LATENT
HOW AI WORKS - FRAME BOOK
VOL. 01·SEP 2026

CHOOSING THE NEXT TOKEN.

THE MODEL NEVER OUTPUTS A WORD. IT OUTPUTS ODDS FOR EVERY TOKEN. A DECODING RULE TURNS THE ODDS INTO ONE CHOICE.

SPIN THE WHEEL.

EACH RING HOLDS THE SAME LOGITS AT A DIFFERENT TEMPERATURE. ONE RANDOM NUMBER u PICKS A TOKEN ON EVERY RING AT ONCE.

PROMPT

The cat sat on the

SEED 1234
uT→0T \to 00.512
0.07thethethethe
0.70thematcatsat
0.90thecataruns
0.97thesatrunsdog

01GREEDY

xt=arg⁡max⁡i pix_t = \arg\max_i \, p_i

Always the top token. Same text every run.

02TEMPERATURE

pi=ezi/T∑jezj/Tp_i = \dfrac{e^{z_i/T}}{\sum_j e^{z_j/T}}

Low T sharpens. High T flattens.

03TOP-K

p~i=pi∑j∈top-kpj\tilde p_i = \dfrac{p_i}{\sum_{j \in \text{top-}k} p_j}

Keep the k best. Rescale to sum 1.

04TOP-P

∑i∈V′pi≥0.9\sum_{i \in V'} p_i \ge 0.9

Keep the fewest tokens covering 90%.

05SEEDS

PROMPTThe cat sat on

  1. SEED 1234u = 0.07themat.
  2. SEED 7u = 0.01thedog.
  3. SEED 256u = 0.89amat.
  4. SEED 1234u = 0.07themat.= RUN 1

SAME SEED →\to SAME TEXT

xt∼p( ⋅∣x<t)x_t \sim p(\,\cdot \mid x_{<t})

Same prompt, new draws, new text.

06TRY IT

FILTER

SEED

1234

pp(next token)

  • the0.40
  • mat0.27
  • cat0.14
  • sat0.07
  • a0.05
  • on0.04
  • runs0.02
  • dog0.01

The cat sat on

LAST DRAWS

    GREEDY: the

    Drag T, choose a filter, sample. Reset replays the seed.

    Sampling &Temperature

    Choosing the Next Token

    THE MODEL ONLY GIVES PROBABILITIES. SAMPLING TURNS THEM INTO TEXT: TEMPERATURE RESHAPES THE ODDS, TOP-K AND TOP-P CUT THE UNLIKELY TAIL, AND ONE RANDOM DRAW PICKS THE TOKEN.

    • T<1T < 1SHARPER · SAFER · MORE REPETITIVE
    • T=1T = 1THE MODEL'S OWN ODDS
    • T>1T > 1FLATTER · MORE VARIED · RISKIER
    • LOGITSziz_i
    • SOFTMAXpi(T)p_i(T)
    • TOP-PV′V'
    • SAMPLEx∼p~x \sim \tilde p
    the
    1. LOGITSziz_i
    2. TEMPERATUREzi/Tz_i / T
    3. SOFTMAXpi=ezi/T∑jezj/Tp_i = \dfrac{e^{z_i/T}}{\sum_j e^{z_j/T}}
    4. TRUNCATEV′=top-p(0.9)V' = \text{top-}p(0.9)
    5. RENORMALIZEp~i=pi /∑j∈V′pj\tilde p_i = p_i \,/ \sum_{j \in V'} p_j
    6. SAMPLEx∼p~x \sim \tilde p