# MMD-Flagger: Leveraging Maximum Mean Discrepancy to Detect Hallucinations

arXiv: https://arxiv.org/abs/2506.01367 · HTML: https://mlsanity.com/paper/2506.01367/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical and scientific domain agents, one of 16 directions in LLM agents and tool use.
- Builds on 59 of its 84 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Placed in

- LLM agents and tool use / [Medical and scientific domain agents](https://mlsanity.com/agents/medical-and-scientific-domain-agents/)

## Builds on (most cited first, 30 of 59)

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- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [fairseq: A Fast, Extensible Toolkit for Sequence Modeling](https://mlsanity.com/paper/1904.01038/) (2019)
- [No Language Left Behind: Scaling Human-Centered Machine Translation](https://mlsanity.com/paper/2207.04672/) (2022)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Language-agnostic BERT Sentence Embedding](https://mlsanity.com/paper/2007.01852/) (2020)
- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Chain-of-Verification Reduces Hallucination in Large Language Models](https://mlsanity.com/paper/2309.11495/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Unsupervised Quality Estimation for Neural Machine Translation](https://mlsanity.com/paper/2005.10608/) (2020)
- [CometKiwi: IST-Unbabel 2022 Submission for the Quality Estimation Shared Task](https://mlsanity.com/paper/2209.06243/) (2022)
- [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)
- [The Effect of Sampling Temperature on Problem Solving in Large Language Models](https://mlsanity.com/paper/2402.05201/) (2024)
- [The Curious Case of Hallucinations in Neural Machine Translation](https://mlsanity.com/paper/2104.06683/) (2021)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)

## Abstract (arXiv)

Large Language Models (LLMs) are increasingly integrated into agentic AI systems, yet their propensity to generate hallucinations remains a critical safety concern. Detecting these factual errors at test-time, particularly without ground-truth labels, is essential for building trustworthy autonomous agents. We propose MMD-Flagger, an hallucination detection method that utilizes Maximum Mean Discrepancy (MMD) and monitors the stability of LLM outputs across varying decoding temperatures. Our method tracks the MMD trajectory between a LLM's response at a certain decoding configuration and a set of stochastic samples, identifying hallucinations based on the trajectory's characteristic shape. We evaluate MMDFlagger on multi-lingual claim verification benchmarks (MUCH) using modern LLMs like Llama-3 families and Gemma-3.