The finale closes the track boundary: exact deterministic selection, named softmax probabilities, and no claim beyond mechanics.
highlighted = computed this step
What is exact
Greedy and top-k selection are exact deterministic operations on integer logits. The final greedy output remains a, b.
exact selection = a , b \text{exact selection}=a,b exact selection = a , b Decode boundary Exact selection plus named softmax boundary. Decode boundary Exact selection plus named softmax boundary. exact selections with named softmax displayed integer logits are the source; ties break by lowest vocab index step 1 logits: a=3, b=1, c=2 token logit rank a 3 1 b 1 3 c 2 2 ranked order: a > c > b top-2: a, c greedy argmax: a softmax probabilities are named, not pinned decimals softmax: a:e^3/(e^3+e^1+e^2); b:e^1/(e^3+e^1+e^2); c:e^2/(e^3+e^1+e^2) exact greedy path with top-k branches tree choices are exact argmax/top-k selections from displayed logits start step 1 choose a a=3, b=1, c=2 top1: a top2: c step 2 choose b a=0, b=4, c=1 top1: b top2: c greedy decode: a,b
What is named
Softmax probabilities are named because they use exponentials. The diagram shows symbols rather than decimal weights.
softmax = named boundary \operatorname{softmax}=\text{named boundary} softmax = named boundary Decode boundary Exact selection plus named softmax boundary. Decode boundary Exact selection plus named softmax boundary. exact selections with named softmax displayed integer logits are the source; ties break by lowest vocab index step 1 logits: a=3, b=1, c=2 token logit rank a 3 1 b 1 3 c 2 2 ranked order: a > c > b top-2: a, c greedy argmax: a softmax probabilities are named, not pinned decimals softmax: a:e^3/(e^3+e^1+e^2); b:e^1/(e^3+e^1+e^2); c:e^2/(e^3+e^1+e^2) exact greedy path with top-k branches tree choices are exact argmax/top-k selections from displayed logits start step 1 choose a a=3, b=1, c=2 top1: a top2: c step 2 choose b a=0, b=4, c=1 top1: b top2: c greedy decode: a,b
Summary
Greedy and top-k selection are exact and deterministic. Softmax probabilities are the named boundary. This pins the decoding mechanics; it is not learning, not meaning, and not a claim that the output is correct or intelligent.
decoding mechanics; named probabilities \text{decoding mechanics; named probabilities} decoding mechanics; named probabilities Decode boundary Exact selection plus named softmax boundary. Decode boundary Exact selection plus named softmax boundary. exact selections with named softmax displayed integer logits are the source; ties break by lowest vocab index step 1 logits: a=3, b=1, c=2 token logit rank a 3 1 b 1 3 c 2 2 ranked order: a > c > b top-2: a, c greedy argmax: a softmax probabilities are named, not pinned decimals softmax: a:e^3/(e^3+e^1+e^2); b:e^1/(e^3+e^1+e^2); c:e^2/(e^3+e^1+e^2) exact greedy path with top-k branches tree choices are exact argmax/top-k selections from displayed logits start step 1 choose a a=3, b=1, c=2 top1: a top2: c step 2 choose b a=0, b=4, c=1 top1: b top2: c greedy decode: a,b