Hallucination in Language Models

Reasoning hallucinations in large language models (LLMs) often appear as fluent yet unsupported conclusions that violate either the given context or underlying factual knowledge. Although such failures are widely observed, the mechanisms by which decoder-only Transformers produce them remain poorly understood. We model next-token prediction as a graph search process over an underlying graph, where entities correspond to nodes and learned transitions form edges. From this perspective, contextual reasoning is a constrained search over a sampled subgraph (intrinsic reasoning), while context-free queries rely on memorized structures in the underlying graph (extrinsic reasoning). We show that reasoning hallucinations arise from two fundamental mechanisms: Path Reuse, where memorized knowledge overrides contextual constraints during early training, and Path Compression, where frequently traversed multi-step paths collapse into shortcut edges in later training. Together, these mechanisms provide a unified explanation for reasoning hallucinations in LLMs and connected to well-known behaviors observed in downstream applications.

Supervised fine-tuning (SFT) with token-level hard labels can amplify overconfident imitation of factually unsupported targets, causing hallucinations that propagate in multi-sentence generation. We study an augmented SFT setting in which training instances include coarse sentence-level factuality risk labels and inter-sentence dependency annotations, providing structured signals about where factual commitments are weakly supported. We propose PRISM, a differentiable risk-gated framework that modifies learning only at fact-critical positions. PRISM augments standard SFT with a lightweight, model-aware probability reallocation objective that penalizes high-confidence predictions on risky target tokens, with its scope controlled by span-level risk weights and model-aware gating. Experiments on hallucination-sensitive factual benchmarks and general evaluations show that PRISM improves factual aggregates across backbones while maintaining a competitive overall capability profile. Ablations further show that the auxiliary signal is most effective when used conservatively, and that knowledge masking and model-aware reallocation play complementary roles in balancing factual correction and capability preservation.

We identify a previously unknown calibration property of large language models: providing one confirmed intermediate fact toward a multi-step reasoning chain increases the model's confident-wrong-answer rate before full evidence eliminates it. We call this anchored confabulation: a partial anchor commits the model to confident parametric completion of remaining reasoning steps. We formalize it as Parametric Hallucination Confidence (PHC) and establish it across six lines of evidence including a causal injection experiment (PHC 0.613 to 0.656 to 0.595 to 0.536, N=160) and capability scaling across five model families (Spearman rho=0.900, p=0.037). The Anchoring Threshold Law k*(n)=floor(n/3) predicts PHC amplification by hop depth with four confirmed predictions. Applied to RAG routing, a LearnedRouter exploiting PHC closes 81.1% of the oracle performance gap (macro F1=0.426, p<1e-6) on 1,800 queries across four benchmarks with no model fine-tuning and 50x fewer labels than prior RL-based work. An epistemic humility prompt reduces the PHC spike by -0.118; explicit self-rating (PHC=0.684, p<0.001) outperforms lexical confidence as a routing signal.

This paper investigates how generative AI produces and propagates hallucinated academic references, focusing on the recurring non-existent citation 'Education Governance and Datafication' attributed to Ben Williamson and Nelli Piattoeva. Drawing on 137 accessible source papers identified through Google Scholar and Google searches, the study analyses the structure, recurrence, and onward citation of this phantom reference. It shows that hallucinated citations are not random inventions but patterned recombinations of real authors, journals, dates, and keywords, with duplication occurring in nearly 30% of cases. The paper also reports a structured interrogation of ChatGPT 5-mini about how it generates citations and finds that, absent verification, the model reconstructs plausible references from learned patterns rather than factual recall. Finally, ten AI-generated essays on datafication and school governance were examined: while most references were genuine or partly accurate, 9.2% remained hallucinated, including an exact match to the most common phantom citation. The findings highlight ongoing risks to academic integrity and show that web-enabled AI still does not fully eliminate fabricated references.

