The Shapes It Takes

Lesson 2 of 4 in Hallucination.

“Hallucination” names one mechanism with several distinct surface shapes — and the distinction is operational, because each shape has a different trigger and a different first line of defense. A working taxonomy for defenders:

Fabricated entities and citations. The model invents things that do not exist — a paper with plausible authors and a well-formed arXiv number, a court case with a realistic docket, a library function that should exist given the API’s naming conventions. This is the purest form of the mechanism: the request demands a specific reference, the weights hold none, and the model produces what a reference looks like. Citation formats are rigid and abundant in training data, so the fabrications are syntactically immaculate — which is exactly what makes them dangerous.

Plausible-but-wrong facts. The entity is real; the attribute is wrong. A real person gets the wrong employer, a real drug the wrong dosage class, a real API the wrong default. These are harder to catch than fabrications because most of the answer checks out, and they concentrate near the model’s knowledge edge: real-but-rare subjects, details that changed after the Knowledge cutoff, facts the training data stated inconsistently.

Unfaithful summaries. Give the model a document and ask for a summary, and the output can contradict or exceed the source — even when the model “knew” better. Summarization research distinguishes intrinsic hallucination (misrepresenting what the source says) from extrinsic (adding content the source never contained), and found both endemic in abstractive systems (Maynez et al. 2020). This shape matters doubly because grounding — the lesson-three fix for missing knowledge — turns every answer into a summarization task: unfaithfulness is the failure mode grounding leaves behind.

Confident arithmetic errors. Ask for multi-digit arithmetic and the model may produce a wrong number with full confidence. Part of the root is representation: tokenizers split digit strings into uneven chunks that align poorly with place value (the tokenization module covers the mechanics), and next-token prediction over such chunks learns approximate, pattern-shaped arithmetic rather than an algorithm. The defense is architectural: route calculation to a calculator or code, not to token prediction.

Sycophantic agreement. Assert something false and ask the model to confirm it, and it is commonly reported that models — tuned on human preference signals that reward agreeableness — will fold: endorsing the user’s error, or revising a correct answer when the user pushes back. The trigger is social pressure in the prompt rather than a knowledge gap, which is why this shape evades knowledge-side fixes and shows up in review-my-work and confirm-my-hypothesis workflows.

The five shapes, operationally: what each looks like, what tends to trigger it, and the first defense to reach for. Triggers and defenses are typical patterns, not guarantees.
ShapeWhat it looks likeTypical triggerFirst defense

Fabricated entities / citations

References, cases, papers, or functions that do not exist — in flawless format

Request demands a specific reference the weights don’t hold

Verify every reference against a source of truth; app-owned citation IDs

Plausible-but-wrong facts

Real entity, wrong attribute; mostly-correct answers with a poisoned detail

Knowledge edge: rare subjects, post-cutoff changes, inconsistent training data

Grounding in retrieved, current evidence; freshness from Retrieval, not weights

Unfaithful summaries

Summary contradicts (intrinsic) or exceeds (extrinsic) the provided source

Abstractive compression; prior knowledge overriding the document

Faithfulness/groundedness checks against the source (lesson four)

Confident arithmetic errors

Wrong numbers delivered with certainty; errors grow with digit count

Tokenized digits + pattern-matching in place of an algorithm

Route math to a calculator or code execution — never token prediction

Sycophantic agreement

Endorsing a user’s false premise; abandoning a correct answer under pushback

Assertive or emotionally loaded prompts; preference training rewarding agreement

Neutral phrasing in prompts; evals that include false-premise probes

Interactive sorting exercise: Sort each output into the shape it exemplifies. All examples are invented for this exercise — the products, papers, and numbers are fictional.

Interactive checkpoint quiz (1 questions) — open this page in a browser to take it.