# CritiCal: Can Critique Help LLM Uncertainty or Confidence Calibration?

arXiv: https://arxiv.org/abs/2510.24505 · HTML: https://mlsanity.com/paper/2510.24505/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 46 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 30 of 34)

- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Generating Sequences by Learning to Self-Correct](https://mlsanity.com/paper/2211.00053/) (2022)
- [Beyond Binary Rewards: Training LMs to Reason About Their Uncertainty](https://mlsanity.com/paper/2507.16806/) (2025)
- [Can Large Language Models Really Improve by Self-critiquing Their Own Plans?](https://mlsanity.com/paper/2310.08118/) (2023)
- [SaySelf: Teaching LLMs to Express Confidence with Self-Reflective Rationales](https://mlsanity.com/paper/2405.20974/) (2024)
- [From Automation to Autonomy: A Survey on Large Language Models in Scientific Discovery](https://mlsanity.com/paper/2505.13259/) (2025)
- [Critique-GRPO: Advancing LLM Reasoning with Natural Language and Numerical Feedback](https://mlsanity.com/paper/2506.03106/) (2025)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [Efficient Test-Time Scaling via Self-Calibration](https://mlsanity.com/paper/2503.00031/) (2025)
- [API Is Enough: Conformal Prediction for Large Language Models Without Logit-Access](https://mlsanity.com/paper/2403.01216/) (2024)
- [ConU: Conformal Uncertainty in Large Language Models with Correctness Coverage Guarantees](https://mlsanity.com/paper/2407.00499/) (2024)
- [Critique Fine-Tuning: Learning to Critique is More Effective than Learning to Imitate](https://mlsanity.com/paper/2501.17703/) (2025)
- [A Survey of Uncertainty Estimation Methods on Large Language Models](https://mlsanity.com/paper/2503.00172/) (2025)
- [ConfTuner: Training Large Language Models to Express Their Confidence Verbally](https://mlsanity.com/paper/2508.18847/) (2025)
- [NewtonBench: Benchmarking Generalizable Scientific Law Discovery in LLM Agents](https://mlsanity.com/paper/2510.07172/) (2025)
- [The Curse of CoT: On the Limitations of Chain-of-Thought in In-Context Learning](https://mlsanity.com/paper/2504.05081/) (2025)

## Built on by (most cited first, 4 of 4)

- [PlanBench-XL: Evaluating Long-Horizon Planning of LLM Tool-Use Agents in Large-Scale Tool Ecosystems](https://mlsanity.com/paper/2606.22388/) (2026)
- [Illusions of Confidence? Diagnosing LLM Truthfulness via Neighborhood Consistency](https://mlsanity.com/paper/2601.05905/) (2026)
- [EvolvingWorld: An Open-Schema Framework for Co-Evolving Role-Play Agents and World Model in Interactive Literary World](https://mlsanity.com/paper/2607.17250/) (2026)
- [MultivationBench: A Benchmark for Multimodal Sequential Motivation Reasoning](https://mlsanity.com/paper/2607.26465/) (2026)

## Abstract (arXiv)

Accurate confidence calibration in Large Language Models (LLMs) is critical for safe use in high-stakes domains, where clear verbalized confidence enhances user trust. Traditional methods that mimic reference confidence expressions often fail to capture the reasoning needed for accurate confidence assessment. We propose natural language critiques as a solution, ideally suited for confidence calibration, as precise gold confidence labels are hard to obtain and often require multiple generations. This paper studies how natural language critiques can enhance verbalized confidence, addressing: (1) What to critique: uncertainty (question-focused) or confidence (answer-specific)? Analysis shows confidence suits multiple-choice tasks, while uncertainty excels in open-ended scenarios. (2) How to critique: self-critique or critique calibration training? We propose Self-Critique, enabling LLMs to critique and optimize their confidence beyond mere accuracy, and CritiCal, a novel Critique Calibration training method that leverages natural language critiques to improve confidence calibration, moving beyond direct numerical optimization. Experiments show that CritiCal significantly outperforms Self-Critique and other competitive baselines, even surpassing its teacher model, GPT-4o, in complex reasoning tasks. CritiCal also shows robust generalization in out-of-distribution settings, advancing LLM's reliability.