Cross-entropy increases as the correct probability decreases. The monotonic direction is a named guide, while the perfect-probability anchor remains exact.

highlighted = computed this step

Lower probability, larger named loss

Cross-entropy gets larger as the correct probability gets smaller. The table shows the exact anchor at probability 1 and named losses at probabilities 1/2 and 1/4.

pklog(pk)named guidep_k\downarrow\Rightarrow -\log(p_k)\uparrow\quad\text{named guide}
Named monotonic guideOnly the exact zero anchor is numeric.lower correct probability means larger named lossp_klossregister10EXACT1/2-log(1/2)NAMED1/4-log(1/4)NAMEDmonotonic guide only; no log decimalsexact one-hot selection plus named log boundary; one loss on one pinned probabilitydistribution; NOT learning

Not a decimal curve

The monotonic row is a guide, not a pinned smooth curve. The only numeric loss shown is 0 at probability 1. The remaining losses are named log symbols.

log(1)=0-\log(1)=0
Named monotonic guideOnly the exact zero anchor is numeric.lower correct probability means larger named lossp_klossregister10EXACT1/2-log(1/2)NAMED1/4-log(1/4)NAMEDmonotonic guide only; no log decimalsexact one-hot selection plus named log boundary; one loss on one pinned probabilitydistribution; NOT learning

Summary

The direction of change is useful, but it is not a table of computed log decimals. Exact-or-named still has no third category.

direction named; anchor exact\text{direction named; anchor exact}
Named monotonic guideOnly the exact zero anchor is numeric.lower correct probability means larger named lossp_klossregister10EXACT1/2-log(1/2)NAMED1/4-log(1/4)NAMEDmonotonic guide only; no log decimalsexact one-hot selection plus named log boundary; one loss on one pinned probabilitydistribution; NOT learning