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While reinforcement learning (RL) demonstrated remarkable success in enhancing the reasoning capabilities of language models, the training dynamics of RL in LLMs remain unclear. In this work, we provide an explanation of the RL training…

Machine Learning · Computer Science 2025-09-30 Xingwu Chen , Tianle Li , Difan Zou

Reinforcement learning with verifiable rewards (RLVR) has delivered impressive gains in mathematical and multimodal reasoning and has become a standard post-training paradigm for contemporary language and vision-language models. However,…

Machine Learning · Computer Science 2025-10-28 Hoang Phan , Xianjun Yang , Kevin Yao , Jingyu Zhang , Shengjie Bi , Xiaocheng Tang , Madian Khabsa , Lijuan Liu , Deren Lei

Reinforcement learning with verifiable rewards (RLVR) has driven significant performance gains in reasoning-oriented large language models (LLMs), yet its internal training dynamics remain largely a black box. In this work, we perform a…

Machine Learning · Computer Science 2026-05-22 Tianle Wang , Jiayu Liu , Zhongyuan Wu , Shenghao Jin , Wei Chen , Hao Xu , Ning Miao

Reinforcement learning with verifiable rewards (RLVR) has recently advanced the reasoning capabilities of large language models (LLMs). While prior work has emphasized algorithmic design, data curation, and reward shaping, we investigate…

Machine Learning · Computer Science 2025-07-10 Xinjie Chen , Minpeng Liao , Guoxin Chen , Chengxi Li , Biao Fu , Kai Fan , Xinggao Liu

Long context reasoning in large language models (LLMs) has demonstrated enhancement of their cognitive capabilities via chain-of-thought (CoT) inference. Training such models is usually done via reinforcement learning with verifiable…

Computation and Language · Computer Science 2025-12-05 Purbesh Mitra , Sennur Ulukus

Large language models can generate solutions to complex problems, but training them with reinforcement learning typically requires verifiable rewards that are expensive to create and not possible for all domains. We demonstrate that LLMs…

Machine Learning · Computer Science 2025-08-08 Toby Simonds , Kevin Lopez , Akira Yoshiyama , Dominique Garmier

Reinforcement Learning with Verifiable Rewards (RLVR) has established itself as the dominant paradigm for instilling rigorous reasoning capabilities in Large Language Models. While effective at amplifying dominant behaviors, we identify a…

Machine Learning · Computer Science 2026-02-16 Zesheng Hong , Jiadong Yu , Hui Pan

While Reinforcement Learning with Verifiable Rewards (RLVR) is effective for deterministically checkable tasks, many vision-language tasks are partially verifiable, demanding multi-criteria supervision (e.g., perceptual details, reasoning…

Computer Vision and Pattern Recognition · Computer Science 2026-05-29 Ya-Qi Yu , Hao Wang , Fangyu Hong , Xiangyang Qu , Gaojie Wu , Qiaoyu Luo , Nuo Xu , Huixin Wang , Wuheng Xu , Yongxin Liao , Zihao Chen , Haonan Li , Ziming Li , Dezhi Peng , Minghui Liao , Jihao Wu , Haoyu Ren , Dandan Tu

Reinforcement Learning with verifiable rewards (RLVR) has emerged as a primary learning paradigm for enhancing the reasoning capabilities of multi-modal large language models (MLLMs). However, during RL training, the enormous state space of…

Machine Learning · Computer Science 2026-03-13 Zhuoxu Huang , Mengxi Jia , Hao Sun , Xuelong Li , Jungong Han

Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated remarkable potential in enhancing the reasoning capability of Large Reasoning Models (LRMs). However, RLVR often drives the policy toward over-determinism,…

Machine Learning · Computer Science 2026-03-23 Shimin Zhang , Xianwei Chen , Yufan Shen , Ziyuan Ye , Jibin Wu

Reinforcement Learning (RL) has enabled Large Language Models (LLMs) to achieve remarkable reasoning in domains like mathematics and coding, where verifiable rewards provide clear signals. However, extending this paradigm to financial…

