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The ability of Large Language Models (LLMs) to perform complex, multi-step reasoning is a central focus of modern AI research. To evaluate and enhance this capability, the pass@k metric, which measures the probability of obtaining at least…

Machine Learning · Computer Science 2025-11-21 Yang Yu

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

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

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

Large language models (LLMs) achieve impressive abilities in numerous domains, but exhibit inconsistent performance in response to minor input changes. Rather than view this as a drawback, in this paper we introduce a novel method for…

Machine Learning · Computer Science 2025-05-21 Uri Dalal , Meirav Segal , Zvika Ben-Haim , Dan Lahav , Omer Nevo

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

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

We investigate a failure mode that arises during the training of reasoning models, where the diversity of generations begins to collapse, leading to suboptimal test-time scaling. Notably, the Pass@1 rate reliably improves during supervised…

Machine Learning · Computer Science 2025-10-09 Xingyu Dang , Christina Baek , Kaiyue Wen , Zico Kolter , Aditi Raghunathan

Recent advances in reasoning with large language models (LLMs) have demonstrated strong performance on complex mathematical tasks, including combinatorial optimization. Techniques such as Chain-of-Thought and In-Context Learning have…

Artificial Intelligence · Computer Science 2025-09-17 Marylou Fauchard , Florian Carichon , Margarida Carvalho , Golnoosh Farnadi

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

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how…

Machine Learning · Computer Science 2025-11-26 Feng Chen , Allan Raventos , Nan Cheng , Surya Ganguli , Shaul Druckmann

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

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 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

Repeated sampling with a verifier is the standard way to allocate test-time compute for code generation, with pass@$K$ as the canonical metric. Yet the standard policy class draws $K$ independent samples from a single answer distribution,…

Computation and Language · Computer Science 2026-05-27 Yilong Li , Suman Banerjee , Tong Che

Automated prompt optimization methods (e.g., DSpy, TextGrad) can substantially improve the performance of large language model (LLM), however, their generalization ability across different tasks remains underperformed. In practice, the…

Computation and Language · Computer Science 2026-05-27 Shuzhi Gong , Hechuan Wen

Assessing the capabilities and risks of frontier AI systems is a critical area of research, and recent work has shown that repeated sampling from models can dramatically increase both. For instance, repeated sampling has been shown to…

Artificial Intelligence · Computer Science 2025-10-08 Joshua Kazdan , Rylan Schaeffer , Youssef Allouah , Colin Sullivan , Kyssen Yu , Noam Levi , Sanmi Koyejo

Pass@k and other methods of scaling inference compute can improve language model performance in domains with external verifiers, including mathematics and code, where incorrect candidates can be filtered reliably. This raises a natural…

Machine Learning · Computer Science 2026-03-10 Yegor Denisov-Blanch , Joshua Kazdan , Jessica Chudnovsky , Rylan Schaeffer , Sheng Guan , Soji Adeshina , Sanmi Koyejo

Background and Context. The increasing integration of large language models (LLMs) in computing education presents an emerging challenge in understanding how students use LLMs and craft prompts to solve computational tasks. Prior research…

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
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