Compare Two Candidate Distributions - Cross-Entropy, Exactly

Two exact probability vectors can be compared by the selected true-class probability while the log losses remain named.

highlighted = computed this step

Two candidate distributions

Use the same one-hot target for both candidates. The left distribution selects 1/2; the right distribution selects 1/4.

p_{\text{true,left}}=1/2,\quad p_{\text{true,right}}=1/4

1/2 is greater than 1/4, so -log(1/2) is better than -log(1/4) for this one target.

1/2>1/4\Rightarrow -\log(1/2)\text{ better than }-\log(1/4)

The comparison ranks two pinned probability vectors for one example only. The log losses stay named, not decimalized.

\text{rank by exact }p_{\text{true}}\text{; log remains named}