Hallucination in Language Models

Hallucinated information can propagate through multi-stage LLM systems and become part of the context for subsequent reasoning. Existing studies of post-hallucination reasoning (PHR) mainly characterize changes in final outcomes and aggregate reasoning dynamics, leaving how models resolve hallucinated premises at the response level insufficiently understood. In this work, we introduce PHRBench, a controlled benchmark for behaviorally structured PHR across four domains and 18 large language models. PHRBench characterizes each reasoning trajectory independently of final-answer correctness through Hallucination Compliance, Hallucination Avoidance, and Heuristic Correction, and defines an insightful trajectory as successful correction that ultimately reaches the correct answer. Across 4820 controlled instances, we find that successful recovery remains relatively rare and is associated with more frequent belief updates along the reasoning trajectory. We further find that properties of the hallucinated prompt contain substantial predictive signal for successful recovery, with a lightweight predictor achieving an AUROC of 0.847. These findings provide a behavioral view of post-hallucination reasoning, characterizing how LLMs resolve erroneous context and when successful recovery is likely to occur.

Large language models (LLMs) are expected to answer questions faithfully based on the provided context, abstaining when the context information is insufficient to answer the questions. Existing faithfulness evaluations typically assess each question-context instance in isolation; however, such instance-level evaluation fails to capture a fundamental requirement of faithful behavior: the ability to adapt model responses to changes in available contexts. In particular, a model should provide correct answers when sufficient evidence is present and abstain when it is not. In this work, we propose a Pairwise Faithfulness Benchmark (PFaithBench) that evaluates whether a model can switch between answering and abstaining for the same question under supporting versus non-supporting contexts. Our evaluations across thirty-nine models with seven model families demonstrate that faithfulness fundamentally involves a trade-off between answering and abstaining, and that most current models exhibit a strong bias toward answering, with most faithfulness errors arising from over-answering, i.e., models tend to fabricate a response even when the provided context is insufficient. We further conduct a series of studies on faithfulness training under different data constructions. Our results show that training outcomes are highly sensitive to the specific composition of answering and abstaining data. Constructing answering and abstaining data from mismatched sources can cause models to rely on dataset-specific shortcuts rather than actual context sufficiency. Moreover, increasing answer-supervised data improves answering performance but exacerbates over-answering, while increasing abstaining data reduces hallucination but leads to over-abstention. The code and data are released at https://github.com/tmlr-group/PFaithBench.

Reasoning errors can propagate into later decisions and memory. This survey synthesizes 312 papers and first-party reports on text-based reasoning hallucinations around three questions: what evidence is observable, what study designs establish, and which corrective actions the evidence supports. UIPCA records unsupported premises (U), invalid inferences (I), dependent reuse (P), visible answer-trace consistency (C), and action-policy failures (A). Across 58 reviewed sources, no comparison establishes that a specified intervention improves reasoning while reducing factual reliability under matched conditions. The synthesis connects diagnosis to verification, repair, selective release, and persistent-state control across memory, tools, and training feedback.

Large Language Model (LLM) agents are increasingly deployed as populations of interacting entities, in which consensus --agreement on a shared answer-- emerges as a collective, unengineered behaviour. Prior work on LLM consensus shows that agents can cross-verify their answers and converge towards more factual responses, treating agreement as a proxy for correctness. However, these studies usually fix a single interaction structure, leaving open how consensus depends on how agents interact. We address this gap by introducing RHEON, a physics-inspired framework that recasts a population drawn from a single frozen model as an evolving $O(n)$ spin system on a ladder of interaction geometries of increasing effective dimension --from a 1D ring to a full-coupling mean-field graph-- with the sampling temperature $T$ as the tunable source of thermal disorder, evolved through a Glauber-like asynchronous dynamics. Sweeping RHEON across $432$ configurations of prompt, population size, communication topology, and sampling temperature yields Eraclitus-4.7M, a tagged evolutionary corpus of $4.7$ million responses. We find that agents reach their strongest consensus gain within the first few update sweeps and that increasing the number of neighbours per agent accelerates convergence on average. We further show that whether a configuration settles on factually correct or hallucinated consensus is not predictable from its initial state alone, and that the hallucination-minimising temperature depends on how the agents are coupled, so the common near-greedy default is not automatically the safest. Finally, semantic agreement correlates positively with factual convergence, and interaction strengthens the association, yet never enough for unanimity to certify correctness.

