The Confident MachinePre-print

Part IV: Measuring & Detecting · Page 9 of 14

How Do We Know It's Wrong?

Four benchmark lenses

A single "hallucination score" doesn't exist, because there isn't a single kind of failure to score. Four widely used benchmarks each check a different one:

BenchmarkTestsResultDoesn’t capture
TruthfulQARepeats a common misconception instead of the plain truth, on questions people themselves tend to answer wrong.Best model 58% truthful · Humans 94%Only checks against a fixed list of known myths, not facts outside the question set.[9]
SimpleQAGets a short, single-fact question right, and whether it guesses or admits it doesn’t know.GPT-4o: 38.2% correct · 1.0% not attempted · 60.8% incorrectShort, single-fact questions only, each with one verifiable answer.[29]
HaluEvalTells a hallucinated answer apart from the correct one when both are shown side by side.ChatGPT: 62.6% correct (QA split)Picking the hallucinated one out of a pair isn’t the same as catching one with nothing to compare it to.[30]
FActScoreWhat fraction of the individual factual claims in a long-form answer are supported by a reliable source.ChatGPT average: 58.3% supportedNeeds a reliable source to check against, and scores only precision, not what got left out.[31]

These are different lenses, not interchangeable measures of one universal hallucination score.

What a score hides

A benchmark's headline number can mislead two separate ways: the grader itself can be wrong, or a mix of guessing and abstaining can hide inside one aggregate figure.

Exact-match vs. human grading

“What was the city of Beijing previously known as?”

Model: “Jicheng” (a real former name) · Reference: “Peking”

✗ exact-match fails: no lexical match

EM 12.6%Human 71.4%

NQ-open, 301 questions.[32] A correct answer worded differently, like “Jicheng” above, fails exact-match but passes human review.

Same “correct” rate, different failure

GPT-4o-mini

8.6% correct · 0.9% not attempted · 90.5% incorrect

OpenAI o1-mini

8.1% correct · 28.5% not attempted · 63.4% incorrect

correctnot attemptedincorrect

Both get about 8% right, but GPT-4o-mini guesses on nearly every question (90.5% wrong) while o1-mini abstains instead of guessing on over a quarter of them (63.4% wrong).[29]

One score can hide whether failure came from a bad grader, an incorrect guess, or a refusal to answer.

Confidence is informative, not decisive

Benchmarks grade after the fact. But a model computes a probability for every token it generates internally, whether or not the chat interface in front of it ever shows that number.

Calibration is what would make that internal number worth trusting. A model is calibrated if, across every answer it gives at 70% confidence, roughly 70% turn out correct, a property of the whole curve of stated confidence against accuracy, checked across many predictions, not a claim about any single one.[33]

GPT-4 · held-out MMLU slice

Pretrained and after-RLHF, against perfect calibration.

00252550507575100100Stated confidence (%)Actual accuracy (%)84%50%
Perfect calibrationPretrained (ECE 0.007)After RLHF (ECE 0.074)

Approximate: the nine points per curve are read from the published figure; the ECE values are exact, printed in the original.[34][6]

But calibration in aggregate doesn't rescue any one fluent, high-probability sentence: a model can be well calibrated overall and still generate a wrong answer with high token probability, because calibration describes a distribution of outcomes, not a guarantee on any one output.[6]