Cross-Lingual Reasoning in Language Models

Retrieval heads, a subset of attention heads in Transformers, were studied in English, showing its crucial role in retrieving information from the context. We expand the study of retrieval heads to multilingual context and find that while nearly half of all retrieval heads are often shared across multiple languages, language-specific retrieval heads also emerge. We further design a cross-lingual needle-in-the-haystack task, to identify $\textit{Retrieval Transition Heads (RTH)}$ that retrieve key information and further map it to target-language output. Our experiments reveal that RTHs do not always overlap with RH, and can be more vital for Chain-of-Thought reasoning in multilingual LLMs. Across four multilingual benchmarks (MMLU-ProX, MGSM, MLQA, and XQuAD) and two model families (Qwen2.5-7B Instruct and Llama3.1-8B Instruct), we demonstrate that masking RTH induces bigger performance drop than masking Retrieval Heads (RH). Specifically, for Llama3.1-8B Instruct, masking the top-25 RTHs results in an average 37.3-point drop (against 19.5-point drop from RH masking) in reasoning accuracy (MMLU-ProX, MGSM) and 9.0 F1-score reduction (against 5.1 drop for RH) in extractive QA (MLQA, XQuAD). Our work advances the understanding of multilingual LMs by isolating the attention heads responsible for mapping to target languages.

Current large reasoning models (LRMs) have shown strong ability on challenging tasks after reinforcement learning (RL) based post-training. However, previous work mainly focuses on English reasoning in expectation of the strongest performance, despite the demonstrated potential advantage of multilingual thinking, as well as the requirement for native thinking traces by global users. In this paper, we propose ExpLang, a novel LLM post-training pipeline that enables on-policy thinking language selection to improve exploration and exploitation during RL with the use of multiple languages. The results show that our method steadily outperforms English-only training with the same training budget, while showing high thinking language compliance for both seen and unseen languages. Analysis shows that, by enabling on-policy thinking language selection as an action during RL, ExpLang effectively extends the RL exploration space with diversified language preference and improves the RL exploitation outcome with leveraged non-English advantage. The method is orthogonal to most RL algorithms and opens up a new perspective on using multilinguality to improve LRMs.

The rapid advancement of large language models (LLMs) necessitates evaluation frameworks that reflect real-world academic rigor and multilingual complexity. This paper introduces IndicEval, a scalable benchmarking platform designed to assess LLM performance using authentic high-stakes examination questions from UPSC, JEE, and NEET across STEM and humanities domains in both English and Hindi. Unlike synthetic benchmarks, IndicEval grounds evaluation in real examination standards, enabling realistic measurement of reasoning, domain knowledge, and bilingual adaptability. The framework automates assessment using Zero-Shot, Few-Shot, and Chain-of-Thought (CoT) prompting strategies and supports modular integration of new models and languages. Experiments conducted on Gemini 2.0 Flash, GPT-4, Claude, and LLaMA 3-70B reveal three major findings. First, CoT prompting consistently improves reasoning accuracy, with substantial gains across subjects and languages. Second, significant cross-model performance disparities persist, particularly in high-complexity examinations. Third, multilingual degradation remains a critical challenge, with marked accuracy drops in Hindi compared to English, especially under Zero-Shot conditions. These results highlight persistent gaps in bilingual reasoning and domain transfer. Overall, IndicEval provides a practice-oriented, extensible foundation for rigorous, equitable evaluation of LLMs in multilingual educational settings and offers actionable insights for improving reasoning robustness and language adaptability.

Reasoning-oriented large language models (RLMs) achieve strong gains on tasks such as mathematics and coding by generating explicit intermediate reasoning. However, their impact on machine translation (MT) remains underexplored. We systematically evaluate several open- and closed-weights RLMs on the WMT24++ benchmark and find that enabling explicit reasoning consistently degrades translation quality across languages and models. Analysis reveals that MT reasoning traces are highly linear, lacking revision, self-correction and exploration of alternative translations, which limits their usefulness. Furthermore, injecting higher-quality reasoning traces from stronger models does not reliably improve weaker models' performance. To address this mismatch, we propose a structured reasoning framework tailored to translation, based on multi-step drafting, adequacy refinement, fluency improvement, and selective iterative revision. We curate a synthetic dataset of dynamic structured reasoning traces and post-train a large reasoning model on this data. Experiments show significant improvements over standard translation fine-tuning and injected generic reasoning baselines. Our findings demonstrate that reasoning must be task-structured to benefit MT.

