Language Models · 5 Interactives

The Confident Machine That Cannot Say "I Don't Know"

A language model never looks anything up. It always does the same move: output the most plausible continuation. When plausible and true line up, it looks like knowledge. When they split apart, you get a hallucination — same mechanism, same confident tone. These five machines let you find the split yourself.

① Plausible ≠ true② The knowledge boundary③ Calibration, live④ The citation factory⑤ The "I don't know" dial
EP 01

The plausibility engine — it answers with fame, not fact

A model completes “The capital of Australia is ___” by asking one question: which city appears most often next to “Australia” in text? Below, the bars are exactly that — co-occurrence statistics, not a lookup table. Pick a country, see what the machine would say, then flip on the truth.

The mental model: for France, fame and fact point at the same city — the statistics are the knowledge, and the model looks brilliant. For Australia or Turkey, fame and fact diverge, and the model confidently outputs the famous wrong answer. Hallucination is not a glitch; it's the normal mechanism running on a question where plausibility and truth disagree.
EP 02

The boundary it cannot see — a map of what it knows

Imagine every possible question as a point on a map, and the model's training data as a lit region. Ask questions one by one. Crucially: the model has no sensor for the boundary. A question outside its knowledge produces text through the exact same machinery — fluent, specific, confident. First ask a few blind, then reveal the map.

Press “Ask a question” — each question lands somewhere on the map.

Before the reveal, every dot is the same color on purpose — that is the model's point of view. It cannot tell which of its own answers are grounded.

Why it matters: GPT-scale models were trained on trillions of tokens, so the lit region is enormous — but it still has edges (your private life, last week's local news, made-up companies). Questions past the edge don't fail loudly; they get answered in the same fluent voice. The danger is that the seam is invisible from the outside too.
EP 03

Build a calibration plot — is 90% sure right 90% of the time?

A model is calibrated if its confidence matches its accuracy: of everything it says with 80% confidence, 80% should be true. Quiz this toy model live and watch the plot fill in. Green dots land on top (correct), red on the bottom (wrong); the mustard curve is measured accuracy per confidence bucket. Then switch the question mix and watch calibration break.

Simulated quiz for illustration — the shapes match what real calibration studies measure on LLMs.

The pattern you just built: on familiar ground the curve hugs the diagonal — confidence is honest. Mix in novel questions and the curve sags below it: the model still feels 85% sure while being right far less often, because its confidence comes from fluency, not evidence. This gap is what researchers mean by “LLMs are miscalibrated on the tail.”
EP 04

The citation factory — perfectly formatted, entirely fake

Why do models invent references? Because a citation is a pattern: plausible surname + year + title-shaped phrase + journal + DOI. Each slot is filled with something statistically typical, so the whole looks real — the parts are color-coded below so you can see the assembly. Generate a few, then check them against the library.

Press “Write me a citation.”

authors from surname statistics · year from the typical range · title from topic phrase templates · venue & DOI from format patterns. Every slot is plausible; the conjunction was never checked against anything.

The good case is the exception that proves the rule: “Attention Is All You Need” appears so many times in training data that the pattern is the fact — the model reproduces it verbatim. Everything rarer gets rebuilt from parts. This is exactly how real chatbots produced fake legal precedents that got lawyers sanctioned: right format, right style, no referent.
EP 05

The “I don't know” dial — trading hallucinations for refusals

The classic fix: let the model refuse whenever its confidence is below a threshold. Slide the dial and re-run the 40-question exam. Each square is one question: green = answered correctly, red = hallucination (confidently wrong), dark = refused, outlined = over-refusal (it refused something it actually knew). The curves show the whole trade-off at once.

There is no free lunch, only a dial: at 0% you get the plausibility trap — every unknown question becomes a confident fabrication. At 95% the model refuses questions it knew cold. Real labs tune exactly this precision/recall trade-off with RLHF and abstention training — and different products (search engine vs. creative writer) deliberately park the dial in different places.
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