# Kernel Token Contradiction: a Fast and Principled Approach for LLM Claim Uncertainty Quantification

arXiv: https://arxiv.org/abs/2608.22506 · HTML: https://mlsanity.com/paper/2608.22506/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 36 references that are in the map.
- First posted on arXiv 23 Aug 2026.

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [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)
- [The Falcon Series of Open Language Models](https://mlsanity.com/paper/2311.16867/) (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)
- [Fact-Checking the Output of Large Language Models via Token-Level Uncertainty Quantification](https://mlsanity.com/paper/2403.04696/) (2024)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Models](https://mlsanity.com/paper/2307.01379/) (2023)
- [To Believe or Not to Believe Your LLM](https://mlsanity.com/paper/2406.02543/) (2024)
- [A Comprehensive Survey of Hallucination in Large Language, Image, Video and Audio Foundation Models](https://mlsanity.com/paper/2405.09589/) (2024)
- [Enhancing Uncertainty-Based Hallucination Detection with Stronger Focus](https://mlsanity.com/paper/2311.13230/) (2023)
- [Looking for a Needle in a Haystack: A Comprehensive Study of Hallucinations in Neural Machine Translation](https://mlsanity.com/paper/2208.05309/) (2022)
- [CroissantLLM: A Truly Bilingual French-English Language Model](https://mlsanity.com/paper/2402.00786/) (2024)
- [Beyond Semantic Entropy: Boosting LLM Uncertainty Quantification with Pairwise Semantic Similarity](https://mlsanity.com/paper/2506.00245/) (2025)
- [SemEval-2025 Task 3: Mu-SHROOM, the Multilingual Shared Task on Hallucinations and Related Observable Overgeneration Mistakes](https://mlsanity.com/paper/2504.11975/) (2025)
- [Cost-Effective Hallucination Detection for LLMs](https://mlsanity.com/paper/2407.21424/) (2024)
- [When Models Lie, We Learn: Multilingual Span-Level Hallucination Detection with PsiloQA](https://mlsanity.com/paper/2510.04849/) (2025)
- [HalluEntity: Benchmarking and Understanding Entity-Level Hallucination Detection](https://mlsanity.com/paper/2502.11948/) (2025)
- [Improving Semantic Uncertainty Quantification in LVLMs with Semantic Gaussian Processes](https://mlsanity.com/paper/2512.14177/) (2025)
- [Developing a Reliable, Fast, General-Purpose Hallucination Detection and Mitigation Service](https://mlsanity.com/paper/2407.15441/) (2024)
- [MUCH: A Multilingual Claim Hallucination Benchmark](https://mlsanity.com/paper/2511.17081/) (2025)

## Abstract (arXiv)

Claim-level Uncertainty Quantification (UQ) aims to mitigate the lack of reliability of Large Language Models (LLMs) by evaluating the factuality of each claim in their outputs. We introduce Kernel Token Contradiction (KTC), a lightweight approach to compute claim-level UQ under realistic white-box conditions. KTC represents the candidate tokens involved in LLM generation as a positive semi-definite kernel that integrates both the LLM's conditional distribution and a token contradiction score. We then use the Von Neumann entropy to quantify the uncertainty of this kernel. To estimate token contradiction, we develop a new approach based on frequency statistics from the Wikipedia corpus. Although CPU-only, our approach achieves over an 8.2x speedup compared to state-of-the-art GPU-accelerated methods based on cross-encoders, and over a 65x speedup compared to CPU-only methods with comparable performance. Our evaluation spans two benchmarks across four European languages and 16 different models. KTC not only matches the average performance of existing methods but also outperforms them in high-precision regimes. This combination of computational efficiency and accuracy makes real-time monitoring of LLM outputs practical in production.