Language models detect false premises when asked directly but absorb them under conversational pressure, producing authoritative professional output built on errors they already identified. This failure - order-gap hallucination - is invisible to output inspection because the error migrates into the activation space of the safety circuit, suppressed but not erased. We introduce Squish and Release (S&R), an activation-patching architecture with two components: a fixed detector body (layers 24-31, the localized safety evaluation circuit) and a swappable detector core (an activation vector controlling perception direction). A safety core shifts the model from compliance toward detection; an absorb core reverses it. We evaluate on OLMo-2 7B using the Order-Gap Benchmark - 500 chains across 500 domains, all manually graded. Key findings: cascade collapse is near-total (99.8% compliance at O5); the detector body is binary and localized (layers 24-31 shift 93.6%, layers 0-23 contribute zero, p<10^-189); a synthetically engineered core releases 76.6% of collapsed chains; detection is the more stable attractor (83% restore vs 58% suppress); and epistemic specificity is confirmed (false-premise core releases 45.4%, true-premise core releases 0.0%). The contribution is the framework - body/core architecture, benchmark, and core engineering methodology - which is model-agnostic by design.

We present H-Node Adversarial Noise Cancellation (H-Node ANC), a mechanistic framework that identifies, exploits, and defends hallucination representations in transformer-based large language models (LLMs) at the level of individual hidden-state dimensions. A logistic regression probe trained on last-token hidden states localizes hallucination signal to a small set of high-variance dimensions -- termed Hallucination Nodes (H-Nodes) -- with probe AUC reaching 0.90 across four architectures. A white-box adversarial attack amplifies these dimensions at inference time via a real-time forward hook, achieving a selectivity of 3.02x with less than 10% visibility to the defender. Adaptive ANC defense suppresses H-Node excess in-pass using confidence-weighted cancellation, reducing grounded activation drift by 33-42% over static cancellation. A dynamic iterative extension that re-ranks cancellation targets across successive passes recovers up to 0.69 robustness from a single-pass baseline of 8%. All contributions are validated on OPT-125M, Phi-3-mini-4k-instruct, LLaMA-3-8B-Instruct, and Mistral-7B-Instruct-v0.3 (125M-8B parameters). Perplexity impact is surgical (<5%) and MMLU degradation is at most 3%, confirming that the defense does not impair general reasoning capability.

Recent work identifies a sparse set of "hallucination neurons" (H-neurons), less than 0.1% of feed-forward network neurons, that reliably predict when large language models will hallucinate. These neurons are identified on general-knowledge question answering and shown to generalize to new evaluation instances. We ask a natural follow-up question: do H-neurons generalize across knowledge domains? Using a systematic cross-domain transfer protocol across 6 domains (general QA, legal, financial, science, moral reasoning, and code vulnerability) and 5 open-weight models (3B to 8B parameters), we find they do not. Classifiers trained on one domain's H-neurons achieve AUROC 0.783 within-domain but only 0.563 when transferred to a different domain (delta = 0.220, p < 0.001), a degradation consistent across all models tested. Our results suggest that hallucination is not a single mechanism with a universal neural signature, but rather involves domain-specific neuron populations that differ depending on the knowledge type being queried. This finding has direct implications for the deployment of neuron-level hallucination detectors, which must be calibrated per domain rather than trained once and applied universally.

Large vision-language models (LVLMs) are increasingly being applied to multi-view image inputs captured from diverse viewpoints. Despite this growing use, current LVLMs often generate incorrect responses due to visual interference from non-target instances or viewpoints, a phenomenon we term multi-view hallucination (MVH). To systematically analyze this problem, we construct MVH-Bench, a benchmark comprising 4.8k question-answer pairs targeting two types of hallucination: cross-instance and cross-view. Empirical results show that MVH is prevalent across recent LVLMs. To address this issue, we propose Reference Shift Contrastive Decoding (RSCD), a training-free decoding technique that suppresses visual interference by generating negative logits through attention masking. Experiments on MVH-Bench with LLaVA-OneVision and Qwen2.5-VL demonstrate that RSCD improves performance by up to 25.7 and 94.8 points over existing hallucination mitigation methods, highlighting the effectiveness of RSCD.

