Lyapunov Probes for Hallucination Detection in Large Foundation Models

Large Language Models (LLMs) are powerful and widely adopted, but their practical impact is limited by the well-known hallucination phenomenon. While recent hallucination detection methods have made notable progress, we find most of them overlook the dynamic nature and underlying mechanisms of it. To address this gap, we propose HalluSAE, a phase transition-inspired framework that models hallucination as a critical shift in the model's latent dynamics. By modeling the generation process as a trajectory through a potential energy landscape, HalluSAE identifies critical transition zones and attributes factual errors to specific high-energy sparse features. Our approach consists of three stages: (1) Potential Energy Empowered Phase Zone Localization via sparse autoencoders and a geometric potential energy metric; (2) Hallucination-related Sparse Feature Attribution using contrastive logit attribution; and (3) Probing-based Causal Hallucination Detection through linear probes on disentangled features. Extensive experiments on Gemma-2-9B demonstrate that HalluSAE achieves state-of-the-art hallucination detection performance.

Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing tasks. However, their tendency to generate hallucinations, namely factually incorrect or unfaithful outputs, poses a critical obstacle to their deployment in high-stakes applications. Although recent hallucination detection methods have made encouraging progress, they typically rely on costly output-level consistency checks or static hidden-state probes that capture shallow dataset-specific patterns, leading to substantial degradation under cross-dataset evaluation. In this work, we propose AURORA, a novel hallucination detection framework that shifts the focus from static representations to the weight-gradient dynamics of LLMs. Our key insight is that hallucinated and faithful answers induce qualitatively different gradient update patterns on the model's parameters. Specifically, hallucinated samples trigger asymmetric and structurally misaligned gradients, which can be captured through two complementary features: (1) the skewness of the cosine similarity distribution between weight matrices and their gradient update directions, and (2) the rotation ratio, which quantifies how much the gradient update reorients the singular-vector basis of weight matrices via SVD. AURORA achieves strong hallucination detection performance across four model families and four benchmark datasets. Further analyses demonstrate that our method scales effectively across model sizes and transfers to out-of-domain tasks, including mathematical reasoning and vision-language scenarios.

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.