Introduction
GPT-style models (Sequences tab, topic 4.5) don't write a whole paragraph at once. They generate one token at a time: predict a probability for every possible next token, pick one, append it to the text, and repeat. This is autoregressive generation: each new output depends on all the previous outputs.
How you pick each token matters enormously. Always picking the most likely one gives safe but dull, often repetitive text. Picking randomly from the full distribution gives variety but sometimes nonsense. Sampling strategies like temperature, top-k and top-p let you choose a point between "predictable" and "creative".
Think of a jazz musician improvising. At each beat they choose the next note. A cautious player always plays the most expected note: correct but boring. A wild player picks any note: surprising but often wrong. Great improvisers choose among the good options, with a bit of surprise. That's what good sampling does.