# Entropy Distribution as a Fingerprint for Hallucinations in Generative Models

arXiv: https://arxiv.org/abs/2605.28264 · HTML: https://mlsanity.com/paper/2605.28264/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 47 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 30 of 36)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [The Falcon Series of Open Language Models](https://mlsanity.com/paper/2311.16867/) (2023)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [A Stitch in Time Saves Nine: Detecting and Mitigating Hallucinations of LLMs by Validating Low-Confidence Generation](https://mlsanity.com/paper/2307.03987/) (2023)
- [Out-of-Distribution Detection and Selective Generation for Conditional Language Models](https://mlsanity.com/paper/2209.15558/) (2022)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Long-form factuality in large language models](https://mlsanity.com/paper/2403.18802/) (2024)
- [Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Models](https://mlsanity.com/paper/2307.01379/) (2023)
- [Fine-grained Hallucination Detection and Editing for Language Models](https://mlsanity.com/paper/2401.06855/) (2024)
- [Lookback Lens: Detecting and Mitigating Contextual Hallucinations in Large Language Models Using Only Attention Maps](https://mlsanity.com/paper/2407.07071/) (2024)
- [Conformal Prediction with Large Language Models for Multi-Choice Question Answering](https://mlsanity.com/paper/2305.18404/) (2023)
- [HaloScope: Harnessing Unlabeled LLM Generations for Hallucination Detection](https://mlsanity.com/paper/2409.17504/) (2024)
- [A Survey of Uncertainty Estimation Methods on Large Language Models](https://mlsanity.com/paper/2503.00172/) (2025)
- [Do LLMs Know about Hallucination? An Empirical Investigation of LLM's Hidden States](https://mlsanity.com/paper/2402.09733/) (2024)
- [Look Before You Leap: An Exploratory Study of Uncertainty Measurement for Large Language Models](https://mlsanity.com/paper/2307.10236/) (2023)

## Abstract (arXiv)

Large Language Models (LLMs) often generate factually incorrect outputs, commonly termed hallucinations, that undermine trust and limit deployment in high-stakes settings. Existing hallucination detection methods typically require multiple forward passes, or access to model internals. In this work, we provide theoretical background and empirical evidence that the distribution of token-level entropies, beyond the mean captured by perplexity or length-normalised entropy, serves as a fingerprint of hallucination, with distributional shape and tail behaviour carrying independent signal. We formalize hallucination detection as a statistical hypothesis test and propose the Calibrated Entropy Score (CES), a lightweight algorithm requiring only a single forward pass and black-box access to token logits. CES combines the mean signal with the maximum signal of the generated entropy through a calibrated reference CDF, producing scores that are directly comparable across models and tasks. We establish finite-sample calibration guarantees via a novel random-length Dvoretzky--Kiefer--Wolfowitz inequality, and also prove that CES detects hallucinations with probability converging to one exponentially fast in the generation length. Across eight QA benchmarks and ten generator models spanning open-source and API access models, CES achieves the highest detection performance among all single-pass black-box methods while providing formal error guarantees that existing heuristics lack. Remarkably, CES is statistically indistinguishable from multi-sample methods that require far greater computational cost, closing the gap between lightweight and expensive detection and making it suitable for real-time, large-scale deployment.