Hallucination Types in Language Models: A Complete Guide › Factual Errors

Factual errors are hallucinations that occur in open-domain generation, where the model makes incorrect claims about the world without any source document to contradict. These do not need a reference document to identify: they are wrong with respect to established facts.

Factual errors are perhaps the most common hallucination type users encounter in everyday use of language models. When someone asks a model to explain a historical event, describe a scientific concept, or provide information about a public figure, the model draws on parametric knowledge acquired during pretraining. This knowledge is incomplete, unevenly distributed, and susceptible to the same statistical conflation mechanisms that produce other hallucination types. The result is a broad category of factual errors that spans wrong attributes, incorrect numbers, outdated information, and misrepresented relationships.

The most common factual errors involve incorrect attributes assigned to real entities: people, places, organizations, or events. Common patterns include:

• Wrong dates: "Albert Einstein was born in 1871" (he was born in 1879)
• Wrong places: Attributing an event to the wrong city or country
• Wrong roles or titles: Misattributing a title or position that was held by someone else
• Wrong relationships: "Darwin published On the Origin of Species in collaboration with Alfred Wallace" (he published it independently)

These errors are often plausible: the incorrect fact shares a structure with the correct one (a year, a place name, a title). This plausibility is what makes them dangerous. A reader without prior knowledge of the fact may have no way to identify the error. The model confidently states something that fits the template of the correct answer while substituting a wrong value, and there is no surface signal to alert the reader that the specific value is wrong.

The root cause in many cases is conflation: the model has learned many similar facts about many similar entities and blends them incorrectly. A model that has seen thousands of scientist birth years might confuse the specific year attached to a specific name, producing an error that fits the template perfectly while getting the value wrong. This is analogous to the false-memory phenomenon in human cognition, where a person confidently remembers something that did not happen because it fits a plausible narrative they have constructed. The model's "memory" is the statistical associations learned during training, and those associations do not always preserve the exact values attached to each entity.

The density of an entity's representation in training data also matters. A model trained predominantly on English-language web data will have seen far more information about certain entities than others. Well-documented historical figures with thousands of Wikipedia revisions, book entries, and news articles are less likely to produce entity errors than lesser-known figures who appear in only a handful of training documents. The model's factual reliability is, in a sense, proportional to the richness of evidence it saw during training.

Numerical facts are particularly prone to hallucination. Models encounter many numbers during training but often fail to correctly encode and retrieve specific values. Common patterns include:

• Wrong statistics: Citing a percentage, count, or rate that is off by a significant margin
• Wrong magnitudes: Off by a factor of 10 or 100, especially with large numbers
• Wrong directions: A decrease stated as an increase, or vice versa
• Calculation errors: Wrong arithmetic in chain-of-thought reasoning, where intermediate steps compound errors

Numerical errors are especially problematic in high-stakes domains: medical dosages, financial figures, scientific measurements. A model that confidently cites the wrong clinical trial result or the wrong drug interaction threshold could cause real harm. A model that misstates a company's revenue by an order of magnitude could mislead financial analysis. The stakes are high precisely because numbers are precise, and a wrong number is not approximately right but definitively wrong.

Part of why numbers are particularly hard for language models comes down to representation. Unlike words, which appear in varied contexts that help disambiguate their meanings, specific numbers often appear in only a small number of contexts in training data. The number 1879 (Einstein's birth year) and 1871 (a plausible-but-wrong alternative) may both appear in training text, associated with similar surrounding language. The model learns that "Einstein was born in [year]" is a valid pattern, but without a mechanism to reliably retrieve the correct year, it may produce whichever year was most statistically associated in its training data.

Additionally, numbers are often tokenized as sequences of digit tokens, which means the model treats them as a sequence of symbols rather than as a numeric value. This makes arithmetic especially brittle: the model has no internal representation of magnitude or ordering that a programmer would take for granted. When a model performs chain-of-thought arithmetic and produces an intermediate value, subsequent steps inherit any error in that value, and the final answer may be confidently wrong even when each reasoning step looks individually plausible.

Research on numerical hallucinations has also found a systematic bias toward round numbers and common statistical values. Models are more likely to confuse 47% with 50%, or to report that a study used 100 participants when it used 94, because round numbers are more common in training text. This is not random noise but a structured distortion that reflects the statistics of the training corpus.

Language models have a training data cutoff: they know nothing about events that occurred after their training data was collected. This creates a category of errors that are technically factual (the model is reporting what was true at training time) but misleading because they are no longer current:

• Describing a company's current CEO when leadership has changed
• Citing a model's performance benchmarks that have since been surpassed
• Describing a law, regulation, or policy that has since been amended
• Referring to a product's current price, availability, or feature set that has changed

This is sometimes called a knowledge cutoff error rather than a hallucination proper, but the practical effect is the same: the user receives false information presented as current. The distinction matters for mitigation: knowledge cutoff errors can often be addressed with retrieval augmentation (fetching current information), while hallucinations that stem from incorrect stored knowledge require different approaches.

The knowledge cutoff problem is compounded by a subtler issue: models may not accurately know their own training cutoff. A model trained on data through October of one year may have seen far less content about events in the months immediately before that cutoff than about earlier periods, simply because it takes time for events to generate substantial written commentary. This means that a model's effective knowledge degrades gradually before the nominal cutoff rather than ending sharply on a specific date.

Beyond individual attribute errors, models sometimes make mistakes about the relationships between entities:

• Reversing the direction of causality ("A because of B" vs "B because of A")
• Confusing which entity performed an action
• Getting the sequence of events wrong
• Misattributing quotes or ideas to the wrong person

These errors often arise from the same conflation mechanism as wrong entity facts. The model has the right type of fact but attaches it to the wrong entity or reverses the direction.

A concrete example: "Alan Turing broke the Enigma code at Bletchley Park, a discovery that led to the development of the stored-program computer." A relationship hallucination might correctly link Turing to Bletchley Park but incorrectly claim that Enigma's decryption directly caused the stored-program computer, a conceptual leap that misrepresents the historical relationship between those developments. The individual facts are grounded; the relationship between them is not.

Relationship errors can be especially pernicious in reasoning chains. A model explaining a causal sequence might correctly identify the actors and events but describe them in the wrong order or reverse which entity caused which effect. In domains like medicine or law, where the direction of a relationship is precisely what matters, these errors can completely invert the meaning of an otherwise factually grounded statement. A claim like "drug A reduces the risk of condition B" and "condition B reduces the risk if drug A is administered" differ only in the relationship structure, yet have opposite clinical implications.

The frequency of relationship errors increases with the complexity of the knowledge graph being implicitly modeled. Simple, widely-documented relationships (A invented B, C led to D) are less prone to reversal than complex, multi-step causal chains or relationships that involve nuance about the degree of causation. When a model is asked to describe how multiple factors interact, it is drawing on a more sparsely-supported part of its parametric knowledge, and the risk of relationship errors grows accordingly.