Artificial Intelligence · Computer Science 2026-01-09 Rui Sun , Yifan Sun , Sheng Xu , Li Zhao , Jing Li , Daxin Jiang , Cheng Hua , Zuo Bai

Recent advances in large reasoning models (LRMs) demonstrate that sophisticated behaviors such as multi-step reasoning and self-reflection can emerge via reinforcement learning with verifiable rewards~(\textit{RLVR}). However, existing…

Machine Learning · Computer Science 2025-06-24 Jianhao Yan , Yafu Li , Zican Hu , Zhi Wang , Ganqu Cui , Xiaoye Qu , Yu Cheng , Yue Zhang

Large Language Models (LLMs) empowered with Tool-Integrated Reasoning (TIR) can iteratively plan, call external tools, and integrate returned information to solve complex, long-horizon reasoning tasks. Agentic Reinforcement Learning…

Computation and Language · Computer Science 2026-01-21 Jianghao Su , Xia Zeng , Luhui Liu , Chao Luo , Ye Chen , Zhuoran Zhuang

Recent AI advancements, such as OpenAI's new models, are transforming LLMs into LRMs (Large Reasoning Models) that perform reasoning during inference, taking extra time and compute for higher-quality outputs. We aim to uncover the…

Artificial Intelligence · Computer Science 2025-02-11 Guanghao Ye , Khiem Duc Pham , Xinzhi Zhang , Sivakanth Gopi , Baolin Peng , Beibin Li , Janardhan Kulkarni , Huseyin A. Inan

Reinforcement learning (RL) can refine the reasoning abilities of large language models (LLMs), but critically depends on a key prerequisite: the LLM can already generate high-utility reasoning paths with non-negligible probability. For…

Artificial Intelligence · Computer Science 2025-10-30 Tianqianjin Lin , Xi Zhao , Xingyao Zhang , Rujiao Long , Yi Xu , Zhuoren Jiang , Wenbo Su , Bo Zheng

Reinforcement learning from verifiable rewards (RLVR) has shown strong promise for LLM reasoning, but outcome-based RLVR remains inefficient on hard problems because correct final-answer rollouts are rare and sample-level credit assignment…

Machine Learning · Computer Science 2026-05-22 Xitai Jiang , Zihan Tang , Wenze Lin , Yang Yue , Shenzhi Wang , Gao Huang

Reinforcement Learning with Verifiable Rewards (RLVR) has been an effective approach for improving Large Language Models' reasoning in domains such as coding and mathematics. Here, we apply RLVR methods towards forecasting future real-world…

Machine Learning · Computer Science 2025-12-02 Benjamin Turtel , Danny Franklin , Kris Skotheim , Luke Hewitt , Philipp Schoenegger

With respect to improving the reasoning accuracy of LLMs, the representative reinforcement learning (RL) method GRPO faces failure due to insignificant reward variance, while verification methods based on process reward models (PRMs) suffer…

Artificial Intelligence · Computer Science 2025-09-09 Sining Zhoubian , Dan Zhang , Jie Tang

Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced the reasoning capacity of Large Language Models (LLMs). However, RLVR solely relies on final answers as outcome rewards, neglecting the correctness of…

Machine Learning · Computer Science 2026-03-12 Sijia Cui , Pengyu Cheng , Jiajun Song , Yongbo Gai , Guojun Zhang , Zhechao Yu , Jianhe Lin , Xiaoxi Jiang , Guanjun Jiang

Reinforcement Learning with Verifiable Rewards (RLVR) effectively trains reasoning models that rely on abundant perfect labels, but its vulnerability to unavoidable noisy labels due to expert scarcity remains critically underexplored. In…

Machine Learning · Computer Science 2026-04-07 Shenzhi Yang , Guangcheng Zhu , Bowen Song , Sharon Li , Haobo Wang , Xing Zheng , Yingfan Ma , Zhongqi Chen , Weiqiang Wang , Gang Chen