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

🚀 HalluGuard: Demystifying Data-Driven and Reasoning-Driven Hallucinations in LLMs
Accepted at ICLR 2026

In this work, we introduce HalluGuard, a unified, theory-driven framework for hallucination detection in large language models, accepted at ICLR 2026.
Rather than treating hallucination as a single failure mode, HalluGuard explicitly decomposes hallucinations into data-driven and reasoning-driven components—and detects both at inference time, with no retraining, no labels, and no external references.

😆 Key Takeaways

🧠 Two Sources of Hallucination

LLM hallucinations arise from two fundamentally different mechanisms:

• Data-driven hallucinations
  Errors rooted in biased, incomplete, or mismatched knowledge acquired during pretraining or finetuning.

• Reasoning-driven hallucinations
  Errors caused by instability and error amplification during multi-step autoregressive decoding.

Most existing detectors focus on only one of these. HalluGuard shows that real hallucinations often emerge from their interaction and evolve across decoding steps.

📐 Hallucination Risk Bound (Theory)

We introduce a Hallucination Risk Bound, which formally decomposes total hallucination risk into:

• a representation bias term (training-time mismatch), and
• a decoding instability term (inference-time amplification).

The analysis reveals a key insight:
hallucinations originate from semantic approximation gaps and are then exponentially amplified during long-horizon generation.

This provides a principled explanation of how hallucinations emerge and evolve in LLMs.

🔍 HalluGuard Score (Method)

Building on this theory, we propose HalluGuard, a lightweight NTK-based hallucination score:

$$\mathrm{H}\mathrm{A}\mathrm{L}\mathrm{L}\mathrm{U}\mathrm{G}\mathrm{U}\mathrm{A}\mathrm{R}\mathrm{D}(u_h)=\det (K)+\log {\sigma }_{\max }-\log \text{\hspace{0.17em}⁣}(\kappa (K{)}^2)\mathrm{.}\backslash mathrm\{HALLUGUARD\}(u\_h)\; =\; \backslash det(K)\; +\; \backslash log\; \backslash sigma\_\{\backslash max\}\; -\; \backslash log\backslash !\backslash big(\backslash kappa(K)^2\backslash big).$$

Higher HalluGuard score ⇒ lower hallucination risk.

📊 Strong Empirical Results

We evaluate HalluGuard across:

• 10 benchmarks (QA, math reasoning, instruction following),
• 11 competitive baselines, and
• 9 LLM backbones (from GPT-2 to 70B-scale models).

Results:

• 🏆 Consistent state-of-the-art AUROC / AUPRC across all task families
• 🔍 Especially strong gains on multi-step reasoning benchmarks (MATH-500, BBH)
• 🧩 Robust detection of fine-grained semantic hallucinations (PAWS), even when surface forms are nearly identical

🧭 Beyond Detection: Test-Time Guidance

HalluGuard can also be used to guide test-time inference, significantly improving reasoning accuracy by steering generation away from unstable trajectories—without modifying or retraining the model.

🔑 Takeaway

HalluGuard (ICLR 2026) provides:

• a theoretical lens for understanding how hallucinations emerge and evolve, and
• a practical, plug-and-play detector for modern LLMs.

It bridges representation geometry and decoding dynamics, offering a unified foundation for reliable reasoning and uncertainty-aware inference.

Feedback and discussion are very welcome 🙌