse $1. The number of sets 3 Kekse is 54 = 18, Revenue from Kekse = 18 x = dollars.
3
2. Calculate the revenue from Cupcakes: They sold 20 Cupcakes at $2 cach. Revenue from
Cupcakes = 20 2 40 dollars.
Calculate the
from Brownies: They sold 35 Brownies $1 each. Revenue from dollars.
Brownies 35
4. Calculate the total revenue:
Total revenue Revenue from Kekse Revenue from Cupcakes + Revenue from Brownies- - Total revenue 18 + 40 + 35 = 93 dollars.
5. Calculate the profit: Cost to make the items $15. Profit Total revenue Cost to make
the items Profit 93 15 78 dollars. Therefore, the profit 78
Reinforcement Learning (with German Data and with Consistency Reward):
Zuerst berechnen wir den Einnahmen von den Keksen. Da sie drei Kekse für $1 verkaufen,
erhalten sic: 54 + 3 = 18 Doppelsätze, 18 x 2 = 36 Dollar Für die Cupcakes erhalten sie:
20 + 2 = 10 Stück, 10 x 2 = 20 Dollar Für die Brownies erhalten sie: 35 : 1 35 Stück,
35 x 1 35 Dollar Die Gesamtsumme ihrer Einnahmen beträgt: 36 + 20 + 35 91 Dollar
Da ihnen $15 gekostet hat, die Artikel backen, erhalten sie: 91 15 76 Dollar Die
Gewinnsumme beträgt 76
23


Reviews:
[{"review_id": "d0Qu0F8o55", "reviewer": "Reviewer_hEuo", "summary": "This paper investigates if RL could be beneficial for cross-lingual generalization compare to that of SFT. The authors train Qwen2.5-3B-Base on translated GSM8K and LUFFY datasets (into Chinese and German) and ablate training on SFT and RL. The models are evaluated across ten languages on 4 benchmarks (MGSM, MMath500, MMLU-ProX-Lite, and MGPQA-Diamond), where RL consistently outperforms SFT across different settings.", "questions": "See weaknesses above", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "1. This paper addresses an important question of how RL training affects cross-lingual generalization, and the finding that RL shows better generalization is very insightful for practitioners.\n\n2. The paper is written very clearly, and it was easy to follow the content while reading.\n\n3. The findings in Section 4.2., in that online optimization is also beneficial for cross-lingual generalization (in addition to \"reasoning\", which the community has most focused on) highlights the benefit of how the learning algorithms could affect generalization in a broader scope. The analysis shown in Figure 4 can also be adopted in future work.", "weaknesses": "1. Across Table 1,2,3,4, the performance of base model, SFT'ed model, and RL'ed model are shown. In practice, a lot of people also first apply SFT (referred to as cold-start) and then apply RL on top of that. Would the performance of such baseline outperform the only RL'ed variant or not? I think such cold-start is adopted a lot in practice, so there should be a baseline added.\n\n2. Taking the French scores on MGSM (Table 1) for example, when training with SFT, the Chinese dataset yields higher performance than German dataset (56.1 vs 52.8). However, with RL, the German dataset yields higher performance than Chinese dataset (80.0 vs 76.1). What could be the reason why the transferability differs across training algorithms and how does that relate to the similarity between the language used for training and the target language that is evaluated? Although it might be difficult to answer this question holistically, I think since the motivation of this work is on cross-lingual generalization w.r.t different algorithms, there should be a minimal explanation related to this.\n\n3. How would the performance differ when applying SFT or RL with English, Chinese, and German datasets combined? I think this is the typical set-up done for improving multilingual capabilities of LMs, hence it should be added to the results section. Does the performance drop compared to that of training on a single target language?\n\n4. How is the language consistency reward defined in Equation 1, and how is it implmeneted/measured? I think there should be more explanation of this in the text body.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Dl8pAcRKYj", "reviewer": "Reviewer_fFzm", "summary": "The paper investigates how reinforcement learning (RL) vs. supervised fine-tuning (SFT) affects cross-lingual reasoning when training small LLMs (Qwen2.5-3B-Base, plus a check on SmolLM3-3B-Base). The key findings are: (1) RL substantially outperforms SFT on multilingual benchmarks and transfers better across languages; (2) non-English RL training (notably German, also Chinese/Japanese/French) produces higher average accuracy and generalization than English RL, a pattern not observed for SFT. Mechanistic analyses point to (i) language inconsistency during reasoning (models trained with German instructions frequently reason in mixed/non-German), (ii) benefits of on-policy sampling/exploration beyond SFT/RFT, and (iii) smaller semantic drift from pretraining features correlating with better cross-lingual generalization.", "questions": "1. Prompt/consistency vs. accuracy inversion (Fig. 2 & Table 6): could you run a crossed intervention where the prompt explicitly requests mixed/other language while the reward penalizes similarity to the input language (an inconsistency reward)—i.e., the opposite of your current setting? This would help stress-test whether encouraged inconsistency further improves RL, or whether the benefit is emergent rather than enforced. \n2. Why is German so strong for RL? Please discuss whether advantages come from (a) dataset bias/translation quality in LUFFY/GSM8K translations, (b) pretraining distribution (German coverage/quality), or (c) intrinsic linguistic properties (morphology/compounding influencing tokenization and reasoning decomposability). Any measurements—e.g., token length, subword overlap with English/Chinese, or per-language perplexity/coverage—would help separate these hypotheses.