Large language models (LLMs) have achieved strong results in mathematical reasoning, and are increasingly deployed as tutoring and learning support tools in educational settings. However, their reliability for students working in non-English languages, especially low-resource languages, remains poorly understood. We examine this gap by evaluating mathematical reasoning in Sinhala and Tamil -- two languages widely used in South Asian schools but underrepresented in artificial intelligence (AI) research. Using a taxonomy of six math problem types, from basic arithmetic to complex unit conflict and optimization problems, we evaluate four prominent large language models. To avoid translation artifacts that confound language ability with translation quality, we construct a parallel dataset in which each problem is independently authored in Sinhala and Tamil by native speakers, and in English by fluent speakers, all with strong mathematical backgrounds. Our analysis demonstrates that while basic arithmetic reasoning transfers robustly across languages, complex reasoning tasks show significant degradation in Tamil and Sinhala. The pattern of failures varies by model and problem type, suggesting that strong performance in English does not guarantee reliable performance across languages. These findings have direct implications for the deployment of AI tools in multilingual classrooms, and highlight the need for language-specific evaluation before adopting large language models as math tutoring aids in non-English educational contexts.

The real-world information sources are inherently multilingual, which naturally raises a question about whether language models can synthesize information across languages. In this paper, we introduce a simple two-hop question answering setting, where answering a question requires making inferences over two multilingual documents. We find that language models are more sensitive to language variation in answer-span documents than in those providing bridging information, despite the equal importance of both documents for answering a question. Under a step-by-step sub-question evaluation, we further show that in up to 33% of multilingual cases, models fail to infer the bridging information in the first step yet still answer the overall question correctly. This indicates that reasoning in language models, especially in multilingual settings, does not follow a faithful step-by-step decomposition. Subsequently, we show that the absence of reasoning decomposition leads to around 18% composition failure, where both sub-questions are answered correctly but fail for the final two-hop questions. To mitigate this, we propose a simple three-stage SUBQ prompting method to guide the multi-step reasoning with sub-questions, which boosts accuracy from 10.1% to 66.5%.

We create high-quality datasets for LLM evaluation of logical reasoning skills across nine different languages, which have been manually checked by fluent speakers. The datasets consist of so-called zebra puzzles, and we analyse different ways of tuning the difficulty of the puzzles to fit modern LLMs. This includes the size of the puzzle (number of objects and number of clues), as well as a novel addition of red herring clues containing only irrelevant information. We show that presence of red herrings indeed makes the puzzles significantly harder for the models, and we find puzzle sizes 2x3 and 4x5 are sufficiently challenging for GPT-4o mini (a non-reasoning model) and o3-mini (a reasoning model), respectively. We analyse whether LLM performance of these are sensitive to the language, the cultural sensitivity of the puzzle theme, and the choice of clue types. These analyses are conducted with English and Danish, where we show that there is no significant difference for either of these three aspects, at least for the OpenAI models GPT-4o mini and o3-mini, chosen as representative non-reasoning and reasoning models, respectively. We publish the datasets for each of the nine languages for the identified sizes 2x3 and 4x5. We also publish the code used to generate the puzzles, which can be used to extend the benchmark into more languages.

Recent advances in Reinforcement Post-Training (RPT) have substantially improved the mathematical reasoning capabilities of large language models (LLMs), but it remains unclear how well such gains transfer across languages. In this work, we study cross-lingual mathematical reasoning transfer in English-centric LLMs under controlled multilingual evaluation. We first evaluate a range of English-centric reasoning models on multilingual mathematical reasoning benchmarks and find that transfer is highly variable across initial model choice, target language, and training paradigm. Through controlled comparative experiments, we further find that stronger English-centric initialization does not necessarily lead to stronger relative transfer efficiency, even when it yields higher multilingual reasoning accuracy. Finally, we show that the largest improvement comes from moving beyond English-only supervision: adding a single parallel language yields a substantial gain, while further gains from additional languages are smaller but consistent. Overall, our results highlight the need to evaluate multilingual mathematical reasoning directly, using both absolute performance and relative transfer-efficiency metrics.

Large Language Models (LLMs) are increasingly deployed across multilingual and multicultural settings, yet it remains unclear whether changing language leads models to adopt community-specific moral reasoning or merely changes how shared learned abstractions are expressed. We conduct a controlled multilingual evaluation across six geographically, culturally, and linguistically diverse languages (Arabic, Chinese, English, Hindi, Russian, and Spanish), using parallel moral reasoning benchmarks with English-origin, Chinese-origin, and natively elicited ground-truth judgments. Across 13 open-weight LLMs spanning 2B-70B parameters, we find substantial cross-lingual divergence in moral judgments, with English generally achieving the highest performance even when ground-truth judgments originate in Chinese or are collected natively in each language. Yet the reasoning underlying these divergent judgments is considerably more convergent: Utilitarianism dominates in five of six languages, reasoning follows broadly shared stages, and language-specific moral-value associations correspond only sparsely and inconsistently to values measured in the corresponding human communities. Finally, a large-scale OLMoTrace analysis of pretraining data sources reveals little direct reproduction of training text across languages, while the corpus composition, training stage, and cultural provenance of retrieved training evidence vary substantially by response language. Thus, similar moral reasoning structures emerge even from heterogeneous and often linguistically localized training evidence. Our findings, collectively, reveal a central disconnect in multilingual moral reasoning: language changes models' moral judgments and the training evidence associated with their reasoning, but does not correspondingly localize the moral abstractions they apply.