The adoption of generative AI across commercial and legal professions offers dramatic efficiency gains -- yet for law in particular, it introduces a perilous failure mode in which the AI fabricates fictitious case law, statutes, and judicial holdings that appear entirely authentic. Attorneys who unknowingly file such fabrications face professional sanctions, malpractice exposure, and reputational harm, while courts confront a novel threat to the integrity of the adversarial process. This failure mode is commonly dismissed as random hallucination', but recent physics-based analysis of the Transformer's core mechanism reveals a deterministic component: the AI's internal state can cross a calculable threshold, causing its output to flip from reliable legal reasoning to authoritative-sounding fabrication. Here we present this science in a legal-industry setting, walking through a simulated brief-drafting scenario. Our analysis suggests that fabrication risk is not an anomalous glitch but a foreseeable consequence of the technology's design, with direct implications for the evolving duty of technological competence. We propose that legal professionals, courts, and regulators replace the outdated black box' mental model with verification protocols based on how these systems actually fail.

Adversarial vulnerability in vision and hallucination in large language models are conventionally viewed as separate problems, each addressed with modality-specific patches. This study first reveals that they share a common geometric origin: the input and its loss gradient are conjugate observables subject to an irreducible uncertainty bound. Formalizing a Neural Uncertainty Principle (NUP) under a loss-induced state, we find that in near-bound regimes, further compression must be accompanied by increased sensitivity dispersion (adversarial fragility), while weak prompt-gradient coupling leaves generation under-constrained (hallucination). Crucially, this bound is modulated by an input-gradient correlation channel, captured by a specifically designed single-backward probe. In vision, masking highly coupled components improves robustness without costly adversarial training; in language, the same prefill-stage probe detects hallucination risk before generating any answer tokens. NUP thus turns two seemingly separate failure taxonomies into a shared uncertainty-budget view and provides a principled lens for reliability analysis. Guided by this NUP theory, we propose ConjMask (masking high-contribution input components) and LogitReg (logit-side regularization) to improve robustness without adversarial training, and use the probe as a decoding-free risk signal for LLMs, enabling hallucination detection and prompt selection. NUP thus provides a unified, practical framework for diagnosing and mitigating boundary anomalies across perception and generation tasks.

Knowledge-grounded dialogue systems aim to generate informative, contextually relevant responses by conditioning on external knowledge sources. However, most existing approaches focus exclusively on English, lack explicit citation mechanisms for verifying factual claims, and offer limited transparency into model decision-making. We present XKD-Dial, a progressive four-stage training pipeline for explainable, knowledge-grounded dialogue generation in a bilingual (English-Hindi) setting, comprising: (1) multilingual adaptation, (2) English dialogue SFT with citation grounding, (3) bilingual dialogue SFT, and (4) GRPO alignment with citation-aware rewards. We evaluate six models spanning encoder-decoder (250M-3B) and decoder-only (1B-7B) architectures at every pipeline stage. Our key contributions are: (i) three post-hoc explainability analyses - cross-attention alignment, Integrated Gradients attribution, and occlusion-based causal grounding - applied systematically across the training trajectory to reveal how citation behaviour is learned, not only whether it is learned; (ii) citation-grounded SFT reduces hallucination to 0.0% for encoder-decoder models from Stage 2 onward; (iii) the progressive pipeline prevents catastrophic forgetting while improving Hindi capabilities; (iv) smaller models match larger models on English after SFT; and (v) GRPO provides marginal improvement over well-designed SFT for structured citation tasks. We evaluate across six automatic metrics (BLEU, ROUGE, BERTScore, FactScore, Citation-F1, and hallucination rate).

Large language models (LLMs) often hallucinate, producing fluent but false information, partly because supervised fine-tuning (SFT) implicitly rewards always responding. We introduce $\textit{HypoTermInstruct}$, an SFT dataset (31,487 responses for 11,151 questions) designed to teach models epistemological humility-the ability to recognize the limits of their own knowledge and admit uncertainty. This is achieved through questions about non-existent "hypothetical" terms. We also release $\textit{HypoTermQA-Enhanced}$, a benchmark for hallucination tendency strengthened through multiple validations. We conducted 800 controlled LoRA SFT runs across $\textit{Llama3.1-8B}$ and $\textit{Gemma3-4B}$ (base and instruct), testing 100 fine-tuning configurations with paired controls. Our results demonstrate that replacing generic instruction data with $\textit{HypoTermInstruct}$ significantly improves the HypoTerm Score (median increases of 0.19% to 25.91%) and FactScore (+0.39% to +0.86%), while maintaining stable performance on MMLU (minimal decreases of 0.26% to 0.35%). Our work demonstrates that targeted, high-quality SFT data teaching meta-cognitive skills can effectively reduce hallucination without preference/RL pipelines, providing mechanistic insights and a practical path toward more reliable AI systems.

