From Flat Facts to Sharp Hallucinations: Detecting Stubborn Errors via Gradient Sensitivity

Yee Zhing Liew; Andrew Huey Ping Tan; Anwar P. P. Abdul Majeed

cs.LGMay 1, 2026

From Flat Facts to Sharp Hallucinations: Detecting Stubborn Errors via Gradient Sensitivity

Authors: Yee Zhing Liew, Andrew Huey Ping Tan, Anwar P. P. Abdul Majeed

Organizations: School of Intelligent Manufacturing Ecosystem, Xi’an Jiaotong-Liverpool University, People’s Republic of China · Department of Computer Science, University of Liverpool, United Kingdom · Faculty of Engineering and Technology, Sunway University, Malaysia · School of Robotics, Xi’an Jiaotong-Liverpool University, People’s Republic of China

Abstract

Traditional hallucination detection fails on "Stubborn Hallucinations" - errors where LLMs are confidently wrong. We propose a geometric solution: Embedding-Perturbed Gradient Sensitivity (EPGS). We hypothesize that while robust facts reside in flat minima, stubborn hallucinations sit in sharp minima, supported by brittle memorization. EPGS detects this sharpness by perturbing input embeddings with Gaussian noise and measuring the resulting spike in gradient magnitude. This acts as an efficient proxy for the Hessian spectrum, differentiating stable knowledge from unstable memorization. Our experiments show that EPGS significantly outperforms entropy-based and representation-based baselines, providing a robust signal for detecting high-confidence factual errors.

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May 29, 2026 · cs.LGJ/K move · Enter open · S save

FLaG: Fine-Grained Latent Grouping for Hallucination Detection

Wentao Ye, Liyao Li, Zhiqing Xiao, Muzhi Zhu+5

Zhejiang University · Hangzhou, Zhejiang, China · Nanyang Technological University · Singapore, Singapore

Hallucinations in large language models (LLMs) arise from heterogeneous failure mechanisms, making reliable detection difficult for any single global uncertainty score. In this work, we formulate hallucination detection as a mechanism-aware evidence aggregation problem, where diverse representation- and token-level signals must be interpreted under multiple latent explanations. We propose FLaG, a lightweight hallucination detection framework that models correctness through a set of latent evidence groups. Each instance is softly associated with multiple groups via an energy-based routing mechanism, and group-conditional reliability signals are combined through a principled log-marginal aggregation. This design enables FLaG to capture heterogeneous hallucination patterns while remaining invariant to decision thresholds and evaluation metrics. The framework operates as a frozen-model head, requires no modification to the underlying language model, and incurs minimal computational overhead. We further provide a theoretical perspective that connects FLaG to optimal evidence aggregation under heterogeneous error mechanisms, showing that the Bayes-optimal test statistic necessarily admits a log-marginal form and that FLaG constitutes a tractable approximation with a controllable error bound. Extensive experiments across multiple benchmarks and LLM backbones demonstrate that FLaG consistently achieves SOTA performance, while exhibiting robust transfer across datasets and models, and remaining effective under limited supervision.

Hallucination Detection

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Abstract

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