Cross-Lingual Reasoning in Language Models

Recent reasoning Large Language Models produce a chain-of-thought (CoT) predominantly in English, even when prompted in non-English languages. Prior work suggests that forcing the CoT to remain in the input language (\emph{native reasoning}) substantially degrades performance relative to allowing the model to reason in English before answering in the input language (\emph{English-pivoted reasoning}). However, most studies of this native reasoning gap rely on inference-time interventions or limited native-language training data. We revisit this comparison at a larger scale and under comparable supervision. We construct long multilingual reasoning datasets across six languages (English, French, German, Spanish, Chinese and Swahili); fine-tune specialists in both native and English-pivoted regimes on top of \texttt{Qwen/Qwen3-8B-Base}, and evaluate across mathematics, science, general knowledge, and code. In this setting, the average native reasoning gap shrinks to 1.9--3.5% across the five non-English languages, considerably smaller than previously reported. Weight-space analysis of the native specialists reveals aligned fine-tuning updates in the middle layers and divergence in the outer layers. This points to a largely language-agnostic reasoning core surrounded by language-specific layers. Exploiting this structure, we introduce a Layer Swap: transferring the English specialist's stronger reasoning mid-layers into each native specialist, closing most of the native reasoning gap across the five non-English languages while preserving CoT in the target language. We release all models and datasets.

Reinforcement learning has proven effective for enhancing multi-step reasoning in large language models (LLMs), yet its benefits have not fully translated to multilingual contexts. Existing methods struggle with a fundamental trade-off: prioritizing input-language consistency severely hampers reasoning quality, while prioritizing reasoning often leads to unintended language drift toward English. We address this challenge with LANG, a novel framework that leverages language-conditioned hints to guide exploration in non-English reasoning tasks. Our method incorporates two key mechanisms to prevent dependency on these hints: a progressive decay schedule that gradually withdraws scaffolding, and a language-adaptive switch that tailors learning horizons to specific language difficulties. Empirical results on challenging multilingual mathematical benchmarks reveal that LANG substantially enhances reasoning performance without compromising language consistency. Moreover, we show that our framework generalizes beyond mathematics, fostering more consistent language alignment across model layers

LLMs deployed multilingually are often audited via English explanations for non-English inputs. We evaluate extractive explanations ''where the model identifies input token spans as evidence alongside a generated rationale'' and uncover a systematic trade-off: English-pivot explanations can achieve higher span agreement with human rationales while their evidence becomes less causally grounded in the model's prediction, as measured by both comprehensiveness and sufficiency. Across 3 tasks, 5languages, and 2multilingual LLM families, we find that English explanations frequently produce fluent but loosely anchored rationales, with comprehensiveness degrading by up to 5.7x relative to native-language conditions - even as task accuracy remains stable across settings. For socially nuanced classification, English pivots also fail to preserve pragmatic cues, reducing both faithfulness and span agreement. We recommend auditing explanations in the input language, reporting multi-faceted faithfulness metrics beyond lexical overlap, and treating English rationales as communication summaries rather than faithful decision traces.

Large language models (LLMs) have achieved remarkable progress in mathematical reasoning, but this ability is not equally accessible across languages. Especially low-resource languages exhibit much lower reasoning performance. To address this, we propose Crosslingual On-Policy Self-Distillation (COPSD), which transfers a model's own high-resource reasoning behavior to low-resource languages. COPSD uses the same model as student and teacher: the student sees only the low-resource problem, while the teacher receives privileged crosslingual context, including the problem translation and reference solution in English. Training minimizes full-distribution token-level divergence on the student's own rollouts, providing dense supervision while avoiding the sparsity and instability of outcome-only reinforcement learning (RL). Experiments on 17 low-resource African languages show that COPSD consistently improves low-resource mathematical reasoning across model sizes and substantially outperforms Group Relative Policy Optimization (GRPO). Further analyses show that COPSD improves answer-format adherence, strengthens test-time scaling, and generalizes to harder multilingual reasoning benchmarks, with especially large gains for lower-resource languages. We make our code and data available at: https://github.com/cisnlp/COPSD.

