What Makes Good Multilingual Reasoning? Disentangling Traces with Measurable Features

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

While Large Reasoning Models (LRMs) show strong performance in English, they often fail to reason in the language of the query, a phenomenon known as language collapse. Existing RL-based fixes typically add a binary language fidelity reward to the accuracy objective, yet still incur trade-off in accuracy, mid-trace code-switching, and excessive token usage. In this work, we propose AdaMame, a two-stage training recipe for multilingual mathematical reasoning that addresses these limitations by adaptively aligning the reasoning language to the query language without compromising accuracy. The first SFT stage fine-tunes on non-MT reasoning traces across five languages to establish multilingual reasoning capability. In the subsequent RL stage, we introduce AdaMame-GRPO, an adaptation of Group Relative Policy Optimization (GRPO) in which a query-conditioned alignment factor grows progressively during training, guiding the model to first explore diverse reasoning languages before exploiting reasoning in the query language. Evaluated across two benchmarks, two LRMs, and 12 languages, AdaMame-GRPO achieves Pareto-optimal performance across reasoning accuracy, language fidelity, and token efficiency over all baselines, with the strongest gains on out-of-domain, lower-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.