HalluGuard: Demystifying Data-Driven and Reasoning-Driven Hallucinations in LLMs

TL;DR

The paper tackles hallucinations in LLMs by separating data-driven and reasoning-driven sources and introduces Hallucination Risk Bound as a unified framework that decomposes risk into training-time mismatches and inference-time instabilities. Building on this, HalluGuard uses an NTK-based proxy, combining representational adequacy, rollout amplification, and spectral conditioning to jointly detect both types of hallucinations. Empirical validation across 10 benchmarks, 11 baselines, and 9 backbones shows HalluGuard achieving state-of-the-art performance, with additional gains for test-time inference and fine-grained semantic checks. The work offers a principled approach for robust deployment of LLMs in high-stakes domains and suggests paths toward prognostic indicators in interactive dialogue settings.

Abstract

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.

Figures (14)

• Figure 1: An illustration of hallucination emerging and evolving in the context of disease diagnosis.
• Figure 2: Ablation results comparing individual terms with ground-truth trends on SQuAD (top) and Math-500 (bottom).
• Figure 3: Ablation study of the stability term ($-\log \kappa^2$) on MATH500.
• Figure 4: Per-Question Inference Time (Seconds) on BBH Across Hallucination Detection Methods.
• Figure 5: Per-Question Inference Time (Seconds) on HaluEval Across Hallucination Detection Methods.

Theorems & Definitions (12)

• Lemma B.1: Best-approximation error under source condition
• proof
• Lemma B.2: Lower-bounding $\lambda_r$ by $\det(\mathcal{K})$
• proof
• Theorem B.3: Determinant-based adequacy bound with explicit constants
• proof
• Theorem B.4: Amplification bound with exact constant
• proof
• Lemma B.5: Projector perturbation bound
• proof : Proof idea