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

arXiv: https://arxiv.org/abs/2607.01612 · HTML: https://mlsanity.com/paper/2607.01612/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 30 of its 48 references that are in the map.
- First posted on arXiv 2 Jul 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 30)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Are We on the Right Way for Evaluating Large Vision-Language Models?](https://mlsanity.com/paper/2403.20330/) (2024)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [LogicVista: Multimodal LLM Logical Reasoning Benchmark in Visual Contexts](https://mlsanity.com/paper/2407.04973/) (2024)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [General-Reasoner: Advancing LLM Reasoning Across All Domains](https://mlsanity.com/paper/2505.14652/) (2025)
- [Beyond Binary Rewards: Training LMs to Reason About Their Uncertainty](https://mlsanity.com/paper/2507.16806/) (2025)
- [Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs](https://mlsanity.com/paper/2305.11860/) (2023)
- [R-Tuning: Instructing Large Language Models to Say `I Don't Know'](https://mlsanity.com/paper/2311.09677/) (2023)
- [SaySelf: Teaching LLMs to Express Confidence with Self-Reflective Rationales](https://mlsanity.com/paper/2405.20974/) (2024)
- [On Verbalized Confidence Scores for LLMs](https://mlsanity.com/paper/2412.14737/) (2024)
- [Alignment for Honesty](https://mlsanity.com/paper/2312.07000/) (2023)
- [LogiQA: A Challenge Dataset for Machine Reading Comprehension with Logical Reasoning](https://mlsanity.com/paper/2007.08124/) (2020)
- [Reasoning Models Better Express Their Confidence](https://mlsanity.com/paper/2505.14489/) (2025)
- [Learning to Trust Your Feelings: Leveraging Self-awareness in LLMs for Hallucination Mitigation](https://mlsanity.com/paper/2401.15449/) (2024)
- [Reasoning about Uncertainty: Do Reasoning Models Know When They Don't Know?](https://mlsanity.com/paper/2506.18183/) (2025)
- [ALCUNA: Large Language Models Meet New Knowledge](https://mlsanity.com/paper/2310.14820/) (2023)
- [Fact-and-Reflection (FaR) Improves Confidence Calibration of Large Language Models](https://mlsanity.com/paper/2402.17124/) (2024)
- [Trust Me, I'm Wrong: LLMs Hallucinate with Certainty Despite Knowing the Answer](https://mlsanity.com/paper/2502.12964/) (2025)
- [Turning Dust into Gold: Distilling Complex Reasoning Capabilities from LLMs by Leveraging Negative Data](https://mlsanity.com/paper/2312.12832/) (2023)

## Built on by (most cited first, 3 of 3)

- [SVR: Self-Verifying Refinement via Joint Verdict-Confidence Reinforcement Learning for Adaptive Test-Time Compute](https://mlsanity.com/paper/2607.28457/) (2026)
- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)
- [On the Pitfalls of Verbalized Confidence Priors for Calibrating Large Reasoning Models](https://mlsanity.com/paper/2609.32470/) (2026)

## Abstract (arXiv)

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 Correctness and Confidence Calibration Reinforcement Learning (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 Confidence-based Adaptive Test Time Scaling (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.