Audio-visual large language models (AVLLMs) have made remarkable progress in multimodal understanding and reasoning through interactions among visual, auditory, and linguistic information. However, recent studies show that AVLLMs face a critical challenge: $\textbf{source-confused grounding hallucination}$, where cues from the unused modality induce responses that the required modality does not support, undermining reliability in real-world applications. Existing methods have made progress in mitigating this failure, yet how it arises from internal cross-modal interactions remains insufficiently understood. To address this gap, we conduct path-intervention and representation analyses, revealing a $\textbf{question-relay}$ mechanism: question states carry interfering cues alongside required-source evidence, undermining grounding in required-modality evidence. Cutting pathways from interfering modality to question states yields greater correct-answer logit recovery than cutting those to the generation position. Motivated by these findings, we propose $\textbf{SECRET}$ ($\textbf{S}$ourc$\textbf{E}$-$\textbf{C}$onditioned $\textbf{RE}$lay s$\textbf{T}$eering), a training-free method that mitigates cross-modal interference at the question relay. Using contrasting question representations elicited through different modality-pathway interventions, SECRET steers the original question states toward required-source evidence. Experiments on two widely adopted benchmarks CMM and AVHBench across three AVLLMs show that SECRET consistently outperforms prior training-free methods, substantially mitigating source-confused grounding hallucinations (e.g., up to +18.0 and +7.1 percentage points over base models). Modality-specific captioning further demonstrates its generalizability to open-ended generation.

Activation verbalization methods such as Activation Oracle and Natural Language Autoencoders decode hidden representations of large language models into human-readable natural language. However, existing methods can produce incomplete or hallucinated descriptions, making their activation verbalizations difficult to trust and use reliably in practice. To this end, we introduce AVPO, a two-stage framework that first reconstructs source text from a hidden activation and then evaluates the resulting text with a separate frozen question-answering model, yielding an explicit and inspectable intermediate readout. We further optimize the inverter with direct preference optimization (DPO), using rewards that capture both semantic recoverability and lexical fidelity. Across six text families, AVPO improves gist- and detail-level information recovery over the strongest baseline by up to 17.1 and 9.3 percentage points, respectively. Crucially, the gains arise from preference optimization rather than fine-tuning on selected reconstructions alone, enabling compact cross-model inverters to surpass donor-matched question-conditioned verbalizers while improving both semantic recoverability and lexical fidelity. Moreover, out-of-distribution case study shows that AVPO better recovers high-level semantics while fabricating fewer details.

Faithfulness evaluation of abstractive summaries remains an open challenge, with existing metrics addressing only isolated hallucination types: factual entity errors, relational inconsistencies, or numerical fabrications, without capturing their co-occurrence or interaction. We introduce CHI (Composite Hallucination Index), the first unified hallucination metric that decomposes faithfulness errors into three orthogonal dimensions: entity hallucination (EHI), relation hallucination (RHI*), and quantity hallucination (QHI). Each dimension employs a shared softmax-normalized architecture over Venn diagram-derived factors representing extractiveness, positive hallucination, over-focus, negative hallucination, and lost focus. The novel QHI component introduces tolerance-aware numerical matching with exact, epsilon, derived, and temporal comparison modes. We fuse the three dimensions via harmonic mean to produce a single composite score that penalizes weakness in any dimension. We validate CHI on 800 source articles spanning four domains (news, medical, legal, financial) with summaries from five generation systems. Empirical results demonstrate that: (i) the three dimensions are statistically orthogonal (mean rho = 0.148), confirming they capture distinct error types; (ii) CHI achieves the highest system-level correlation with human judgments (rho = 0.66, p = 0.006) on SummEval, outperforming ROUGE (rho = 0.53), EHI (rho = 0.58), and all individual components; and (iii) ablation studies confirm that all three dimensions contribute unique variance, with the full composite outperforming any individual component while providing decomposable error diagnostics unavailable from single-score baselines. CHI provides practitioners with a decomposable, interpretable, and efficient faithfulness metric suitable for both offline evaluation and online monitoring of summarization systems.

Language models (LMs) often hallucinate by committing to confident answers rather than abstaining, even when they do not have enough information to answer reliably. A large body of existing work mitigates hallucination through detection or abstention mechanisms, but leaves open how models internally arrive at the decision to commit or abstain in the first place. We study this decision through mechanistic analysis, framing hallucination as unsupported commitment: the model commits despite exhibiting signals of unanswerability. Using causal gating, we identify a Commit-Abstain Circuit (CAC), a sparse, causally localised subset of attention heads and MLP sublayers underlying this decision. Across ten LMs (3B-14B) from five families and three benchmarks, the CAC exhibits a recurring accumulate-yet-undercorrect pattern: commitment-promoting components build up commitment in earlier layers, while abstention-promoting components act later as corrective signals that are often insufficient to overturn the accumulated commitment. Building on this finding, a lightweight policy trained on CAC activations improves decision accuracy by 12.2 points over the model's intrinsic commit-abstain margin, reduces false abstentions by 2.5 times, transfers to unseen benchmarks, and extends to larger models (27B-35B). The CAC is both diagnostic, clarifying how models overcommit, and practical, enabling improved abstention decisions.

