# When an LLM is apprehensive about its answers -- and when its uncertainty is justified

arXiv: https://arxiv.org/abs/2503.01688 · HTML: https://mlsanity.com/paper/2503.01688/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Builds on (most cited first, 18 of 18)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [Fact-Checking the Output of Large Language Models via Token-Level Uncertainty Quantification](https://mlsanity.com/paper/2403.04696/) (2024)
- [Large Legal Fictions: Profiling Legal Hallucinations in Large Language Models](https://mlsanity.com/paper/2401.01301/) (2024)
- [LM-Polygraph: Uncertainty Estimation for Language Models](https://mlsanity.com/paper/2311.07383/) (2023)
- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [To Believe or Not to Believe Your LLM](https://mlsanity.com/paper/2406.02543/) (2024)
- [Mind the Confidence Gap: Overconfidence, Calibration, and Distractor Effects in Large Language Models](https://mlsanity.com/paper/2502.11028/) (2025)
- [SciQAG: A Framework for Auto-Generated Science Question Answering Dataset with Fine-grained Evaluation](https://mlsanity.com/paper/2405.09939/) (2024)
- [Word-Sequence Entropy: Towards Uncertainty Estimation in Free-Form Medical Question Answering Applications and Beyond](https://mlsanity.com/paper/2402.14259/) (2024)
- [WiCkeD: A Simple Method to Make Multiple Choice Benchmarks More Challenging](https://mlsanity.com/paper/2502.18316/) (2025)

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

- [Beyond Early-Token Bias: Model-Specific and Language-Specific Position Effects in Multilingual LLMs](https://mlsanity.com/paper/2505.16134/) (2025)
- [Are LLM Evaluators Really Narcissists? Sanity Checking Self-Preference Evaluations](https://mlsanity.com/paper/2601.22548/) (2026)
- [Complexity-aware fine-tuning](https://mlsanity.com/paper/2506.21220/) (2025)
- [Beyond Confidence: The Rhythms of Reasoning in Generative Models](https://mlsanity.com/paper/2602.10816/) (2026)

## Abstract (arXiv)

Uncertainty estimation is crucial for evaluating Large Language Models (LLMs), particularly in high-stakes domains where incorrect answers result in significant consequences. Numerous approaches consider this problem, while focusing on a specific type of uncertainty, ignoring others. We investigate what estimates, specifically token-wise entropy and model-as-judge (MASJ), would work for multiple-choice question-answering tasks for different question topics. Our experiments consider three LLMs: Phi-4, Mistral, and Qwen of different sizes from 1.5B to 72B and 14 topics. While MASJ performs similarly to a random error predictor, the response entropy predicts model error in knowledge-dependent domains and serves as an effective indicator of question difficulty: for biology ROC AUC is 0.73. This correlation vanishes for the reasoning-dependent domain: for math questions ROC-AUC is 0.55. More principally, we found out that the entropy measure required a reasoning amount. Thus, data-uncertainty related entropy should be integrated within uncertainty estimates frameworks, while MASJ requires refinement. Moreover, existing MMLU-Pro samples are biased, and should balance required amount of reasoning for different subdomains to provide a more fair assessment of LLMs performance.