Curriculum learning helps language models tackle complex reasoning by gradually increasing task difficulty. However, it often fails to generate consistent step-by-step reasoning, especially in multilingual and low-resource settings where cross-lingual transfer from English to Indian languages remains limited. We propose IRIS: Interleaved Reinforcement with Incremental Staged Curriculum, a two-axis framework that combines Supervised Fine-Tuning on progressively harder problems (vertical axis) with Reverse Curriculum Reinforcement Learning to reduce reliance on step-by-step guidance (horizontal axis). We design a composite reward combining correctness, step-wise alignment, continuity, and numeric incentives, optimized via Group Relative Policy Optimization (GRPO). We release CL-Math, a dataset of 29k problems with step-level annotations in English, Hindi, and Marathi. Across standard benchmarks and curated multilingual test sets, IRIS consistently improves performance, with strong results on math reasoning tasks and substantial gains in low-resource and bilingual settings, alongside modest improvements in high-resource languages.

As LLMs reduce English-centric bias, a surprising trend emerges: non-English responses sometimes outperform English on reasoning tasks. We hypothesize that language functions as a latent variable that structurally modulates the model's internal inference pathways, rather than merely serving as an output medium. To test this, we conducted a Polyglot Thinking Experiment, in which models were prompted to solve identical problems under language-constrained and language-unconstrained conditions. Results show that non-English responses often achieve higher accuracy, and the best performance frequently occur when language is unconstrained, suggesting that multilinguality broadens the model's latent reasoning space. Based on this insight, we propose polyGRPO (Polyglot Group Relative Policy Optimization), an RL framework that treats language variation as an implicit exploration signal. It generates polyglot preference data online under language-constrained and unconstrained conditions, optimizing the policy with respect to both answer accuracy and reasoning structure. Trained on only 18.1K multilingual math problems without chain-of-thought annotations, polyGRPO improves the base model (Qwen2.5-7B-Instruct) by 6.72% absolute accuracy on four English reasoning testset and 6.89% in their multilingual benchmark. Remarkably, it is the only method that surpasses the base LLM on English commonsense reasoning task (4.9%), despite being trained solely on math data-highlighting its strong cross-task generalization. Further analysis reveals that treating language as a latent variable expands the model's latent reasoning space, yielding consistent and generalizable improvements in reasoning performance.

Cross-lingual chain-of-thought (XCoT) with self-consistency markedly enhances multilingual reasoning, yet existing methods remain costly due to extensive sampling of full trajectories across languages. Moreover, multilingual LLM representations vary strongly by language, hindering direct feature comparisons and effective pruning. Motivated by this, we introduce UL-XCoT, the first efficient unified logic cross-lingual reasoning framework that minimizes redundancy in token usage and latency, yielding the greatest efficiency under limited sampling budgets during inference. Specifically, UL-XCoT (1) achieves less languages by selecting, per query, a small candidate language set in a language-invariant unified logic space, (2) enables less tokens by monitoring logic-space trajectory dynamics during decoding to prune low-quality reasoning paths, and (3) aggregates the remaining high-quality trajectories via voting. Experiments on PolyMath across 18 languages and MMLU-ProX-Lite across 29 languages with DeepSeek-R1-DistillQwen-7B demonstrate that UL-XCoT achieves competitive accuracy while sharply cutting over 50% decoding token cost versus prior sampling baselines. UL-XCoT also delivers more stable gains on low-resource languages, underscoring consistently superior robustness where standard XCoT self-consistency method fails.

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 introduce x1, 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, x1 is 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 across multilingual mathematical reasoning and culturally grounded tasks. Moreover, our results challenge a simplistic view of scaling laws: while scaling reduces cross-lingual disparities in procedural domains such as math reasoning, it does not eliminate the advantages of culture-associated languages in culturally grounded tasks, 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.