Interpretable machine learning for Large Language Models (LLMs) increasingly relies on sparse probing methods that identify small sets of neurons claimed to detect and causally influence behaviors such as factuality recall, safety alignment, and hallucination. These claims have important implications for model auditing and behavioral steering, yet they are rarely tested against known failure modes of $L_1$-regularized probing in correlated, high-dimensional feature spaces. We propose a five-step diagnostic protocol covering feature correlation, bootstrap stability, sparse versus dense ranking disagreement, intervention baselines, and cross-dataset evaluation as a minimum standard for sparse-neuron localization claims. We investigate prior work using our proposed approach, specifically on H-neurons using open-source LLMs across TriviaQA, BioASQ, and NQ-Open datasets. Our results demonstrate detection replicates across both models and datasets, and exceeds the original reported AUROC gaps for TriviaQA and BioASQ datasets. Gemma 3 4B consistently outperforms MedGemma 4B on matched datasets, with AUROC gaps of +0.311 versus +0.235 on TriviaQA, +0.474 versus +0.455 on BioASQ, and +0.128 versus +0.112 on NQ-Open respectively. Causal validation at $n = 500$ with five random seeds shows statistically significant effects beyond random same-layer baselines. At the same time, the diagnostic results indicate that the selected neurons are not uniquely localized. Across the three Gemma 3 4B settings, 19 of 22 selected H-Neurons have Pearson $|r| > 0.7$ with other features, bootstrap selections show only moderate stability, and sparse and dense rankings overlap only weakly. Our findings show that sparse predictive structure can coexist with non-unique neuron selection. Routine diagnostic validation is necessary to distinguish detection claims from localization claims in mechanistic interpretability.

Large language models can hallucinate even when the knowledge required for a correct answer is already available. We study this failure through a latent-key view of inference, where answer selection depends on competition among associations acquired during pretraining. We show that model predictions can be highly sensitive to individual query keywords, that these influential keywords exhibit entity-specific binding, and that their effects are systematically shaped by pretraining frequency. Multiple bindings can also compete and exhibit higher-order interactions within the same query. Based on this mechanism, we introduce a two-stage keyword-perturbation method for hallucination detection. By removing influential keywords and measuring how the model reorganizes its prediction, the method distinguishes errors caused by misleading key associations from correct decisions supported by diagnostic evidence. Across multiple models and benchmarks, perturbation provides a strong and transferable detection signal, reaching $0.910$ AUROC on probe-known ScientistQA. Finally, we extend the same probabilistic framework to four hallucination regimes: knowledge deficit, wrong knowledge, context distraction, and unstable inference. Their operational distributions across benchmarks provide diagnostic context for why different detector families succeed in different settings.

Factual hallucination in closed-book question answering is often treated as a coverage problem: a model fails because the relevant fact is absent from its internal memory. This view misses a second source of error. Even when a fact has been observed, finite memory may force it to be stored only approximately. We study this effect through a simple coverage--compression model of factual recall. We consider an unstructured question-answering task with $N$ possible queries and $K$ possible answers. A learner observes $M$ training facts, compresses them into at most $B$ bits, and answers uniformly drawn test queries without retrieval. For a uniformly random ground-truth mapping, we prove $\mathcal{E} \geq \frac{M}{N}\delta^\star\!\left(\frac{B}{M}\right) + \left(1-\frac{M}{N}\right)\left(1-\frac{1}{K}\right)$, where $\delta^\star(r)$ is the inverse rate-distortion function of a uniform $K$-ary source under zero-one loss. The two terms separate compression distortion on observed facts from missing coverage on unobserved facts. The bound gives a compact way to reason about selective memory, forced compression, structure, retrieval, abstention, and long-context organization. We study the predicted signatures with theory-implied simulations and controlled fact-injection probes in modern language models that vary fact load and effective trainable memory. The result is not a complete theory of hallucination, but an information-theoretic account of a separable failure mode: lossy recall of observed facts under finite memory.

