# Fact-and-Reflection (FaR) Improves Confidence Calibration of Large Language Models

arXiv: https://arxiv.org/abs/2402.17124 · HTML: https://mlsanity.com/paper/2402.17124/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 48 references that are in the map.
- First posted on arXiv 27 Feb 2024.

## Builds on (most cited first, 29 of 29)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [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)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [Baichuan 2: Open Large-scale Language Models](https://mlsanity.com/paper/2309.10305/) (2023)
- [Enabling Large Language Models to Generate Text with Citations](https://mlsanity.com/paper/2305.14627/) (2023)
- [Calibration of Pre-trained Transformers](https://mlsanity.com/paper/2003.07892/) (2020)
- [Prompting GPT-3 To Be Reliable](https://mlsanity.com/paper/2210.09150/) (2022)
- [Generated Knowledge Prompting for Commonsense Reasoning](https://mlsanity.com/paper/2110.08387/) (2021)
- [A Stitch in Time Saves Nine: Detecting and Mitigating Hallucinations of LLMs by Validating Low-Confidence Generation](https://mlsanity.com/paper/2307.03987/) (2023)
- [Relying on the Unreliable: The Impact of Language Models' Reluctance to Express Uncertainty](https://mlsanity.com/paper/2401.06730/) (2024)
- [ExpertQA: Expert-Curated Questions and Attributed Answers](https://mlsanity.com/paper/2309.07852/) (2023)
- [Navigating the Grey Area: How Expressions of Uncertainty and Overconfidence Affect Language Models](https://mlsanity.com/paper/2302.13439/) (2023)
- [Improving Faithfulness in Abstractive Summarization with Contrast Candidate Generation and Selection](https://mlsanity.com/paper/2104.09061/) (2021)
- [Question Answering with Subgraph Embeddings](https://mlsanity.com/paper/1406.3676/) (2014)
- ["According to ...": Prompting Language Models Improves Quoting from Pre-Training Data](https://mlsanity.com/paper/2305.13252/) (2023)

## Built on by (most cited first, 27 of 27)

- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Self-Correcting Decoding with Generative Feedback for Mitigating Hallucinations in Large Vision-Language Models](https://mlsanity.com/paper/2502.06130/) (2025)
- [Cycles of Thought: Measuring LLM Confidence through Stable Explanations](https://mlsanity.com/paper/2406.03441/) (2024)
- [A Survey on the Honesty of Large Language Models](https://mlsanity.com/paper/2409.18786/) (2024)
- [Large Language Models Do Multi-Label Classification Differently](https://mlsanity.com/paper/2505.17510/) (2025)
- [Read Your Own Mind: Reasoning Helps Surface Self-Confidence Signals in LLMs](https://mlsanity.com/paper/2505.23845/) (2025)
- [Long Context Scaling: Divide and Conquer via Multi-Agent Question-driven Collaboration](https://mlsanity.com/paper/2505.20625/) (2025)
- [Prompt4Trust: A Reinforcement Learning Prompt Augmentation Framework for Clinically-Aligned Confidence Calibration in Multimodal Large Language Models](https://mlsanity.com/paper/2507.09279/) (2025)
- [Mind the Generation Process: Fine-Grained Confidence Estimation During LLM Generation](https://mlsanity.com/paper/2508.12040/) (2025)
- [Seven simple steps for log analysis in AI systems](https://mlsanity.com/paper/2604.09563/) (2026)
- [Hallucinations Undermine Trust; Metacognition is a Way Forward](https://mlsanity.com/paper/2605.01428/) (2026)
- [Comparing Uncertainty Measurement and Mitigation Methods for Large Language Models: A Systematic Review](https://mlsanity.com/paper/2504.18346/) (2025)
- [LLM Hallucination Detection: A Fast Fourier Transform Method Based on Hidden Layer Temporal Signals](https://mlsanity.com/paper/2509.13154/) (2025)
- [CoFi-Dec: Hallucination-Resistant Decoding via Coarse-to-Fine Generative Feedback in Large Vision-Language Models](https://mlsanity.com/paper/2512.23453/) (2025)
- [Scaling with Confidence: Calibrating Confidence of LLMs for Adaptive Test Time Scaling](https://mlsanity.com/paper/2607.01612/) (2026)
- [Generation Space Size: Understanding and Calibrating Open-Endedness of LLM Generations](https://mlsanity.com/paper/2510.12699/) (2025)
- [Can LLMs Use Linguistic Uncertainty Markers to Reliably Reflect Intrinsic Confidence?](https://mlsanity.com/paper/2605.28778/) (2026)
- [Improving constraint-based discovery with robust propagation and reliable LLM priors](https://mlsanity.com/paper/2509.23570/) (2025)
- [LLM Hallucination Detection: HSAD](https://mlsanity.com/paper/2509.23580/) (2025)
- [Mitigating hallucinations in healthcare LLMs with granular fact-checking and domain-specific adaptation](https://mlsanity.com/paper/2512.16189/) (2025)
- [Metacognition in LLMs: Foundations, Progress, and Opportunities](https://mlsanity.com/paper/2607.11881/) (2026)
- [Fact-Checking with Large Language Models via Probabilistic Certainty and Consistency](https://mlsanity.com/paper/2601.02574/) (2026)
- [CORE: Comprehensive Ontological Relation Evaluation for Large Language Models](https://mlsanity.com/paper/2602.06446/) (2026)
- [Deep Learning-based Method for Expressing Knowledge Boundary of Black-Box LLM](https://mlsanity.com/paper/2602.10801/) (2026)
- [Latent Confidence Alignment for LLM Self-Assessment](https://mlsanity.com/paper/2606.21937/) (2026)
- [Routing Without Training: Controllable-Ratio LLM Offloading via Reliability Gating](https://mlsanity.com/paper/2607.20481/) (2026)
- [Evaluating and Recalibrating Probabilistic Classifiers from One-Bit Threshold Queries](https://mlsanity.com/paper/2609.05125/) (2026)

## Abstract (arXiv)

For a LLM to be trustworthy, its confidence level should be well-calibrated with its actual performance. While it is now common sense that LLM performances are greatly impacted by prompts, the confidence calibration in prompting LLMs has yet to be thoroughly explored. In this paper, we explore how different prompting strategies influence LLM confidence calibration and how it could be improved. We conduct extensive experiments on six prompting methods in the question-answering context and we observe that, while these methods help improve the expected LLM calibration, they also trigger LLMs to be over-confident when responding to some instances. Inspired by human cognition, we propose Fact-and-Reflection (FaR) prompting, which improves the LLM calibration in two steps. First, FaR elicits the known "facts" that are relevant to the input prompt from the LLM. And then it asks the model to "reflect" over them to generate the final answer. Experiments show that FaR prompting achieves significantly better calibration; it lowers the Expected Calibration Error by 23.5% on our multi-purpose QA tasks. Notably, FaR prompting even elicits the capability of verbally expressing concerns in less confident scenarios, which helps trigger retrieval augmentation for solving these harder instances.