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To enhance Large Language Models' (LLMs) reliability, calibration is essential -- the model's assessed confidence scores should align with the actual likelihood of its responses being correct. However, current confidence elicitation methods…

Computation and Language · Computer Science 2024-10-29 Yukun Huang , Yixin Liu , Raghuveer Thirukovalluru , Arman Cohan , Bhuwan Dhingra

With rapid adoption of deep learning in critical applications, the question of when and how much to trust these models often arises, which drives the need to quantify the inherent uncertainties. While identifying all sources that account…

Machine Learning · Statistics 2019-11-22 Jayaraman J. Thiagarajan , Bindya Venkatesh , Prasanna Sattigeri , Peer-Timo Bremer

Verifiers are crucial components for enhancing modern LLMs' reasoning capability. Typicalverifiers require resource-intensive superviseddataset construction, which is costly and faceslimitations in data diversity. In this paper, wepropose…

Computation and Language · Computer Science 2026-05-08 Xinyu Wang , Changzhi Sun , Lian Cheng , Yuanbin Wu , Dell Zhang , Xiaoling Wang , Xuelong Li

Large language models (LLMs) increasingly rely on reinforcement learning (RL) to enhance their reasoning capabilities through feedback. A critical challenge is verifying the consistency of model-generated responses and reference answers,…

Artificial Intelligence · Computer Science 2025-07-29 Xuzhao Li , Xuchen Li , Shiyu Hu , Yongzhen Guo , Wentao Zhang

As large language model agents tackle increasingly complex long-horizon tasks, effective post-training becomes critical. Prior work faces fundamental challenges: outcome-only rewards fail to precisely attribute credit to intermediate steps,…

Computation and Language · Computer Science 2026-04-30 Mukai Li , Qingcheng Zeng , Tianqing Fang , Zhenwen Liang , Linfeng Song , Qi Liu , Haitao Mi , Dong Yu

Accurate uncertainty quantification is critical for reliable predictive modeling. Existing methods typically address either aleatoric uncertainty due to measurement noise or epistemic uncertainty resulting from limited data, but not both in…

Machine Learning · Statistics 2026-03-04 Ilia Azizi , Juraj Bodik , Jakob Heiss , Bin Yu

Self-improvement at scale has been a longstanding goal for reasoning models, and there are two natural places to do it: at test time, through verification-refinement (V-R) loops; and at training time, through self-training methods. Both are…

Machine Learning · Computer Science 2026-05-29 Chen Henry Wu , Aditi Raghunathan

Reinforcement Learning with Verified Reward (RLVR) has emerged as a critical paradigm for advancing the reasoning capabilities of Large Language Models (LLMs). Most existing RLVR methods, such as GRPO and its variants, ensure stable updates…

Machine Learning · Computer Science 2026-02-10 Qingyuan Wu , Yuhui Wang , Simon Sinong Zhan , Yanning Dai , Shilong Deng , Sarra Habchi , Qi Zhu , Matthias Gallé , Chao Huang

Uncertainty quantification is essential for assessing the reliability and trustworthiness of modern AI systems. Among existing approaches, verbalized uncertainty, where models express their confidence through natural language, has emerged…

Computer Vision and Pattern Recognition · Computer Science 2025-05-27 Weihao Xuan , Qingcheng Zeng , Heli Qi , Junjue Wang , Naoto Yokoya

Large Language Models (LLMs) show great promise in complex reasoning, with Reinforcement Learning with Verifiable Rewards (RLVR) being a key enhancement strategy. However, a prevalent issue is ``superficial self-reflection'', where models…

Artificial Intelligence · Computer Science 2025-05-20 Xiaoyuan Liu , Tian Liang , Zhiwei He , Jiahao Xu , Wenxuan Wang , Pinjia He , Zhaopeng Tu , Haitao Mi , Dong Yu

Reinforcement learning with verifiable rewards has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models particularly in mathematics. Current approaches in this domain present a clear trade-off:…

Computation and Language · Computer Science 2026-02-03 Batuhan K. Karaman , Aditya Rawal , Suhaila Shakiah , Mohammad Ghavamzadeh , Mingyi Hong , Arijit Biswas , Ruida Zhou

We study calibration in question answering, estimating whether model correctly predicts answer for each question. Unlike prior work which mainly rely on the model's confidence score, our calibrator incorporates information about the input…

Computation and Language · Computer Science 2021-06-04 Shujian Zhang , Chengyue Gong , Eunsol Choi

This paper proposes the use of "multicalibration" to yield interpretable and reliable confidence scores for outputs generated by large language models (LLMs). Multicalibration asks for calibration not just marginally, but simultaneously…

Machine Learning · Statistics 2024-04-09 Gianluca Detommaso , Martin Bertran , Riccardo Fogliato , Aaron Roth

Recent advancements in post-training methodologies for large language models (LLMs) have highlighted reinforcement learning (RL) as a critical component for enhancing reasoning. However, the substantial computational costs associated with…

Computation and Language · Computer Science 2025-07-29 Songjun Tu , Jiahao Lin , Xiangyu Tian , Qichao Zhang , Linjing Li , Yuqian Fu , Nan Xu , Wei He , Xiangyuan Lan , Dongmei Jiang , Dongbin Zhao

Existing Reinforcement Learning from Verifiable Rewards (RLVR) methods, such as Group Relative Policy Optimization (GRPO), have achieved remarkable progress in improving the reasoning capabilities of Large Reasoning Models (LRMs). However,…

Machine Learning · Computer Science 2026-04-16 Hsiu-Yuan Huang , Chenming Tang , Weijie Liu , Clive Bai , Saiyong Yang , Yunfang Wu

Reinforcement Learning with Verifiable Rewards has recently advanced the capabilities of Large Language Models in complex reasoning tasks by providing explicit rule-based supervision. Among RLVR methods, GRPO and its variants have achieved…

Machine Learning · Computer Science 2026-03-11 Zepeng Zhai , Meilin Chen , Jiaxuan Zhao , Junlang Qian , Lei Shen , Yuan Lu

Reasoning quality in large language models depends not only on producing correct answers but also on generating valid intermediate steps. We study this through multiple-choice question answering (MCQA), which provides a controlled setting…

Artificial Intelligence · Computer Science 2025-10-01 Raphael Schumann , Stefan Riezler

Reinforcement learning from verifiable rewards has emerged as a powerful technique for enhancing the complex reasoning abilities of Large Language Models (LLMs). However, these methods are fundamentally constrained by the ''learning cliff''…

Computation and Language · Computer Science 2026-03-03 Xichen Zhang , Sitong Wu , Yinghao Zhu , Haoru Tan , Shaozuo Yu , Ziyi He , Jiaya Jia

Through reinforcement learning with verifiable rewards (RLVR), large language models have achieved substantial progress in domains with easily verifiable outcomes, such as mathematics and coding. However, when applied to more complex tasks…

Computation and Language · Computer Science 2025-10-01 Qiyao Ma , Yunsheng Shi , Hongtao Tian , Chao Wang , Weiming Chang , Ting Yao

Language model calibration refers to the alignment between the confidence of the model and the actual performance of its responses. While previous studies point out the overconfidence phenomenon in Large Language Models (LLMs) and show that…

Computation and Language · Computer Science 2025-03-04 Jixuan Leng , Chengsong Huang , Banghua Zhu , Jiaxin Huang
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