ExpLang: Improved Exploration and Exploitation in LLM Reasoning with On-Policy Thinking Language Selection

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.

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.

Exploration is a cornerstone of learning from experience: it enables agents to find solutions to complex problems, generalize to novel ones, and scale performance with test-time compute. In this paper, we present a framework for post-training language models (LMs) that explicitly encourages optimistic exploration and promotes a synergy between exploration and exploitation. The central idea is to train the LM to generate sets of responses that are collectively accurate under the reward function and exploratory in their reasoning strategies. We first develop a general recipe for optimizing LMs with set reinforcement learning (set RL) under arbitrary objective functions, showing how standard RL algorithms can be adapted to this setting through a modification to the advantage computation. We then propose Polychromic Exploratory Policy Optimization (Poly-EPO), which instantiates this framework with an objective that explicitly synergizes exploration and exploitation. Across a range of reasoning benchmarks, we show that Poly-EPO improves generalization, as evidenced by higher pass@$k$ coverage, preserves greater diversity in model generations, and effectively scales with test-time compute.