Background. Large language models are increasingly used to help write biomedical text but may fabricate references to nonexistent work. How often large language models do so is not well characterized. Methods. We prompted 26 language models from eight developers (2023 to 2026) to supply a missing reference for each of 69 biomedical passages across ten domains. References were classified as verifiable (real paper with a resolving identifier), partial matches (real paper without a resolving identifier), fabricated (no matching indexed paper), or declined (the model refused to supply a reference). A reference was considered correct in every evaluated bibliographic field only when it was verifiable and its journal, year, and listed authors matched those of the cited paper. Results. Fabrication ranged from 10.2% (Claude Opus 4.8, which declined 52.1% of prompts) to 98.4% (Ministral 3B, which produced no verifiable reference). Claude Opus 4.6 and Claude Sonnet 4.5 produced similar proportions of verifiable references (77.6% and 76.6%) but named authors correctly in 78.7% and 28.7% of author-evaluable verifiable references, respectively, and were correct in every evaluated field in 54.6% and 19.9% of responses. GPT-5.5 was correct in every field in 48.1%. Across all models, 55.4% of responses were fabricated and 14.9% were correct in every field. Among the five tested models first released in 2026, the corresponding proportions were 35.3% and 31.8%, respectively. Conclusions. Fabrication remained common, and no model was correct in every evaluated bibliographic field in more than 54.6% of responses. Models that identify real papers may still misstate their metadata, so references produced with model assistance require verification before use.

Current LLM memory systems treat all personal facts identically, so stores grow without bound while retrieval precision degrades. The core challenge is lifecycle management: which memories should persist, which should be replaced, and at what rate, conditioned on the behavioral type of each fact. Fortunate Recall (FR) is a composable policy layer that classifies personal facts into a 10+1 behavioral ontology and applies category-specific lifecycle policies (differential temporal decay, slot-key supersession, event-time validity, and category-aware retrieval routing) as deterministic functions over LLM-extracted metadata. FR-Bank, our infrastructure-independent implementation, reaches a 76.9% pass rate on LifecycleBench, a new 516-question temporal-disambiguation benchmark, ahead of Mem0, A-MEM, Memory-R1, and MemoryOS (61% to 70.5%), and 75.2% on the full LongMemEval-S under the canonical Wu et al. judge protocol, so lifecycle policies impose no measurable cost on standard retrieval. A pre-registered ablation locates the gains: replacing the typed layer with three generic lifecycle primitives leaves correctness statistically unchanged (-1.7pp, 95% CI [-6.0, +2.7]), so the generic lifecycle metadata carries the correctness advantage, while the behavioral ontology carries calibration, halving downstream confabulation (12.0% vs 24.2%, p<0.001). End-to-end, FR-Bank cuts confabulation from Mem0's 45.1% to 22.4% over answered queries and from 32.2% to 13.0% over all queries while answering more of them correctly (31.2% vs 18.6%); the ranking replicates on the open-weight Kimi K2.5. The decomposition transfers to BEAM, an independently built benchmark: 46.8% correct vs Mem0's 32.9% over 280 questions, with the ontology's benefit concentrated in contradiction resolution and saturating near seven policy clusters. The ontology, benchmark, and code are released.

As large language models are increasingly deployed as tool-augmented legal agents, they introduce agentic hallucinations where tool-call and reasoning errors cascade into fabricated holdings and miscited authority. However, existing legal benchmarks evaluate only single-turn QA with outcome-level metrics, while agentic hallucination benchmarks lack legal-specific diagnostic capability. Neither answers to what extent and how a legal agent hallucinates along its trajectory. To address these limitations, we introduce LexAgentHallu, a legal agentic hallucination benchmark designed to evaluate to what extent and how legal agents fail along multi-step trajectories. Built through a four-stage expert-in-the-loop pipeline, LexAgentHallu contains 3414 instances across 17 legal categories and 6 task types. Each instance is annotated under a dual-layer hallucination taxonomy of 7 high-level categories and 27 fine-grained subclasses, covering both substantive errors and agent-procedural failures. We further design fine-grained metrics that quantify to what extent and localize how each failure occurs along an agent's execution path. Our evaluation across 18 proprietary and open-source agents uncovers a Right-Answer-Wrong-Reason effect and reveals that hallucination subclasses cluster rather than scatter, forming distinct agentic framework, legal task, and category profiles. These findings, invisible to outcome-level evaluation, validate the diagnostic power of LexAgentHallu for evaluating agentic hallucination in law.

