Hallucination Detection in LLMs

• Hallucination detection in LLMs is the process of identifying unfaithful, factually incorrect outputs using internal representation analysis, graph-theoretic methods, and clustering techniques.
• The field employs diverse methodologies like uncertainty quantification, spectral feature extraction, and hypothesis testing to accurately pinpoint inconsistencies in generated text.
• Ensemble and cost-effective multi-scoring approaches merge heterogeneous signals, enabling robust, real-time detection suitable for deployment in safety-critical and production environments.

Hallucination detection in LLMs refers to the systematic identification of generated content that is unfaithful, factually incorrect, or inconsistent with the provided input, context, or external knowledge. The proliferation of LLMs in safety-critical domains has made reliable hallucination detection an urgent research focus, spurring the development of a wide range of methodologies that draw on uncertainty quantification, representational analysis, signal processing, graph theory, hypothesis testing, and supervised learning. This article presents a comprehensive technical survey of these paradigms, recent advances, and empirical insights.

1. Internal and Representation-Based Detection

Early hallucination detectors assessed output uncertainty at the token (logit) level or via shallow post-hoc analyses. Subsequent studies established that internal LLM representations encode much richer, more localized truthfulness cues.

Multiple Instance Learning and Adaptive Token Selection

The HaMI framework (Niu et al., 10 Apr 2025) models hallucination detection as a multiple instance learning (MIL) problem, treating each generation as a "bag" of token-level internal representations. Instead of relying on features from predetermined token positions (e.g., first/last output token—whose informativeness is unstable), HaMI adaptively selects the subset of tokens most indicative of hallucination. The scoring function $f_\theta$ is jointly optimized across all tokens in the sequence (bag) using a margin-based MIL loss: $$\mathcal{L}_{MIL} = \max(0, 1 - \max_{n \in \mathcal{B}^+} f_{\theta}(\mathbf{h}_n^+) + \max_{n \in \mathcal{B}^-} f_{\theta}(\mathbf{h}_n^-))$$ and a smoothness constraint over neighboring tokens.

Crucially, HaMI enriches token representations with predictive uncertainty ($p_i$, sentence-level perplexity $P_s$, semantic consistency $P_{c_m}$), combining internal state features with output-derived confidence. Empirically, HaMI achieves a mean AUROC gain of 4–8% over first/last/mean token baselines, with cross-dataset generalization drop <4%—significantly outperforming prior state-of-the-art.

Direct Hidden-State Analysis

Other representation-driven proposals include INSIDE (Chen et al., 6 Feb 2024), which leverages the covariance structure of internal sentence embeddings extracted across multiple generations. The EigenScore,

$$E(\mathcal{Y}|\bm{x}, \bm{\theta}) = \frac{1}{K} \log \det(\bm{\Sigma} + \alpha \mathbf{I}_K),$$

measures differential entropy among response representations, highlighting semantic self-consistency. Feature clipping—suppressing extreme neuron activations—enables the detection of self-consistent yet incorrect hallucinations, which frequently evade entropy-based detectors. INSIDE achieves competitive AUROC on various LLMs/QAs, especially on hard sets such as TruthfulQA.

2. Graph-Theoretic and Topological Approaches

Attention modules in transformers encode generation context in a graph structure, yielding a fertile ground for structural analysis.

Topological Divergence (TOHA)

The TOHA method (Bazarova et al., 14 Apr 2025) interprets attention matrices as weighted graphs over all tokens (prompt/response), with edge weights $w_{ij} = 1 - W_{ij}$. For each attention head, it computes the minimal spanning forest (MSF) cost connecting response tokens to prompt tokens: $$\text{MTop-Div}(R, P) = \sum_{e \in \text{MSF}(R, P)} w(e)$$ Higher topological divergence (MSF length) signals that response tokens form new, nearly disconnected components—an indicator of hallucination. Head selection is guided by empirical discriminative power. TOHA delivers state-of-the-art ROC-AUC among unsupervised detectors, demonstrates transferability across LLMs/datasets, and is an order of magnitude faster than sampling-based baselines.

