Foundations — Zero-shot and few-shot prompting

Before you can understand zero-shot and few-shot prompting, the parent note throws a lot of symbols at you: $x_t$, $x_{<t}$, $P_{\theta }$, $\prod$, $\arg \max$, $k$, $D=\{(x_i,y_i)\}$. A smart 12-year-old has seen none of these. This page builds each one from nothing, in the order they depend on each other, and anchors every one to a picture.

0. The picture behind everything: a chain of words

Look at the arrow chain in the figure. Each box is a word. The pink arrow into the empty box is the model asking "given everything to my left, what word is most likely here?" That single question is the whole engine. Every symbol in the parent note is just precise notation for this arrow.

1. Token — the atom of text

Why the topic needs it. The parent note says the model is a "next-token predictor". You cannot understand that phrase until "token" means "one box in the chain." Words like shot, demo, query are all just runs of tokens the model reads.

2. Position index $t$ and the sequence $x_1,x_2,\dots$

Why the topic needs it. The whole model is defined in terms of "the token at position $t$" and "everything before position $t$". Without a name for position, we could not write that.

3. "Everything before" — the shorthand $x_{<t}$ and range $x_{1:T}$

4. Probability $P$ — a number between 0 and 1 for "how likely"

5. The conditional bar | — "given that"

Putting symbols 1–5 together, the parent note's central formula $P_{\theta }(x_t\mid x_1,x_2,\dots ,x_{t-1})$ now reads in plain words: "the probability the model assigns to the next token, given every token so far." You can read every piece.

6. The subscript $\theta$ — the frozen brain

7. The product $\prod$ — multiply a whole row together

8. $\arg \max$ — "which choice wins?"

So the parent note's $\text{answer}=\arg {\max }_y{P}_{\theta }(y\mid \text{demos},\text{query})$ reads: "the answer is whichever output $y$ the model rates most likely, given your examples and your question." Few-shot works by making the right $y$ the tallest bar.

9. $k$, demos, and the demo-set $D=\{(x_i,y_i){\}}_{i=1}^k$

How these feed the topic

Read top to bottom: tokens give positions, positions give the sequence, the sequence gives "context so far", context plus the conditional bar plus the locked brain $\theta$ give the next-token probability, the product turns that into whole-sentence probability, and $\arg \max$ over the demo-conditioned distribution is the final answer — which is exactly what few-shot steers.

Equipment checklist

Test yourself — cover the right side of each line.

If every line above felt easy, you are ready for Zero-shot and Few-shot prompting. If any felt shaky, reread its section — the parent note assumes all of them. See also Large Language Models for the machine itself and Context window for the limit on how many demos fit.