Financial large language models are increasingly deployed for summarization of reports and disclosures, where numerical hallucination poses significant practical risks. While prior work often attributes such hallucination to insufficient numerical reasoning, this assumption has not been systematically tested under controlled fine-tuning settings. In this paper, we conduct a cost-effective, controlled study of numerical hallucination in financial summarization across three model variants: a base instruction-tuned model, a domain language-adapted model (FT-A), and a numeracy-enhanced domain model (FT-A+B+C). We introduce a three-level detectability taxonomy distinguishing between overt hallucination (currency-denominated fabrication), covert-explicit hallucination (professional-convention numbers), and covert-implicit hallucination (ungrounded quantitative claims). Our results reveal that domain fine-tuning substantially degrades numerical restraint at all detectability levels. While the Base model maintains near-zero hallucination rates (5.4%), FT-A exhibits 82.5% overt hallucination and FT-A+B+C reaches 98%. Contrary to intuition, numeracy supervision amplifies rather than mitigates hallucination across all levels. We identify template injection---the insertion of memorized canonical values regardless of input content---as a primary hallucination mechanism in fine-tuned models. These findings demonstrate that numerical hallucination in financial summarization is driven by the degradation of numerical restraint through domain adaptation, not by insufficient numerical reasoning. We recommend that evaluation protocols assess hallucination across all detectability levels and that deployment practices include explicit mechanisms for grounding-aware generation or abstention.

Large language models (LLMs) have significantly advanced automated program repair (APR), yet existing evaluations remain largely result-centric and provide limited insight into hallucination during repair. In APR, hallucination may arise not only in final patches but also in the intermediate artifacts that guide patch generation. To address this gap, we perform a multi-layered analysis of hallucination throughout the APR process. Specifically, we characterize hallucination as the production of patches or intermediate artifacts that are not faithfully grounded in the available repair evidence. We examine repair hallucination in final patches and understanding hallucination in intermediate artifacts through three tasks, namely triggering testcase identification, line coverage prediction, and additional testcase generation. We then evaluate three representative LLMs on 832 Defects4J bugs through automatic evaluation and manual analysis. Our results show that both repair and understanding hallucinations remain prevalent. Across models and settings, only 21.0%-55.9% of generated patches pass the developer-written test suite. Moreover, although more accurate intermediate artifacts are generally associated with successful repairs, this relationship does not always hold. Manual analysis of 812 sampled repairs identifies repair hallucinations in 72.7% of cases, including patches that pass all available tests; incorrect causal localization and incorrect repair strategies account for 45.9% and 18.5% of these hallucinations, respectively. Meanwhile, models frequently misidentify triggering testcases, mispredict line coverage involving branching control flow, and generate additional testcases with missing bug-triggering conditions or incorrect expected behavior.

Role-playing large language models (LLMs) are expected to adopt a character's style while also respecting that character's knowledge boundaries. Prior evaluations detect character hallucination but rarely distinguish whether errors arise from failure to recognize a boundary or from failure to comply despite recognition. We introduce CHARM, a multicultural benchmark of 40 real and fictional characters drawn from five cultural-linguistic regions, and validated by native reviewers. It probes two boundary types, Temporal (historical vs. modern) and Cross-Universe (entities outside a character's narrative or historical universe), using abstention-enabled multiple-choice questions. We propose a two-stage evaluation that separates Boundary-Awareness (explicit recognition that a query is out of scope) from Boundary-Compliance (abstention when answering concrete questions). Evaluations across six LLMs show that hallucination is driven predominantly by compliance failures. Models frequently acknowledge that a query lies outside the character's knowledge yet still provide factual, out-of-character answers. By re-posing the same questions to the target character, we confirm that a large fraction of these cases are verified parametric overrides; the model stores the relevant fact but fails to suppress it. We also observe systematic cultural variation in these failures, consistent with imbalances in how characters from different regions are represented in model knowledge.

Both privacy and factual accuracy are paramount in high-stakes domains like healthcare. Concerningly, we uncover and investigate a privacy-hallucination tradeoff in differentially private (DP) language models. First, we empirically show that models pre-trained or fine-tuned with DP tend to produce more hallucinations than non-DP counterparts, with increased severity as the privacy budget grows stricter. Second, we investigate model properties driving this tradeoff, demonstrating that DP mechanisms flatten output distributions, potentially redistributing probability mass toward factually incorrect alternatives. Third, through experiments where we control fact frequency in training data, we characterize how information frequency can reduce hallucination risks in DP models. Overall, our findings underscore the need for more nuanced privacy-preserving interventions that offer rigorous privacy guarantees without compromising factual accuracy.

