The reliability of Large Language Models (LLMs) in high-stakes domains such as healthcare, law, and scientific discovery is often compromised by hallucinations. These failures typically stem from two sources: data-driven hallucinations and reasoning-driven hallucinations. However, existing detection methods usually address only one source and rely on task-specific heuristics, limiting their generalization to complex scenarios. To overcome these limitations, we introduce the Hallucination Risk Bound, a unified theoretical framework that formally decomposes hallucination risk into data-driven and reasoning-driven components, linked respectively to training-time mismatches and inference-time instabilities. This provides a principled foundation for analyzing how hallucinations emerge and evolve. Building on this foundation, we introduce HalluGuard, an NTK-based score that leverages the induced geometry and captured representations of the NTK to jointly identify data-driven and reasoning-driven hallucinations. We evaluate HalluGuard on 10 diverse benchmarks, 11 competitive baselines, and 9 popular LLM backbones, consistently achieving state-of-the-art performance in detecting diverse forms of LLM hallucinations.

翻译：大语言模型在医疗、法律和科学发现等高风险领域中的可靠性常因幻觉问题而受到损害。这些故障通常源于两个根源：数据驱动的幻觉与推理驱动的幻觉。然而，现有的检测方法通常仅针对单一根源，且依赖于特定任务的启发式规则，限制了其在复杂场景中的泛化能力。为克服这些局限，我们提出了幻觉风险边界——一个统一的理论框架，该框架将幻觉风险形式化地分解为数据驱动与推理驱动两个组成部分，分别关联于训练时的失配与推理时的不稳定性。这为分析幻觉如何产生与演化提供了原则性基础。基于此框架，我们提出了HalluGuard，一种基于神经正切核的评分方法，该方法利用神经正切核所诱导的几何结构及其捕获的表征，以联合识别数据驱动与推理驱动的幻觉。我们在10个多样化基准测试、11个竞争性基线方法与9个主流大语言模型骨干网络上对HalluGuard进行评估，其在检测多种形式的大语言模型幻觉方面始终达到最先进的性能水平。