Before softmax probabilities appear, the displayed integer logits already have an exact order and exact gaps. This lesson compares a, c, and b on the first row, then leaves the full greedy decode step to the next lesson.

highlighted = computed this step

Order the logits first

The first row of logits is a=3, b=1, c=2. On the number line, the exact order is a > c > b. That ordering is enough for greedy argmax before any probability mass is computed.

a:3  >  c:2  >  b:1a:3\;>\;c:2\;>\;b:1
Logit gaps before probabilitiesStep-one logits ordered on a number line before softmax.step-one logits ordered exactly: a=3, c=2, b=101234argmax aa=3b=1c=2exact logit comparison; NOT probability; NOT sampling; NOT generalization

Measure the top gaps

The top logit is a=3. Its exact gap a-c is 1, and its exact gap a-b is 2. These are integer differences between displayed logits, not probabilities.

ac=  3    2  =  1,ab=  3    1  =  2\ell_a-\ell_c=\;3\;-\;2\;=\;1,\quad \ell_a-\ell_b=\;3\;-\;1\;=\;2
Logit gaps before probabilitiesStep-one logits ordered on a number line before softmax.step-one logits ordered exactly: a=3, c=2, b=101234argmax aa=3b=1c=2exact logit comparison; NOT probability; NOT sampling; NOT generalization

The remaining gap

The gap c-b is also exact: c-b = 1. Softmax would preserve this same ordering, but this lesson does not compute probability weights.

cb=  2    1  =  1\ell_c-\ell_b=\;2\;-\;1\;=\;1
Logit gaps before probabilitiesStep-one logits ordered on a number line before softmax.step-one logits ordered exactly: a=3, c=2, b=101234argmax aa=3b=1c=2exact logit comparison; NOT probability; NOT sampling; NOT generalization

Boundary

Greedy argmax is a from this displayed row. This is one exact logit-row comparison only: no sampling, no probability mass, not model quality, not future behavior, not training, not learning, and not meaning.

argmax{a:3,b:1,c:2}=a\operatorname{argmax}\{a:3,b:1,c:2\}=a
Logit gaps before probabilitiesStep-one logits ordered on a number line before softmax.step-one logits ordered exactly: a=3, c=2, b=101234argmax aa=3b=1c=2exact logit comparison; NOT probability; NOT sampling; NOT generalization