Building and evaluating enterprise AI systems requires synthetic organizational corpora that are internally consistent, temporally structured, and cross-artifact traceable. Existing corpora either carry legal constraints or inherit hallucination artifacts from the generating LLMs, silently corrupting results when timestamps or facts contradict across documents and reinforcing those errors during training. We present OrgForge, an open-source multi-agent simulation framework that enforces a strict physics-cognition boundary: a deterministic Python engine maintains a SimEvent ground-truth bus while LLMs generate only surface prose. OrgForge simulates the organizational processes that produce documents, not the documents themselves. Engineers leave mid-sprint, triggering incident handoffs and CRM ownership lapses. Knowledge gaps emerge when under-documented systems break and recover through organic documentation and incident resolution. Customer emails fire only when simulation state warrants contact; silence is verifiable ground truth. A live CRM state machine extends the physics-cognition boundary to the customer boundary, producing cross-system causal cascades spanning engineering incidents, support escalation, deal risk flagging, and SLA-adjusted invoices. The framework generates fifteen interleaved artifact categories traceable to a shared immutable event log. Four graph-dynamic subsystems govern organizational behavior independently of any LLM. An embedding-based ticket assignment system using the Hungarian algorithm makes the simulation domain-agnostic. An empirical evaluation across ten incidents demonstrates a 0.46 absolute improvement in prose-to-ground-truth fidelity over chained LLM baselines, and isolates a consistent hallucination failure mode in which chaining propagates fabricated facts faithfully across documents without correcting them.

A language model can give the wrong answer even when the correct answer is decodable from its intermediate states. To study this gap between decodability and selection, we distinguish read from write at the first answer token. Read asks whether the gold token can be decoded from intermediate residual states under same-relation decoy controls. Write asks whether the final readout ranks that token first among content tokens. Under three different readers, with a randomized-label control, a substantial fraction of failures remain readable while another content token is selected. We explain this through the selection margin at the final readout, the difference between the answer logit and the logit of its strongest alternative, which is answer support minus alternative support, and can also be split into a context-averaged baseline linked to token frequency and an item-specific term. Setting the answer support to the level typical of successful generations is sufficient to recover first-token selection for the majority of failures in most of the models we study; the original alternative remains ahead in most remaining failures under this edit, and this outcome follows directly from the readout geometry. Removing the frequency direction alone shifts selection but rarely recovers the answer. Prompt variants of the same fact that succeed supply support that transfers to failing variants through the residual stream and through late MLP outputs, with less consistent effects through late attention. First-token recovery leaves most full answers wrong, which limits the recovery achieved by these edits and separates three things that are easily conflated, decodability, recoverability, and generation.

Large language models often produce unsupported claims. We frame this as a misclassification error at the output boundary, where internally generated completions are emitted as if they were grounded in evidence. This motivates a composite intervention that combines instruction-based refusal with a structural abstention gate. The gate computes a support deficit score, St, from three black-box signals: self-consistency (At), paraphrase stability (Pt), and citation coverage (Ct), and blocks output when St exceeds a threshold. In a controlled evaluation across 50 items, five epistemic regimes, and three models, neither mechanism alone was sufficient. Instruction-only prompting reduced hallucination sharply, but still showed over-cautious abstention on answerable items and residual hallucination for GPT-3.5-turbo. The structural gate preserved answerable accuracy across models but missed confident confabulation on conflicting-evidence items. The composite architecture achieved high overall accuracy with low hallucination, while also inheriting some over-abstention from the instruction component. A supplementary 100-item no-context stress test derived from TruthfulQA showed that structural gating provides a capability-independent abstention floor. Overall, instruction-based refusal and structural gating show complementary failure modes, which suggests that effective hallucination control benefits from combining both mechanisms.

