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Autoregressive Generation (sequence diagram)

Tue, 22 Sep 2026 07:15:00 +0900

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A language model writes one token at a time. The prompt is processed once, then each new token is appended to the sequence and fed back in, so generation is a loop between the model and the sampler rather than a single call. The sequence diagram below shows the participants and the messages between them.

A Transformer Training Step (flowchart)

Mon, 21 Sep 2026 14:02:00 +0900

One training step is a fixed cycle: the model predicts, the predictions are scored against the targets, the error is propagated backwards, and the parameters move a little in the direction that reduces it. The diagram below shows that cycle; the repetition is the whole of training.

Decoding as a State Machine (state diagram)

Mon, 21 Sep 2026 10:12:00 +0900

The same generation loop can be described without messages, as a machine with a small number of states. This view is useful when the interesting questions are about transitions — when decoding starts, what keeps it running, and which conditions end it. The state diagram below is the whole lifecycle of one completion.

Nucleus (Top-p) Sampling

Mon, 21 Sep 2026 06:52:00 +0900

A language model does not emit a token; it emits a probability for every token in the vocabulary, and something has to choose one. Choosing the single most probable token makes output repetitive, while sampling from the full distribution occasionally picks from its long tail of near-zero probabilities. Nucleus sampling keeps the smallest set of tokens whose combined probability reaches a threshold and samples only from those.