Recent developments in reasoning capabilities have enabled large language models to solve increasingly complex mathematical, symbolic, and logical tasks. Interestingly, while reasoning models are often trained to generate monolingual text, these models have also been observed to code-switch (i.e., mix languages). Prior works have either viewed code-switching as an undesirable error, attempted to control code-switching through modifications to input prompts or the output decoding process, or focus on narrow subsets of languages, domains, tasks, and models. We address these gaps by introducing the first linguistically and behaviorally motivated fine-tuning framework for identifying beneficial code-switched reasoning behaviors in large language models and teaching these models to code-switch more effectively for reasoning. First, we create and systematically analyze a dataset of reasoning traces from diverse models, languages, tasks, and domains to understand the types of code-switching behaviors found in existing reasoning models. Then, we develop fine-tuning interventions that teach reasoning models to code-switch based on our observations of helpful behaviors in existing models. We find that our framework can significantly increase beneficial code-switched reasoning behaviors in a data-efficient manner. Interestingly, we also find that code-switching behaviors in reasoning models can be modified by fine-tuning for tasks that do not directly demonstrate code-switching in reasoning (e.g., machine translation). Our work suggests that data-efficient interventions can instill helpful forms of code-switching behavior in reasoning models.

Despite the widespread multilingual deployment of large language models, post-training pipelines remain predominantly English-centric, contributing to performance disparities across languages. We present a systematic, controlled study of the interplay between training language coverage, model scale, and task domain, based on 220 supervised fine-tuning runs on parallel translated multilingual data mixtures spanning mathematical reasoning and API calling tasks, with models up to 8B parameters. We find that English-only post-training is typically suboptimal: incorporating even a single non-English language improves both English performance and cross-lingual generalization. Increasing language diversity during post-training generally yields further gains, particularly for low-resource languages, while performance on high-resource languages tends to plateau rather than degrade. Moreover, greater language diversity enables strong zero-shot transfer to unseen languages, reducing the need for direct inclusion, though gains remain limited for typologically distant, low-resource languages.

Large Reasoning Models (LRMs) still exhibit large performance gaps between English and other languages, yet much current work assumes these gaps can be closed simply by making reasoning in every language resemble English reasoning. This work challenges this assumption by asking instead: what actually characterizes successful reasoning traces in multilingual settings, and to what extent do English-derived reasoning features genuinely help in other languages? We first define a suite of measurable reasoning features spanning multilingual alignment, reasoning step, and reasoning flow aspects of reasoning traces, and use logistic regression to quantify how each feature associates with final answer accuracy. We further train sparse autoencoders over multilingual traces to automatically discover latent reasoning concepts that instantiate or extend these features. Finally, we use the features to re-rank traces and measure their impact on accuracy at test time. Across two mathematical reasoning benchmarks, four LRMs, and ten languages, we find that most features are positively associated with accuracy, but the strength of association varies considerably across languages and can even reverse in some. Our findings challenge English-centric reward designs and point toward adaptive objectives that accommodate language-specific reasoning patterns, with concrete implications for multilingual benchmark and reward design.

Recent work has identified a subset of attention heads in Transformer as retrieval heads, which are responsible for retrieving information from the context. In this work, we first investigate retrieval heads in multilingual contexts. In multilingual language models, we find that retrieval heads are often shared across multiple languages. Expanding the study to cross-lingual setting, we identify Retrieval-Transition heads(RTH), which govern the transition to specific target-language output. Our experiments reveal that RTHs are distinct from retrieval heads and more vital for Chain-of-Thought reasoning in multilingual LLMs. Across four multilingual benchmarks (MMLU-ProX, MGSM, MLQA, and XQuaD) and two model families (Qwen-2.5 and Llama-3.1), we demonstrate that masking RTH induces bigger performance drop than masking Retrieval Heads (RH). Our work advances understanding of multilingual LMs by isolating the attention heads responsible for mapping to target languages.

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.

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.