Mental health concerns are often expressed outside clinical settings, including in high-distress help seeking, where safety-critical guidance may be needed. Consumer health informatics systems increasingly incorporate large language models (LLMs) for mental health question answering, yet many evaluations underrepresent narrative, high-distress inquiries. We introduce UTCO (User, Topic, Context, Tone), a prompt construction framework that represents an inquiry as four controllable elements for systematic stress testing. Using 2,075 UTCO-generated prompts, we evaluated Llama 3.3 and annotated hallucinations (fabricated or incorrect clinical content) and omissions (missing clinically necessary or safety-critical guidance). Hallucinations occurred in 6.5% of responses and omissions in 13.2%, with omissions concentrated in crisis and suicidal ideation prompts. Across regression, element-specific matching, and similarity-matched comparisons, failures were most consistently associated with context and tone, while user-background indicators showed no systematic differences after balancing. These findings support evaluating omissions as a primary safety outcome and moving beyond static benchmark question sets.

While reasoning in LLMs plays a natural role in math, code generation, and multi-hop factual questions, its effect on simple, single-hop factual questions remains unclear. Such questions do not require step-by-step logical decomposition, making the utility of reasoning highly counterintuitive. Nevertheless, we find that enabling reasoning substantially expands the capability boundary of the model's parametric knowledge recall, unlocking correct answers that are otherwise effectively unreachable. Why does reasoning aid parametric knowledge recall when there are no complex reasoning steps to be done? To answer this, we design a series of hypothesis-driven controlled experiments, and identify two key driving mechanisms: (1) a computational buffer effect, where the model uses the generated reasoning tokens to perform latent computation independent of their semantic content; and (2) factual priming, where generating topically related facts acts as a semantic bridge that facilitates correct answer retrieval. Importantly, this latter generative self-retrieval mechanism carries inherent risks: we demonstrate that hallucinating intermediate facts during reasoning increases the likelihood of hallucinations in the final answer. Finally, we show that our insights can be harnessed to directly improve model accuracy by prioritizing reasoning trajectories that contain hallucination-free factual statements.

How much do large language models actually hallucinate when answering questions grounded in provided documents? Despite the critical importance of this question for enterprise AI deployments, reliable measurement has been hampered by benchmarks that rely on static datasets vulnerable to contamination, LLM-based judges with documented biases, or evaluation scales too small for statistical confidence. We address this gap using RIKER, a ground-truth-first evaluation methodology that enables deterministic scoring without human annotation. Across 35 open-weight models, three context lengths (32K, 128K, and 200K tokens), four temperature settings, and three hardware platforms (NVIDIA H200, AMD MI300X, and Intel Gaudi 3), we conducted over 172 billion tokens of evaluation - an order of magnitude beyond prior work. Our findings reveal that: (1) even the best-performing models fabricate answers at a non-trivial rate - 1.19% at best at 32K, with top-tier models at 5 - 7% - and fabrication rises steeply with context length, nearly tripling at 128K and exceeding 10% for all models at 200K; (2) model selection dominates all other factors, with overall accuracy spanning a 72-percentage-point range and model family predicting fabrication resistance better than model size; (3) temperature effects are nuanced - T=0.0 yields the best overall accuracy in roughly 60% of cases, but higher temperatures reduce fabrication for the majority of models and dramatically reduce coherence loss (infinite generation loops), which can reach 48x higher rates at T=0.0 versus T=1.0; (4) grounding ability and fabrication resistance are distinct capabilities - models that excel at finding facts may still fabricate facts that do not exist; and (5) results are consistent across hardware platforms, confirming that deployment decisions need not be hardware-dependent.