Large Language Models (LLMs) deployed as AI agents frequently exhibit user specification-grounding failures, executing hallucinated, undesired actions to force a resolution rather than expressing uncertainty. Existing detection methods fail to provide actionable, real-time correction as they either do not localize the hallucinations, or incur prohibitive inference latency. We introduce the Latent Critic, a lightweight low-rank adapter (LoRA) that operates concurrently with a frozen base LLM's generation to actively restructure the transformer's residual stream---amplifying latent grounding signals and translating them into localized, natural language feedback within a single sequence. By refining the base model's native uncertainty signals, this manipulation of the latent space enables reliable, granular detection without the overhead of secondary inference loops. Mechanistic analysis via activation patching and layer-wise probing shows that this rank-invariant behavior restructures pre-existing uncertainty geometry into a linearly separable representation that transfers more reliably than base model representations alone. Using tool-calling as an instantiation of granular hallucinations, we validate the detection and downstream improvements enabled by the Latent Critic architecture across Qwen and Llama-based models. Demonstrating superior real-time efficacy, our approach significantly outperforms equivalent-scale fine-tuned external detectors, semantic entropy baselines, and passive internal probes in isolating hallucinations, achieving 0.966 AUROC and >80% accuracy in localization (e.g., ungrounded: date). When deployed in a closed-loop ReAct environment, the Critic acts as a negligible latency guardrail, intercepting hallucinations before execution to prevent undesired actions while simultaneously leveraging this specific localized feedback to enable efficient agent self-correction.

Large Language Models (LLMs) have achieved strong performance in medical question answering and clinical reasoning tasks. However, their reliability under uncertainty remains poorly understood which raises critical concerns for deployment in high-stakes clinical settings. In such environments, incorrect predictions are inherently risky, but confident incorrect predictions can be particularly harmful as they may mislead clinical decision-making. In this paper, we conduct a systematic behavioral analysis of LLMs under clinical information uncertainty. We propose an evaluation framework based on the MedMCQA dataset consisting of two complementary uncertainty settings. First, we introduce linguistic uncertainty cues through prompt modifications to simulate ambiguous clinical contexts. Second, we construct an answer removal setting, wherein the correct option is deliberately excluded mandating the model to recognize insufficient information and abstain. We analyze both model accuracy and confidence behavior using multiple calibration metrics including calibration gap, Expected Calibration Error (ECE), and Unsafe Confident Error Rate (UCER) across 500 medical questions. Our results reveal a consistent failure mode, i.e., although accuracy degrades under increasing uncertainty, model confidence remains misaligned with accuracy. This leads to a substantial increase in unsafe confident errors, indicating that model confidence remains largely insensitive to clinically meaningful information loss. Furthermore, we observe significant variation across models in their ability to abstain when the correct answer is unavailable, with some models persistently producing high confidence hallucinated answers. These findings expose critical limitations in the epistemic reliability of current LLMs and highlight the need for uncertainty aware evaluation methods prior to their deployment in clinical workflows.

Abstractive text summarization systems frequently generate fluent yet unfaithful summaries by fabricating or distorting relationships between entities and events. Such relation-level hallucinations undermine the reliability of generated summaries, particularly in high-stakes domains. In this work, we present a refined and grounded framework for evaluating relation hallucination in abstractive summarization. We present the empirical Relation Hallucination Index (RHI) by introducing a dependency-aware relation extraction algorithm that incorporates lemmatization-based normalization, named entity grounded subject resolution, passive agent recovery, negation-aware verb modeling, reporting verb filtering, nominal relation fallback, clausal propagation, and systematic deduplication. These enhancements improve the structural fidelity of extracted relation triples and reduce spurious matches during evaluation. In addition, we introduce a normalized formulation of RHI to ensure scale-invariant comparison between datasets and models. The revised metric decomposes hallucination into interpretable components, aggregates relation hallucination metric into a normalized relation faithfulness score. Extensive evaluation across multiple state-of-the-art summarization models demonstrates that the grounded extraction process yields more stable and discriminative hallucination measurements. The proposed framework advances automated relation-level faithfulness evaluation and supports coherence-aware, hallucination-sensitive model analysis.

Large language models (LLMs) are often used in conjunction with external knowledge sources to improve their factual accuracy and decrease hallucinations, through methods such as Retrieval-Augmented Generation (RAG). However, these systems remain susceptible to intrinsic hallucinations, where the model generates unfaithful or fabricated information that is not supported by the retrieved evidence. We propose a novel framework to assess model robustness against this phenomenon by stress-testing using natural, semantically equivalent variations of a user query found via adversarial optimization methods. We apply our framework, which enforces strict semantic equivalence constraints and an intrinsic hallucination objective, to a range of adversarial attack techniques across white-box, gray-box, and black-box adversarial settings. Evaluating these attacks on 5 open-source and 5 closed-source generator models across 3 datasets, we demonstrate that even state-of-the-art models are highly susceptible to meaning-preserving perturbations, which significantly degrade contextual faithfulness (by up to 50% for GPT-5-mini). Our findings indicate that faithful use of in-context evidence remains fragile even in state-of-the-art LLMs, motivating architectures and training objectives that enforce robust grounding independent of surface query form. Code is available at: https://github.com/atriviveksharma/intrinsic_hall