Laplacian Spectral Features

An orthogonal strategy (Binkowski et al., 24 Feb 2025) extracts top-$k$ eigenvalues from the Laplacian of attention maps per head/layer (LapEigvals). These spectral features capture information-flow bottlenecks (over-squashing), and their statistical distribution differentiates hallucinated from grounded generations. Supervised linear probes trained on LapEigvals achieve robust AUROC gains over other attention-based features, with strong generalization and stability with respect to architectural details and input variations.

3. Black-Box Sampling and Embedding-Space Analysis

Black-box approaches dispense with LLM internals, relying instead on properties of the generated outputs.

Semantic Inconsistency via Clustering

SINdex (Abdaljalil et al., 7 Mar 2025) uses semantic sentence embeddings (e.g., all-MiniLM-L6-v2) and agglomerative clustering to partition multiple generations into semantically homogeneous groups. The entropy of the adjusted cluster size, penalized by intra-cluster similarity,

$$\text{SINdex} = -\sum_{i=1}^k p_i' \log( p_i' ), \quad p_i' = p_i \cdot \overline{\mathrm{cos\_sim}(C_i)},$$

quantifies the output's semantic inconsistency and correlates with hallucination likelihood. SINdex achieves up to 9.3% AUROC improvements over prior semantic entropy approaches, and is more than $60\times$ faster than NLI-based detectors.

Fact-Level Consistency and Knowledge Graph Alignment

FactSelfCheck (Sawczyn et al., 21 Mar 2025) introduces fine-grained hallucination scoring at the level of atomic facts, extracted as (subject, relation, object) triples using LLM-based schema induction. For each fact in the main response, frequency- and LLM-consistency-based scores are computed across multiple sampled outputs: $$\mathcal{H}_\text{fact}(f) = 1 - \frac{1}{|S|} \sum_{s \in S} \mathbb{I}\{ f \in \text{KG}_s \}$$ Fact-level aggregation enables more effective and targeted corrections than sentence-level approaches, yielding a 35% factuality improvement when used for downstream filtering/correction.

Probabilistic Embeddings Framework

An alternative (Ricco et al., 10 Feb 2025) posits that hallucinated and genuine responses occupy distinct distributions in semantic embedding space. By measuring Minkowski distances between responses (after keyword selection with KeyBERT and embedding via BERT), and estimating class-conditional densities with KDE, probabilistic inference rules distinguish hallucination with up to 66% accuracy. Statistical tests confirm that distance distribution separation increases with more responses and lower $p$-norm, and this holds stably across keyword or response count.

4. Uncertainty, Hypothesis Testing, and Fusion Approaches

Robust hallucination detection often requires integrating heterogeneous metrics.

Uncertainty and Multiple Testing

A multiple-testing framework (Li et al., 25 Aug 2025) formulates detection as a hypothesis testing problem, aggregating conformal p-values from $k$ independently informative scores (semantic entropy, clustering, spectral eigenvalues, etc.) using a Benjamini--Hochberg (BH) procedure calibrated on accepted outputs: $$q^j_{\text{con}} = \frac{1 + |\{i: s^j(x^c_i) \geq t^j_{\text{test}}\}|}{1 + |\mathcal{C}|}$$ This method guarantees explicit false alarm rate control and delivers stable AUROC/detection power improvements over any single-score method, especially in worst-case scenarios.

Cost-Effective Multi-scoring in Production

Practical deployment settings often demand balancing inference cost and detection robustness. A model-agnostic pipeline (Valentin et al., 31 Jul 2024) benchmarks a range of scoring methods—token probability-based, LLM self-assessment, NLI, and multi-sample consistency measures—then calibrates and fuses scores via logistic regression. Cost-effective subsets are chosen by maximizing detection under latency/budget constraints: $$S^* = \argmin_{S: S \subseteq \{1, ..., N\}} \mathcal{L}(f(\{s_i(\bm{x}, \bm{z})\}_{i \in S})) \quad \text{s.t.}\ \sum_{i \in S} c_i \leq B$$ Combined, this yields ensemble performance nearly equaling the full multi-score, at a fraction of computational cost.