A geometric hallucination taxonomy distinguishes three failure types -- center-drift (Type1), wrong-well convergence (Type2), and coverage gaps (Type3) -- by their signatures in embedding cluster space. Prior work found Types1 and2 indistinguishable in full-dimensional contextual measurement. We address this through PCA-whitening and eigenspectrum decomposition on GPT-2-small, using multi-run stability analysis (20 seeds) with prompt-level aggregation. Whitening transforms the micro-signal regime into a space where peak cluster alignment (max_sim) separates Type2 from Type3 at Holm-corrected significance, with condition means following the taxonomy's predicted ordering: Type2 (highest commitment) $>$ Type1 (intermediate) $>$ Type3 (lowest). A first directionally stable but underpowered hint of Type1/2 separation emerges via the same metric, generating a capacity prediction for larger models. Prompt diversification from 15 to 30 prompts per group eliminates a false positive in whitened entropy that appeared robust at the smaller set, demonstrating prompt-set sensitivity in the micro-signal regime. Eigenspectrum decomposition localizes this artifact to the dominant principal components and confirms that Type1/2 separation does not emerge in any spectral band, rejecting the spectral mixing hypothesis. The contribution is threefold: whitening as preprocessing that reveals cluster commitment as the theoretically correct separating metric, evidence that the Type~1/2 boundary is a capacity limitation rather than a measurement artifact, and a methodological finding about prompt-set fragility in near-saturated representation spaces.

LLMs are increasingly used to draft academic text and to support software engineering (SE) evidence synthesis, but they often hallucinate bibliographic references that look legitimate. We study how deployment-motivated prompting constraints affect citation verifiability in a closed-book setting. Using 144 claims (24 in SE&CS) and a deterministic verification pipeline (Crossref + Semantic Scholar), we evaluate two proprietary models (Claude Sonnet, GPT-4o) and two open-weight models (LLaMA3.1-8B, Qwen2.5-14B) across five regimes: Baseline, Temporal (publication-year window), Survey-style breadth, Non-Disclosure policy, and their combination. Across 17,443 generated citations, no model exceeds a citation-level existence rate of 0.475; Temporal and Combo conditions produce the steepest drops while outputs remain format-compliant (well-formed bibliographic fields). Unresolved outcomes dominate (36-61%); a 100-citation audit indicates that a substantial fraction of Unresolved cases are fabricated. Results motivate post-hoc citation verification before LLM outputs enter SE literature reviews or tooling pipelines.

Large language models (LLMs) have demonstrated remarkable performance in text generation and knowledge-intensive question answering. Nevertheless, they are prone to producing hallucinated content, which severely undermines their reliability in high-stakes application domains. Existing hallucination attribution approaches, based on either external knowledge retrieval or internal model mechanisms, primarily focus on semantic similarity matching or representation-level discrimination. As a result, they have difficulty establishing structured correspondences at the span level between hallucination types, underlying error generation mechanisms, and external factual evidence, thereby limiting the interpretability of hallucinated fragments and the traceability of supporting or opposing evidence. To address these limitations, we propose HART, a fine-grained hallucination attribution and evidence retrieval framework for large language models. HART formalizes hallucination tracing as a structured modeling task comprising four stages: span localization, mechanism attribution, evidence retrieval, and causal tracing. Based upon this formulation, we develop the first structured dataset tailored for hallucination tracing, in which hallucination types, error mechanisms, and sets of counterfactual evidence are jointly annotated to enable causal-level interpretability evaluation. Experimental results on the proposed dataset demonstrate that HART substantially outperforms strong retrieval baselines, including BM25 and DPR, validating the effectiveness and generalization capability of the proposed tracing paradigm for hallucination analysis and evidence alignment.

We test whether a geometric hallucination taxonomy -- classifying failures as center-drift (Type1), wrong-well convergence (Type2), or coverage gaps (Type3) -- can distinguish hallucination types through controlled induction in GPT-2. Using a two-level statistical design with prompts ($N = 15$/group) as the unit of inference, we run each experiment 20 times with different generation seeds to quantify result stability. In static embeddings, Type3 norm separation is robust (significant in 18/20 runs, Holm-corrected in 14/20, median $r = +0.61$). In contextual hidden states, the Type3 norm effect direction is stable (19/20 runs) but underpowered at $N = 15$ (significant in 4/20, median $r = -0.28$). Types1 and2 do not separate in either space (${\leq}\,3/20$ runs). Token-level tests inflate significance by 4--16$\times$ through pseudoreplication -- a finding replicated across all 20 runs. The results establish coverage-gap hallucinations as the most geometrically distinctive failure mode, carried by magnitude rather than direction, and confirm the Type1/2 non-separation as genuine at 124M parameters.

