Scaling with Confidence: Calibrating Confidence of LLMs for Adaptive Test Time Scaling

Xuqing Yang, Yi Yuan, Shanzhe Lei, Xuhong Wang

Training large language models (LLMs) with reinforcement learning (RL) has significantly advanced their performance on reasoning and question-answering tasks. However, prevailing RL reward designs typically prioritize response correctness, neglecting to incentivize models to express their confidence accurately. This leads to a critical problem: performance gains are often accompanied by poor calibration between confidence and accuracy, misleading models to overconfidently hallucinate when uncertain. To address this limitation, we propose $\textbf{C}$orrectness and $\textbf{C}$onfidence $\textbf{C}$alibration $\textbf{R}$einforcement $\textbf{L}$earning ($\textbf{C3RL}$), a novel RL algorithm integrating correctness, calibration and dataset-informed reference accuracy rewards together. Comprehensive evaluation across 8 text and multimodal datasets demonstrates that C3RL enhances calibration without sacrificing accuracy, outperforming the current state-of-the-art method in both performance and calibration metrics. Utilizing the well-calibrated verbalized confidence from C3RL, we further introduce $\textbf{C}$onfidence-based $\textbf{A}$daptive Test Time $\textbf{S}$caling ($\textbf{CAS}$), an adjustable inference-time strategy that allocates computational resources based on response confidence. Experiments show that CAS surpasses majority voting on both in-domain and out-of-domain datasets while reducing the inference budget by up to 12.33 times. We believe the synergy of C3RL and CAS paves the way for deploying more reliable and resource-efficient LLMs. The code, data and models will be released.