When a Model Is Sure and Wrong
Ask It Five Times and Count the Answers
Last timeTwo Different Kinds of Not Knowing
Disagreement between repeated answers measures something a single probability cannot: whether the model is sure because it knows, or sure because it happened to land somewhere.
Asking repeatedly
Decoding is random whenever the temperature is above zero. The same question,
asked five times, produces five runs through the same model with different
random choices at each step, and therefore sometimes five different answers.
The single-pass workflow throws that variation away. It asks once, takes what
came back, and reports the probability attached to it. But the variation is
information: it says how much of the answer was determined by what the model
knows and how much by which way a coin fell.
| step | asking | answer | probability it reported | what happened |
|---|---|---|---|---|
| 1 | 1 | 1947 | 0.91 | Confident, and so far there is nothing to compare it against. |
| 2 | 2 | 1947 | 0.88 | Same answer. Two for two. |
| 3 | 3 | 1947 | 0.93 | Three. |
| 4 | 4 | 1951 | 0.84 | A different answer, reported almost as confidently. The single-pass view would never have seen this. |
| 5 | 5 | 1947 | 0.9 | Four of five agree. The agreement figure is 0.80, against a mean reported probability of 0.89. |
Agreement as a number
Collapse the samples into one figure by counting.
- how many times the question was asked
- how many of those landed on the most common answer
- the agreement fraction, between one over k and one
Two details make it work in practice. Answers have to be compared after
normalising, since 1947 and the year 1947 are the same answer and a string
comparison says otherwise; for open-ended answers this means comparing the claim
rather than the wording, which is usually a second model's job. And k has to be
small enough to afford and large enough to mean something: three is the
practical floor, five is the common choice, and past about ten the figure stops
moving.
The lesson stops here
4 more paragraphs to go
You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.
The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.
See the planThe contentsThis is the reading half
Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.
The contents