Large language model (LLM) hallucinations, meaning fluent but factually incorrect generations, fall into two types: faithfulness violations, where the model misuses provided context, and factuality violations, where answers reflect errors in internal knowledge. Proper mitigation depends on knowing which source drives each answer. We study contributive attribution, i.e. the classification of the dominant knowledge source behind each output, and show that a simple linear probe trained on hidden representations can reliably identify it. We introduce AttriWiki, a self-supervised pipeline that automatically generates labelled training data by prompting models to recall withheld entities from memory or read them from context without relying on knowledge conflicts. Probes trained on AttriWiki achieve up to 0.96 Macro-$F_1$ on Llama-3.1-8B, Mistral-7B, and Qwen-7B, transfer to SQuAD and WebQuestions with 0.94-0.99 Macro-$F_1$, and generalise zero-shot to Tighidet et al. (2024)'s benchmark, outperforming their probe on conflicting settings without retraining. Furthermore, attribution mismatches raise error rates by up to 70%, though correct attribution does not guarantee correct answers, pointing to the need for broader detection frameworks.

Traditional benchmarks like HumanEval and MBPP test logic and syntax effectively, but fail when code must produce dynamic, pedagogical visuals. We introduce ManiBench, a specialized benchmark evaluating LLM performance in generating Manim CE code, where temporal fidelity and version-aware API correctness are critical. ManiBench targets two key failure modes: Syntactic Hallucinations (valid Python referencing non-existent or deprecated Manim APIs) and Visual-Logic Drift (generated visuals diverging from intended mathematical logic through timing errors or missing causal relationships). The benchmark comprises 150-200 problems across five difficulty levels spanning calculus, linear algebra, probability, topology, and AI, grounded in analysis of 3Blue1Brown's ManimGL source (53,000 lines, 143 scene classes). Evaluation uses a four-tier framework measuring Executability, Version-Conflict Error Rate, Alignment Score, and Coverage Score. An open-source framework automates evaluation across multiple models and prompting strategies. Code, data and benchmark suite are available at https://github.com/nabin2004/ManiBench. and the dataset is hosted on https://huggingface.co/datasets/nabin2004/ManiBench.

Large Language Model (LLM) hallucinations are usually treated as defects of the model or its decoding strategy. Drawing on classical linguistics, we argue that a query's form can also shape a listener's (and model's) response. We operationalize this insight by constructing a 22-dimension query feature vector covering clause complexity, lexical rarity, and anaphora, negation, answerability, and intention grounding, all known to affect human comprehension. Using 369,837 real-world queries, we ask: Are there certain types of queries that make hallucination more likely? A large-scale analysis reveals a consistent "risk landscape": certain features such as deep clause nesting and underspecification align with higher hallucination propensity. In contrast, clear intention grounding and answerability align with lower hallucination rates. Others, including domain specificity, show mixed, dataset- and model-dependent effects. Thus, these findings establish an empirically observable query-feature representation correlated with hallucination risk, paving the way for guided query rewriting and future intervention studies.

Large Language Models (LLMs) possess a remarkable capacity to generate persuasive and intelligible language. However, coherence does not equate to truthfulness, as the responses often contain subtle hallucinations. Existing benchmarks are limited by static and narrow questions, leading to limited coverage and misleading evaluations. We present KGHaluBench, a Knowledge Graph-based hallucination benchmark that assesses LLMs across the breadth and depth of their knowledge, providing a fairer and more comprehensive insight into LLM truthfulness. Our framework utilises the KG to dynamically construct challenging, multifaceted questions, whose difficulty is then statistically estimated to address popularity bias. Our automated verification pipeline detects abstentions and verifies the LLM's response at both conceptual and correctness levels to identify different types of hallucinations. We evaluate 25 frontier models, using novel accuracy and hallucination metrics. The results provide a more interpretable insight into the knowledge factors that cause hallucinations across different model sizes. KGHaluBench is publicly available to support future developments in hallucination mitigation.