5. Dynamical and Frequency-Domain Modeling

Recent work frames LLM generation as a temporal dynamical process, seeking hallucination signatures in the evolution of hidden activations.

Hidden Signal Frequency Analysis

HSAD (Li et al., 16 Sep 2025) samples hidden states (attention, residual, MLP, output) at each decoder layer per generated token and organizes them into temporal sequences. Applying FFT to each dimension yields frequency-domain embedding vectors. The strongest non-DC amplitude per channel is extracted; these spectral features reveal abnormal temporal behaviors associated with hallucinations. Binary classifiers trained on these features achieve 10–25 point AUROC improvements over prior SOTA on hard QA datasets, especially when observing signals at answer-segment endpoints.

Neural Differential Equations (NDEs)

HD-NDEs (Li et al., 30 May 2025) treat the full trajectory of hidden states as a continuous path in latent space, modeled using neural ordinary/controlled/stochastic differential equations: $z(t) = z(0) + \int_0^t f(s, z(s); \theta_f) ds$ This dynamical modeling captures non-factuality at any sequence position, overcoming the limitation of final-token-classifiers. On subtle true/false benchmarks, neural CDEs and SDEs outperform earlier classifiers by >14% AUC-ROC, demonstrating the power of continuous modeling for sequence-wide inconsistency detection.

6. Practical, Ensemble, and Production-Oriented Approaches

Hallucination detection must be tractable on real deployment infrastructure.

Efficient Ensembling

Fine-tuned ensembles via BatchEnsemble+LoRA (Arteaga et al., 4 Sep 2024) enable practical predictive uncertainty estimation for <$8$B parameter LLMs on commodity hardware. Ensemble diversity is achieved by applying rank-1 "fast weights" in combination with shared LoRA adapters: $W_i = U \odot (r_i s_i^T)$ The resulting per-token predictive entropy is a strong hallucination indicator. This pipeline is highly memory- and compute-efficient, supporting real-time risk assessment and abstention control.

Modular, Multi-Source Systems

Robust production services (Wang et al., 22 Jul 2024) now combine named entity recognition (NER), natural language inference (NLI), and span-based detectors (SBD), fusing signals in a GBDT ensemble. Iterative, feedback-driven rewriting pipelines (using GPT-4) selectively correct hallucinated spans while balancing latency and cost. Such architectures are confirmed effective both offline (precision $>50\%$ for key-point detection) and in live traffic settings.

7. Benchmarks, Taxonomies, and Future Challenges

Real-World Benchmarks

The AuthenHallu benchmark (Ren et al., 12 Oct 2025) is the first authentic dataset capturing LLM-human hallucination in practical interactions. Hallucination is prevalent (31.4% of cases, up to 60% in Math/Number clusters), especially for input- and context-contradicting errors. Zero-shot LLM detection is not yet reliable: F1 scores plateau at $<65\%$.

Controlled Taxonomies and Clustering

A recent classifier framework (Zavhorodnii et al., 6 Oct 2025) proposes a fine-grained taxonomy: factual contradiction, fabrication, misinterpretation, context inconsistency, and logical hallucination. Embedding and unsupervised clustering (UMAP) reveal robust separability of hallucinated vs. veridical responses, enabling lightweight classification and derivation of severity estimates from inter-centroid distances.

Remaining Open Problems

• Detecting rare or faithfulness-type hallucinations (non-factuality not directly conflicting with known world knowledge).
• Adaptation to closed-source/model black-box settings and multilingual contexts.
• Efficient annotation, calibration, and risk management in production.

Advances in dynamic, spectral, and geometric modeling, as well as unsupervised/semi-supervised learning and principled score fusion, continue to propel the field forward. However, robust, generalizable, and explainable hallucination detection—suitable for high-stakes domains—remains an unresolved research frontier.