Multilingual Reasoning Gym: Multilingual Scaling of Procedural Reasoning Environments

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising approach for training reasoning language models (RLMs) by leveraging supervision from verifiers. Although verifier implementation is easier than solution annotation for many tasks, existing synthetic data generation methods remain largely solution-centric, while verifier-based methods rely on a few hand-crafted procedural environments. In this work, we scale RLVR by introducing ReSyn, a pipeline that generates diverse reasoning environments equipped with instance generators and verifiers, covering tasks such as constraint satisfaction, algorithmic puzzles, and spatial reasoning. A Qwen2.5-7B-Instruct model trained with RL on ReSyn data achieves consistent gains across reasoning benchmarks and out-of-domain math benchmarks, including a 27% relative improvement on the challenging BBEH benchmark. Ablations show that verifier-based supervision and increased task diversity both contribute significantly, providing empirical evidence that generating reasoning environments at scale can enhance reasoning abilities in RLMs

Despite advances in multilingual capabilities, most large language models (LLMs) remain English-centric in their training and, crucially, in the reasoning traces they produce: even for non-English problems, they predominantly reason in English, leaving non-English users with intermediate reasoning they cannot follow. We address this disparity with two contributions. (a) We introduce $\texttt{ReasonXL}$, the first large-scale parallel corpus of cross-domain reasoning traces in five European languages (English, German, French, Italian, and Spanish): over 2.5M aligned samples (11B tokens) per language, each comprising prompt, reasoning trace, and final output, enabling direct supervision of language-specific reasoning. (b) Using $\texttt{ReasonXL}$, we demonstrate that LLMs can be adapted to reason entirely in a target language through a simple two-stage pipeline of supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR), matching or exceeding the base models' English-reasoning performance in two of four languages and recovering most of it in the remaining two.

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