Superhuman game engines in domains like chess have made expert-level evaluations easily accessible, yet they communicate what is true without the natural-language explanations that make such expertise educationally useful to experts and non-experts alike. Large language models could, in principle, bridge this gap, but they frequently hallucinate due to limited domain-specific knowledge, and standard reference-based or LLM-as-a-judge frameworks cannot reliably detect these errors. In this work, we present ACT-Eval, an evaluation framework that decomposes chess commentary into atomic claims and routes them to engine-supported tools and expert-annotated gold references to assess factual correctness, conceptual coverage, and move-quality judgment. We release a benchmark of 325 position--move pairs spanning pedagogical, tournament, and critical positions, including 125 positions with expert-verified gold atoms and a five-class error taxonomy. Evaluating leading proprietary and open-weight models, we find that factual hallucinations remain pervasive in chess commentary: GPT-5.4 without tools produces incorrect sub-claims 22.0% of the time, while smaller open-weight models exceed 40%. Although tool augmentation substantially improves factual correctness and move-quality assessment, coverage of expert strategic and tactical ideas remains limited across all models. Human calibration shows that ACT-Eval's factual judgments fall within the observed range of inter-human agreement, while its coverage scores correlate strongly with human assessments of strategic completeness.

Large language models can generate fluent Arabic answers while introducing factual errors that are difficult to identify and verify. Existing Arabic hallucination resources often assign a binary label to an entire response, indicating whether it is hallucinated or non-hallucinated, but provide limited information about the exact erroneous content, the reason for the error, or the correct factual answer. We present HalluTruthQA-4K, an expanded version of the HalluTruthQA resource containing 4,000 expert-curated Arabic question-answering instances across four knowledge-intensive domains: Islamic knowledge, history, science, and geography. Serving as the official dataset for Track 2 of the HalluScoring 2026 shared task, HalluTruthQA-4K extends our original corpus to 4,000 instances. Each instance pairs an Arabic question with a model-generated response, a verified reference answer, and five plausible distractors. Hallucinated responses are additionally annotated with character-level erroneous spans, human-written explanations, and hierarchical hallucination types. The corpus contains 1,643 hallucinated and 2,357 non-hallucinated responses, with 1,843 annotated erroneous spans. We describe the resource construction and annotation methodology, including question selection, controlled answer generation, candidate construction, expert annotation, independent verification, adjudication, and quality control. We also document the annotation guidelines, taxonomy, data format, inter-annotator agreement, and corpus statistics. HalluTruthQA-4K provides a reusable resource for hallucination detection, span-level error localization, explanation generation, factual verification, and the broader evaluation of factual reliability in Arabic language models.

Large language model (LLM) agents are increasingly deployed in scientific research, where reliability is critical and the underlying knowledge is densely interconnected. In such settings, hallucinations are particularly damaging: a single erroneous claim on a foundational concept can propagate through multi-step reasoning and corrupt entire trajectories. Existing hallucination benchmarks largely operate at the surface level, treating facts in isolation and relying on uniform accuracy metrics that ignore this topological structure. We address this gap with SCHEMA, the first evidence-grounded, topology-aware evaluation framework for hallucinations in scientific agents. SCHEMA automatically constructs scientific concept graphs from benchmark seeds and literature evidence, synthesizes graph-grounded tasks spanning claim verification, multi-hop reasoning, open-ended explanation, and experimental code generation, and evaluates agents with two complementary diagnostics. A trajectory hallucination pipeline audits intermediate reasoning at scale via a topology-weighted severity score, while a multi-agent counterfactual attribution module pinpoints the causal mechanism behind selected failures. SCHEMA reveals that hallucinations concentrate at a small set of highly connected knowledge hubs, and that final-answer accuracy decouples from trajectory honesty; models often reach correct conclusions through structurally flawed reasoning. These results indicate that for high-stakes scientific applications, terminal accuracy alone is an insufficient signal of agent reliability, motivating mechanism-level evaluation grounded in knowledge topology. Code is available at https://github.com/circles-post/SCHEMA.

Large Language Models can produce fluent text that is false, unsupported by the available evidence, or inconsistent with information that appears to be internally represented by the model. We study hallucination detection from the geometry of hidden activations and introduce the D-Score, a simple spectral statistic computed from a single forward pass. For a fixed model, layer, and tolerance parameter, the D-Score counts how many singular directions of the hidden activation matrix have singular values that remain close to the leading one. We use this quantity as a hallucination score, classifying an input text as hallucinated when its D-Score is larger than a pre-defined quantity. The motivation is that, when a model processes a text that conflicts with information available in its own internal state, the hidden representation may encode both the asserted content and some form of counter-evidence, uncertainty, correction, or lack of support; this can make the hidden trajectory spread across additional singular directions. We formalize this intuition through a lightweight spectral argument and evaluate the resulting detector on FAVA-Annotation and RAGTruth. The experiments indicate that the D-Score is a strong hidden-state signal for hallucination detection, while requiring no external verifier, no retrieval step, and no multiple generations.