Large language models can follow complex procedures yet fail at a seemingly trivial final step: reporting a value they themselves computed moments earlier. We study this phenomenon as procedural hallucination: failure to execute a verifiable, prompt-grounded specification even when the correct value is present in context. In long-context binding tasks with a known single-token candidate set, we find that many errors are readout-stage routing failures. Specifically, failures decompose into Stage2A (gating) errors, where the model does not enter answer mode, and Stage2B (binding) errors, where it enters answer mode but selects the wrong candidate (often due to recency bias). In the hard regime, Stage2B accounts for most errors across model families in our tasks (Table1). On Stage2B error trials, a linear probe on the final-layer residual stream recovers the correct value far above chance (e.g., 74% vs.\ 2% on Qwen2.5-3B; Table2), indicating that the answer is encoded but not used. We formalize ``present but not used'' via available vs.\ used mutual information and pseudo-prior interventions, yielding output-computable diagnostics and information-budget certificates. Finally, an oracle checkpointing intervention that restates the true binding near the query can nearly eliminate Stage2B failures at long distance (e.g., Qwen2.5-3B $0/400 \rightarrow 399/400$ at $k = 1024$; Table8).

Uncertainty quantification has emerged as an effective approach to closed-book hallucination detection for LLMs, but existing methods are largely designed for short-form outputs and do not generalize well to long-form generation. We introduce a taxonomy for fine-grained uncertainty quantification in long-form LLM outputs that distinguishes methods by design choices at three stages: response decomposition, unit-level scoring, and response-level aggregation. We formalize several families of consistency-based black-box scorers, providing generalizations and extensions of existing methods. We also introduce FactScore-STEM-Geo, a new 400-question long-form QA dataset spanning four categories across STEM and Geography. In our experiments across multiple LLMs and datasets, we find 1) claim-response entailment consistently performs better or on par with more complex claim-level scorers, 2) claim-level scoring generally yields better results than sentence-level scoring, and 3) uncertainty-aware decoding is highly effective for improving the factuality of long-form outputs. Our framework clarifies relationships between prior methods, enables apples-to-apples comparisons, and provides practical guidance for selecting components for fine-grained UQ.

Hallucinations -- plausible but factually incorrect responses -- pose a major challenge to the reliability of Large Language Models (LLMs), especially in multi-step or agentic settings. Existing work largely frames hallucinations as a consequence of missing knowledge; we show instead that, even when the relevant factual knowledge is present, models still produce hallucinated answers, pointing to retrieval instability rather than knowledge gaps. Building on this observation, we introduce APORIA (Aggregate Prompt-wise Observation Retrieving Instability via Asymmetry -- the state of puzzlement-in-contradiction that hallucinations embody), a geometric framework that studies repeated responses to the same prompt in sentence-embedding space. Our central hypothesis is that genuine responses cluster more tightly than hallucinated ones; we empirically validate this and show that, after Fisher projection, the two response classes become consistently separable. We leverage this asymmetry in geometry via APORIA-LP, an efficient label-propagation method that classifies large collections of responses from as few as 30--50 annotations, achieving F1 scores above 90% across ten small-sized LLMs. To support further research, we release SOCRATES-300K, a fully labelled dataset of 300,000 responses, together with the code for both dataset generation and result reproduction. Our key finding -- framing hallucinations from a geometric perspective in the embedding space -- complements traditional knowledge-centric and single-response evaluation paradigms, paving the way for further research.

Failures in large language models (LLMs) are often analyzed from a behavioral perspective, where incorrect outputs in factual question answering are commonly associated with missing knowledge. In this work, focusing on entity-based factual queries, we suggest that such a view may conflate different failure mechanisms, and propose an internal, mechanism-oriented perspective that separates Knowledge Existence from Behavior Expression. Under this formulation, hallucination and deception correspond to two qualitatively different failure modes that may appear similar at the output level but differ in their underlying mechanisms. To study this distinction, we construct a controlled environment for entity-centric factual questions in which knowledge is preserved while behavioral expression is selectively altered, enabling systematic analysis of four behavioral cases. We analyze these failure modes through representation separability, sparse interpretability, and inference-time activation steering.