Logical Consistency as a Bridge: Improving LLM Hallucination Detection via Label Constraint Modeling between Responses and Self-Judgments

Large Language Models (LLMs) often hallucinate, limiting their reliability in sensitive applications. In black-box settings, several self-consistency-based techniques have been proposed for hallucination detection. We empirically show that these methods perform nearly as well as a supervised (black-box) oracle, leaving limited room for further gains within this paradigm. To address this limitation, we explore cross-model consistency checking between the target model and an additional verifier LLM. With this extra information, we observe improved oracle performance compared to purely self-consistency-based methods. We then propose a budget-friendly, two-stage detection algorithm that calls the verifier model only for a subset of cases. It dynamically switches between self-consistency and cross-consistency based on an uncertainty interval of the self-consistency classifier. We provide a geometric interpretation of consistency-based hallucination detection methods through the lens of kernel mean embeddings, offering deeper theoretical insights. Extensive experiments on QA-style hallucination detection benchmarks show that this approach maintains high detection performance while significantly reducing computational cost.

Hallucination in large language models (LLMs), defined as the generation of factually incorrect or unsupported content, remains a critical barrier to reliable deployment. We present BEACON (Behavioral Entropy Aggregation for Cross-model hallucination detectiON), a black-box hallucination detection framework that operates purely on model outputs without requiring access to internal representations or external knowledge bases. BEACON extracts a 31-dimensional feature vector from structured multi-pass generation, integrating NLI-based semantic entropy, embedding geometry, chain-of-thought consistency, and paraphrase stability signals. A gradient-boosted classifier trained on 7,617 labeled examples across seven benchmarks achieves 0.8123 +/- 0.0102 AUROC (95% CI: 0.7632-0.8251), outperforming standalone semantic entropy (+0.2298) and SelfCheckGPT-style consistency baselines (+0.2457). Feature importance analysis shows that hallucination is inherently multi-dimensional, requiring combined uncertainty signals. An efficient 5-call variant achieves 0.7795 AUROC, enabling practical deployment across black-box LLM APIs.

Large language models (LLMs) often hallucinate by generating factually incorrect or unfaithful content, posing significant risks to their safe use. Detecting such hallucinations is particularly challenging under the zero-source constraint, where no model internals or external references are available, and detection must rely solely on the textual query-answer pair. In this paper, we propose Human-like Criteria Probing for Hallucination Detection (HCPD), a paradigm that emulates the multi-faceted reasoning of human evaluators. Its core is a Human-like Criteria Probing (HCP) mechanism, in which a LLM agent adaptively decomposes its judgment into a weighted set of interpretable criteria and aggregates criterion-specific scores into a final truthfulness measure. To achieve this adaptive capability, we introduce a reward-based alignment scheme using only weak supervision from semantic consistency. At inference, we employ a multi-sampling aggregation strategy to ensure robust decisions while preserving full interpretability. We further provide theoretical analysis supporting the reliability of our approach. Extensive experiments show that HCPD consistently outperforms state-of-the-art baselines, offering an effective and explainable solution for zero-source hallucination detection. Code is available at https://github.com/TRISKEL10N/HCPD.