A conversational AI that cannot tell its own output from what a user said will treat its own mistakes as user-provided facts. In humans, this capacity is called reality monitoring, and its failures are linked to hallucinations, delusions, and confabulation, yet whether LLMs possess it remains untested. Here we show, across two experiments and six LLMs, that source attribution depends on how conversational memory is structured: ceiling accuracy for self-generated content under minimal memory demands reverses to a fragile external-item advantage once episodic delay removes that shortcut. Feedback exposes two failures: in some models, internal and external judgments swap; in others, accuracy improves while confidence decouples from correctness, dissociations invisible to existing benchmarks. Across models, this pattern implicates active, not aggregate, parameter count. This suggests that as AI systems take on autonomous, multi-turn roles, evaluating what they know is not enough: tracking where that knowledge came from may matter equally.

Language generation in the limit is an elegant model introduced by Kleinberg and Mullainathan [KM24] to formally study language generation by an algorithm that learns solely based on example strings. In this model, an algorithm is said to correctly generate from a language if it never makes an error after some finite time. In contrast, even sophisticated language models are known to regularly hallucinate in practice. In this paper, we initiate the study of language generation in the limit with (infinite) hallucination, i.e., the algorithm may generate incorrect strings infinitely often, but the errors occur at a limited rate (possibly even with 0-measure). We first show that hallucination, even at rate 0, makes generation in the limit strictly more powerful: there are language collections that cannot be generated with finite error but can be generated with infinite error, even when errors occur on a 0-measure set of time-steps. Furthermore, while all countable collections are generatable with finite error, we show a strict hierarchy of (uncountable) language collections characterized by the hallucination rate. This hierarchy extends to breadth, the fraction of the target language generated. While all countable collections can attain the optimal breadth of 1/2 [KW26b], we show strict separation at every breadth and hallucination rate. Finally, we study generation in the limit without repetition, where the algorithm may not repeat strings. This lets us compare the sets of correct and incorrect strings generated, rather than the fractions of correct and incorrect time-steps. Once again, we demonstrate a strict hierarchy at every hallucination rate and breadth. Taken together, these results reveal rich structure in language collections generatable in the limit with hallucination and establish hallucination rate as an important parameter in the theoretical study of language generation.

Despite remarkable progress in visual understanding, Multimodal Large Language Models (MLLMs) remain prone to hallucinations when reasoning about spatial relationships, often producing judgments that contradict the true 3D structure of the scene. Though several existing works have proposed to mitigate hallucinations, our analysis indicates that they show limited effectiveness in spatial reasoning, as they fail to bridge the fundamental gap between 2D visual representations and 3D spatial reality. Based on this finding, we define hallucinations arising from insufficient spatial structure modeling as spatial reasoning hallucination, a subcategory of relation hallucination that existing mitigation methods fail to address. We further identify three typical scenarios where such hallucinations frequently occur: perspective effects, object orientation, and viewpoint changes. To this end, we propose Geo3R, a training-free, plug-and-play framework that incorporates geometric evidence and structured 3D reasoning to mitigate spatial reasoning hallucination. Experiments on three benchmarks, covering 18 tasks across all three scenarios, show that Geo3R substantially reduces spatial reasoning hallucination across diverse MLLMs without additional training, outperforming existing models and methods.

Chemical reasoning language models are expected to derive molecular answers through faithful chain-of-thought (CoT). However, across four reasoning model families and twelve chemistry tasks, hallucination is widespread and largely decoupled from answer correctness: correct answers often coexist with fabricated structural claims absent from the relevant molecules. Yet this does not make the reasoning trace computationally irrelevant. Attribution analyses suggest a shared scratchpad function expressed in model-specific forms: Chem-R and ether-0 rely on fragmented SMILES drafts, whereas ChemDFM-R emphasizes scaffold, positional, and naming cues. Notably, perturbing Chem-R's SMILES sketches degrades generation, showing that structural drafts can be causally load-bearing even when verbal structural claims are largely inert. Together, these results show that chemical CoT is neither a faithful explanation nor merely a post-hoc rationalization, but a hallucination-prone molecular scratchpad. This finding cautions against treating CoT as direct evidence of faithful reasoning and motivates process-level supervision beyond answer-only evaluation.