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 2, "strengths": "1. Intuitive central idea with clear, repeated gains over SFT across languages/datasets. \n2. Actionable takeaway for the community: train RL on non-English (esp. German/Chinese) to improve cross-lingual generalization. \n3. Solid experimental practice: MGSM/MMath500/MAIME2024 (6×/6×/16×); ~10 languages;\n4. Insightful analysis:\n- (a) “Trained with German, might not reason strictly in German”—documented via Table 5 examples and Table 6 consistency stats. \n- (b) Prompt/consistency reward decreases accuracy (inverse correlation) → linguistic flexibility appears beneficial. Figure 2 & Table 6. \n- (c) Sampling/online RL > SFT/RFT for exploration and alignment with the model’s distribution. \n- (d) Semantic-shift analysis: smaller representational drift (PCA diffs) aligns with stronger cross-lingual generalization.", "weaknesses": "1. Scale limitation: results are shown on two 3B models; it’s unclear if the “non-English RL > English RL” effect holds at a larger model and dataset scale.\n2. Domain breadth: math and knowledge-oriented reasoning are well covered; fewer open-ended or instruction-following multilingual tasks.\n3. Mechanistic claims are suggestive (correlational): e.g., language inconsistency ↔ performance—great ablations, but causal proof remains preliminary.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "U7W2S3Pnf2", "reviewer": "Reviewer_xepT", "summary": "This paper systematically compared Reinforcement learning (RL) with supervised fine-tuning (SFT) for cross-lingual complex reasoning. Experiments on multilingual mathematical, commonsense, and scientific reasoning benchmarks show that RL yields higher accuracy and stronger cross-lingual generalization than SFT. RL trained on non-English data even generalizes better than RL trained on English data, a pattern not observed in SFT. Mechanistic analyses suggest that RL fosters more robust reasoning strategies.", "questions": "1.The main conclusion is drawn only from experiments on small models (3B). How do you ensure that this phenomenon does not simply arise from limited model capacity and implicit English-centric priors?\n\n2.How do you ensure data translation quality, particularly for low-resource languages?\n\n3.What is the complete implementation setup of RFT, including sampling configuration, filtering criteria?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The paper is well-written and logically structured, making the content easy to follow.\n2. Extensive experiments across multiple multilingual reasoning benchmarks provide solid and convincing results.\n3. The analysis of model semantic feature shift offers interpretability and valuable insights into the underlying mechanisms.", "weaknesses": "1. It would be valuable to investigate whether the observed phenomena also hold for larger models, such as Qwen2.5-7B. Verifying the trends at scale would make the findings more robust and convincing.\n\n2. Prior studies have shown that RL enhances robust reasoning strategies across domains, but this work focuses mainly on multilingual math reasoning, which limits the generality of the conclusions.\n\n3. The training data are obtained through machine translation from English using Qwen3-30B. Given that Qwen3-30B’s multilingual capabilities, this may significantly affect translation quality, especially for low-resource languages. In fact, MathOctopus [1] has already provided a validated multilingual GSM8K dataset(MGSM8K-Instruct).\n\n4. The paper also introduces RFT as a key baseline to analyze the role of sampling, yet crucial experimental details are missing, including sampling size, selection strategy, and decoding temperature.\n\n[1] Breaking Language Barriers in Multilingual Mathematical Reasoning: Insights and Observations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "S8b5QToodP", "reviewer": "Reviewer_58H9", "summary": "This paper performs a systematic investigation into cross-lingual reasoning generalisation of reinforcement learning (RL) and supervised fine-tuning (SFT). Experimental results show that (1) models trained with RL outperform better than SFT and (2) using non-English data achieves better overall performance than using English data.", "questions": "See Weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "- This paper presents a systematic investigation of the difference between RL and SFT in cross-lingual reasoning generalisation\n- This paper shows that using non-English data for RL can more effectively enhance performance and cross-lingual generalisation, which might provide important insights and practice into future multilingual reasoning works\n- The authors perform extensive experiments and analysis on several reasoning tasks", "weaknesses": "- The training dataset size (GSM8K with around 8k samples) is pretty small and simple, which might influence the findings and conlcusions\n- Some details of the experimental setup are missing.   \n(1)  Inference setting of the base model. It is unclear if the authors use zero-shot or few-shot prompting. Since this is a base model without instruction-tuning, it would be more fair to include few-shot prompting as a baseline;   \n(2) Training setting of SFT and RL. The authors do not report the training epoch and stopping setting. Compared to the base model, the improvement of SFT is very limited in some languages, such as English, which is unexpected?\n- As the results indicate that RL-tuned models exhibit a language-mixing pattern in their outputs, it would be interesting to include statistics on language usage in addition to the language (in)consistency analysis already presented in the paper. In other words, this can show which language the model prefers to use to think and reason, which could be used to analyse cross-lingual transfer and show why RL training on non-English data yields better performance\n\n\nOthers:\n- Lines 231-239: The results discussed here are not clearly linked to any table or figure. Is it Table 2?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)