Performance Foundations of Parallel & Distributed Reasoning Language Models

Reinforcement Learning with Verifiable Rewards (RLVR) and other RL-style post-training paradigms have been used for aligning large language models (LLMs) with reasoning standards. The resulting recent Reasoning Language Models (RLMs) such as DeepSeek-R1, o3, and Kimi k1.5 show that such RL-style post-training ("RL-for-LLMs") can substantially improve chain-of-thought reasoning, long-horizon planning, and self-correction. However, the computational footprint of these systems is massive: state-of-the-art RLM training requires millions of GPU-hours and tightly coupled multi-model pipelines that stress modern hardware far beyond classical supervised LLM training. This makes RLM training as much a parallel and distributed systems problem as an algorithmic one. In this work, to facilitate developing RLMs that are simultaneously high-performance, scalable, and cost-effective, we first systematize the RL-for-LLM paradigm and provide a compute-centric analysis of prominent post-training algorithmic frameworks: Proximal Policy Optimization (PPO), Group Relative Policy Optimization (GRPO), as well as their variants. Second, we develop a taxonomy of intra- and inter-model parallelism strategies for RL-for-LLMs, covering both traditional techniques (data, tensor, pipeline, sequence, context, and expert parallelism) as well as novel forms of parallelism and optimization techniques for multi-model RLM training, for example disaggregated placement, stage fusion, hybrid parallelism, and asynchronous execution. We harness the work-depth model of parallel computing to make our taxonomy and its insights rigorous and portable. Finally, we analyze existing RLM frameworks and we distill practical guidelines and outline open research directions for building scalable, fast, and cost-effective RLMs.

Cost of Reasoning in non-English Languages: A Case Study on Japanese

Reasoning Language Models (RLMs) achieve their strongest performance when they reason in English, the language for which reasoning-oriented training data is most abundant. However, reasoning trace is a clue for model interpretability and safety, and useful in practice for both the model users and for model developers. Thus, it is desirable to be able to develop a model that reasons in a language of the user's choice, while still maintaining strong reasoning performance. To this end, we study the feasibility of training a model that reasons in Japanese. We develop a Japanese-reasoning variant of Qwen-3-Swallow-8B, which is a Japanese LLM continually pretrained from Qwen-3-8B, with GRPO and evaluate it across coding, math, and science benchmarks. The study shows that reasoning-language control is feasible by training a Japanese continually pretrained model with GRPO. However, its performance is at best on par with strong English-reasoning baselines on several benchmarks. We also evaluate the trained model on Japanese cultural benchmarks and observe that the model's performance is worse than the baseline models, suggesting that the reasoning in Japanese does not immediately improve performance on culturally relevant tasks for free.

CheckRLM: Effective Knowledge-Thought Coherence Checking in Retrieval-Augmented Reasoning

Reasoning Language Models (RLMs) have significantly improved performance on complex tasks by extending the reasoning chain. However, these chains are prone to containing factual errors, particularly in knowledge-intensive tasks. To address this issue, we propose CheckRLM, a framework that improves the reliability of the reasoning process through Retrieval-Augmented Generation (RAG) by timely checking and correcting factual errors. Specifically, CheckRLM extracts factual claims from the reasoning chain to identify and localize subtle knowledge inconsistencies during inference. Upon detection of errors, a refinement mechanism performs minimal-cost yet precise corrections by leveraging external knowledge, ensuring coherence between the reasoning chain and correct knowledge. Extensive experiments demonstrate that CheckRLM substantially outperforms existing baselines, exhibiting a strong capability to mitigate error accumulation in long-horizon reasoning with lower costs. The code and data are available at https://github.com/AI9Stars/CheckRLM.

Learning When to Translate for Multilingual Reasoning

Reasoning language models (RLMs) achieve strong performance on complex reasoning tasks, but still exhibit substantial multilingual reasoning gaps, largely due to language-understanding failures in non-English inputs. English translation can mitigate these failures by expressing non-English inputs in a form that RLMs can more reliably interpret, yet translating every input is unnecessary when the model can reason reliably from the original query. To address this challenge, we propose Luar, a Language Understanding Boundary-aware Reinforcement Learning framework that trains RLMs to selectively invoke translation when direct understanding is unreliable. Luar trains the model to choose between solving the original input directly and reasoning over its English translation, encouraging translation only when translator-augmented reasoning is expected to substantially outperform direct reasoning. Across multilingual reasoning benchmarks, Luar outperforms standard GRPO and other training-based baselines, with particularly large gains on low-resource languages. Further analysis shows that Luar avoids unnecessary translation in cases where direct reasoning is sufficient, while extending its translator-call behavior to unseen low-resource languages. Together, our work suggests a selective approach to multilingual reasoning: RLMs can learn to invoke translation only when their direct understanding is unreliable. The project will be made publicly available at https://github.com/deokhk/LUAR