Relational Linearity is a Predictor of Hallucinations

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 $.910$ 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.

Hallucinations, where language models (LMs) generate factually ungrounded responses, pose serious risks, as users tend to blindly rely on them. This is particularly concerning in high-stakes domains, where consequences of such model behavior can lead to significant harms. Despite notable progress in understanding hallucinations, it remains unclear how reliably these models can recognize the limits of their knowledge. We introduce PhantomBench, the first large-scale benchmark of its kind, comprising more than 60K non-existent terms and entities derived from real concepts across diverse domains. Using our benchmark, we evaluate a total of 21 models of various types and sizes. We show staggering hallucination rates across the board (with average rates as high as 86.7% in some cases), and note that even frontier models surprisingly fail to abstain on non-existent concepts, especially when the input presumes their existence. We then show that PhantomBench can serve as a proxy for studying model behavior on rare concepts for which models are more prone to hallucinate. We also provide a pipeline to construct PhantomBench, enabling scalable generation of non-existent concepts tailored to the specific needs of researchers and practitioners.

Large language models often produce hallucinated answers that violate prompt-level constraints. A key diagnostic question is whether these failures reflect missing knowledge, or whether the model has the relevant information but follows the wrong inference path. We study this phenomenon as inference misalignment: a mismatch between the answer supported by the prompt and the answer favored by statistically salient latent associations. We formalize this view with a latent key-task model, in which pretraining-frequency imbalance can cause a shortcut path to dominate the constraint-sensitive path and induce positive inference loss. The framework predicts two failure modes: task-retrieval bias in entity disambiguation and key-selection bias in action choice. We introduce TrapQA, a controlled diagnostic testbed with two components. ScientistQA tests disambiguation among similar scientists with supplementary factual probes, while Real-Life Constrained QA tests everyday constraint following under salient shortcuts. Our results show that hallucination can arise from biased latent inference rather than absent knowledge alone.