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Reinforcement learning with verifiable rewards (RLVR), which typically adopts Pass@1 as the reward, has faced the issues in balancing exploration and exploitation, causing policies to prefer conservative actions, converging to a local…

Machine Learning · Computer Science 2025-08-15 Zhipeng Chen , Xiaobo Qin , Youbin Wu , Yue Ling , Qinghao Ye , Wayne Xin Zhao , Guang Shi

Pass@k is a widely used performance metric for verifiable large language model tasks, including mathematical reasoning, code generation, and short-answer reasoning. It defines success if any of $k$ independently sampled solutions passes a…

Machine Learning · Computer Science 2026-02-27 Anas Barakat , Souradip Chakraborty , Khushbu Pahwa , Amrit Singh Bedi

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful paradigm to improve Large Language Models on reasoning tasks such as coding, math or logic. To assess the reasoning boundary (the fraction of problems a model…

Artificial Intelligence · Computer Science 2025-10-22 Marius Dragoi , Ioana Pintilie , Florin Gogianu , Florin Brad

The rapid advancement of large language models (LLMs) has shown remarkable progress in complex reasoning tasks. However, a significant disparity exists between benchmark performances and real-world applications. We attribute this gap…

Artificial Intelligence · Computer Science 2025-08-11 Junnan Liu , Hongwei Liu , Linchen Xiao , Ziyi Wang , Kuikun Liu , Songyang Gao , Wenwei Zhang , Songyang Zhang , Kai Chen

A central paradox in fine-tuning Large Language Models (LLMs) with Reinforcement Learning with Verifiable Reward (RLVR) is the frequent degradation of multi-attempt performance (Pass@k) despite improvements in single-attempt accuracy…

Machine Learning · Computer Science 2026-03-04 Long Li , Zhijian Zhou , Jiaran Hao , Jason Klein Liu , Yanting Miao , Wei Pang , Xiaoyu Tan , Wei Chu , Zhe Wang , Shirui Pan , Chao Qu , Yuan Qi

Reinforcement learning with verifiable rewards (RLVR) has advanced the reasoning capabilities of large language models (LLMs). However, prevailing RLVR methods exhibit a systematic bias toward exploitation over exploration, as evidenced by…

Artificial Intelligence · Computer Science 2025-10-22 Ruotian Peng , Yi Ren , Zhouliang Yu , Weiyang Liu , Yandong Wen

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a key method for improving Large Language Models' reasoning capabilities, yet recent evidence suggests it may paradoxically shrink the reasoning boundary rather than…

Artificial Intelligence · Computer Science 2025-10-03 Phuc Minh Nguyen , Chinh D. La , Duy M. H. Nguyen , Nitesh V. Chawla , Binh T. Nguyen , Khoa D. Doan

Recent advancements in long chain-of-thought (CoT) reasoning, particularly through the Group Relative Policy Optimization algorithm used by DeepSeek-R1, have led to significant interest in the potential of Reinforcement Learning with…

Artificial Intelligence · Computer Science 2025-10-03 Xumeng Wen , Zihan Liu , Shun Zheng , Shengyu Ye , Zhirong Wu , Yang Wang , Zhijian Xu , Xiao Liang , Junjie Li , Ziming Miao , Jiang Bian , Mao Yang

The application of Reinforcement Learning with Verifiable Rewards (RLVR) to mathematical and coding domains has demonstrated significant improvements in the reasoning and problem-solving abilities of Large Language Models. Despite its…

Machine Learning · Computer Science 2025-10-28 Farid Bagirov , Mikhail Arkhipov , Ksenia Sycheva , Evgeniy Glukhov , Egor Bogomolov

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for enhancing Large Language Models (LLMs) on complex reasoning tasks. However, existing methods suffer from an exploration dilemma: the sharply peaked initial…

Artificial Intelligence · Computer Science 2025-09-30 Yuhua Jiang , Jiawei Huang , Yufeng Yuan , Xin Mao , Yu Yue , Qianchuan Zhao , Lin Yan

