Large reasoning models (LRMs) have emerged as a powerful paradigm for solving complex real-world tasks. In practice, these models are predominantly trained via Reinforcement Learning with Verifiable Rewards (RLVR), yet most existing outcome-only RLVR pipelines rely almost exclusively on a binary correctness signal and largely ignore the model's intrinsic uncertainty. We term this discrepancy the uncertainty-reward mismatch, under which high- and low-uncertainty solutions are treated equivalently, preventing the policy from "Know What You Know" and impeding the shift from optimizing for correct answers to optimizing effective reasoning paths. This limitation is especially critical in reasoning-centric tasks such as mathematics and question answering, where performance hinges on the quality of the model's internal reasoning process rather than mere memorization of final answers. To address this, we propose EGPO, a metacognitive entropy calibration framework that explicitly integrates intrinsic uncertainty into RLVR for enhancing LRMs. EGPO estimates per-sample uncertainty using a zero-overhead entropy proxy derived from token-level likelihoods and aligns it with extrinsic correctness through an asymmetric calibration mechanism that preserves correct reasoning while selectively regulating overconfident failures, thereby enabling stable and uncertainty-aware policy optimization. Moreover, EGPO recovers informative learning signals from otherwise degenerate group-based rollouts without modifying the verifier or reward definition. Extensive experiments across multiple benchmarks demonstrate that the proposed EGPO leads to substantial and consistent improvements in reasoning performance, establishing a principled path for advancing LRMs through metacognitive entropy calibration.
Dept. of Computer Science University of Minnesota, Twin Cities（计算机科学系明尼苏达大学双城分校）；Depts. of Computer Science and Psychology University of Minnesota, Twin Cities（计算机科学与心理学系明尼苏达大学双城分校）
Cog-Rethinker: Hierarchical Metacognitive Reinforcement Learning for LLM Reasoning
Baidu Inc.（百度公司）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学人工智能学院）
Beyond Meta-Reasoning: Metacognitive Consolidation for Self-Improving LLM Reasoning
Southeast University（东南大学）；King’s College London（伦敦国王学院）；The Alan Turing Institute（艾伦·图灵研究所）；Qilu University of Technology (Shandong Academy of Sciences)（齐鲁工业大学（山东科学院））
Metacognition as Reward: Reinforcing LLM Reasoning via Knowledge and Regulation Signals
Tongji University（同济大学）；Shanghai AI Laboratory（上海人工智能实验室）；Nanyang Technological University（南洋理工大学）；University of Science and Technology of China（中国科学技术大学）；EPFL（苏黎世联邦理工学院）；Wuhan University（武汉大学）
CoT2-Meta: Budgeted Metacognitive Control for Test-Time Reasoning
Nanyang Technological University（南洋理工大学）；Carnegie Mellon University（卡内基梅隆大学）；Zhejiang University（浙江大学）；Sun Yat-Sen University（中山大学）；National University of Singapore（新加坡国立大学）；Fudan University（复旦大学）；City University of Hong Kong (Dongguan)（香港城市大学（东莞））；Zhejiang Lab（之江实验室）
Inverse Knowledge Search over Verifiable Reasoning: Synthesizing a Scientific Encyclopedia from a Long Chains-of-Thought Knowledge Base
Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics（兰州理论物理中心、甘肃省理论物理重点实验室、教育部量子理论与应用重点实验室、甘肃省量子物理基础学科研究省重点中心）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；DP Technology（DP技术）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Département d’Informatique, École normale supérieure（巴黎高等师范大学计算机系）