Pass$@k$ is widely used to report the reasoning performance of LLMs, but it often produces unstable and potentially misleading rankings, especially when the number of trials (samples) is limited and computational resources are constrained.…

Artificial Intelligence · Computer Science 2026-05-13 Mohsen Hariri , Amirhossein Samandar , Michael Hinczewski , Vipin Chaudhary

Current large language model post-training optimizes a risk-neutral objective that maximizes expected reward, yet evaluation relies heavily on risk-seeking metrics like Pass@k (at least one success in k trials) and Max@k (maximum reward…

Machine Learning · Computer Science 2025-08-05 Kaichen Zhang , Shenghao Gao , Yuzhong Hong , Haipeng Sun , Junwei Bao , Hongfei Jiang , Yang Song , Hong Dingqian , Hui Xiong

Reinforcement Learning (RL) algorithms sample multiple n>1 solution attempts for each problem and reward them independently. This optimizes for pass@1 performance and prioritizes the strength of isolated samples at the expense of the…

Machine Learning · Computer Science 2025-12-16 Christian Walder , Deep Karkhanis

Does reinforcement learning genuinely expand what LLM agents can do, or merely make them more reliable? For static reasoning, recent work answers the second: base and RL pass@k curves converge at large k. We ask whether this holds for…

Machine Learning · Computer Science 2026-04-17 Zhiyuan Zhai , Wenjing Yan , Xiaodan Shao , Xin Wang

Reinforcement Learning with Verifiable Reward (RLVR) is a powerful method for enhancing the reasoning abilities of Large Language Models, but its full potential is limited by a lack of exploration in two key areas: Depth (the difficulty of…

Machine Learning · Computer Science 2026-04-14 Zhicheng Yang , Zhijiang Guo , Yinya Huang , Yongxin Wang , Dongchun Xie , Hanhui Li , Yiwei Wang , Xiaodan Liang , Jing Tang

Reinforcement learning (RL) has emerged as a promising paradigm for training reasoning-oriented models by leveraging rule-based reward signals. However, RL training typically tends to improve single-sample success rates (i.e., Pass@1) while…

Computation and Language · Computer Science 2026-04-21 Yifu Huo , Chenglong Wang , Ziming Zhu , Shunjie Xing , Peinan Feng , Tongran Liu , Qiaozhi He , Tianhua Zhou , Xiaojia Chang , Jingbo Zhu , Zhengtao Yu , Tong Xiao

The performance of large language models (LLMs) on verifiable tasks is usually measured by pass@k, the probability of answering a question correctly at least once in k trials. At a fixed budget, a more suitable metric is coverage@cost, the…

Machine Learning · Computer Science 2026-01-30 Sagi Meir , Tommer D. Keidar , Noam Levi , Shlomi Reuveni , Barak Hirshberg

Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated notable success in enhancing the reasoning performance of large language models (LLMs), particularly on mathematics and programming tasks. Similar to how…

Artificial Intelligence · Computer Science 2025-11-25 Yang Yue , Zhiqi Chen , Rui Lu , Andrew Zhao , Zhaokai Wang , Yang Yue , Shiji Song , Gao Huang

Reinforcement learning (RL) has become a central paradigm for post-training large language models (LLMs), particularly for complex reasoning tasks, yet it often suffers from exploration collapse: policies prematurely concentrate on a small…

Machine Learning · Computer Science 2026-01-16 Zhiyuan Hu , Yucheng Wang , Yufei He , Jiaying Wu , Yilun Zhao , See-Kiong Ng , Cynthia Breazeal , Anh Tuan Luu , Hae Won Park , Bryan Hooi

Large language models (LLMs) have demonstrated impressive performance in various natural language processing tasks, yet their ability to perform multi-step logical reasoning remains an open challenge. Although Chain-of-Thought prompting has…

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