Named Log Loss

The Log Is the Named Boundary

The selected probability is exact, but the logarithm is transcendental. This lesson names the log and shows the one exact zero-loss anchor.

highlighted = computed this step

The log is named

The expression -log(1/2) is the loss for this row, but the log value is transcendental. The diagram names it as a symbol and pins no decimal.

H=−log⁡(1/2)namedH=-\log(1/2)\quad\text{named}
Cross-entropy exactlyOne-hot selection with named log boundary.cross-entropy term selectionclassy_ip_itermA01/40 (one-hot drop)B11/2-log(1/2)C01/40 (one-hot drop)H=-log(1/2)exact one-hot selection plus named log boundary; one loss on one pinned probabilitydistribution; NOT learning

The exact anchor

There is one exact anchor: if the correct probability is 1, then -log(1) equals 0. That perfect-probability case is exact; other log values stay named.

−log⁡(1)=0-\log(1)=0
Exact zero-loss anchorCorrect probability one gives zero loss.cross-entropy term selectionclassy_ip_itermA000 (one-hot drop)B110C000 (one-hot drop)H=0exact one-hot selection plus named log boundary; one loss on one pinned probabilitydistribution; NOT learning

Summary

This lesson marks the boundary: exact rational probability goes in, a named log expression comes out, except for the exact zero-loss anchor.

log⁡ is named; −log⁡(1)=0\log\text{ is named; }-\log(1)=0
Exact zero-loss anchorCorrect probability one gives zero loss.cross-entropy term selectionclassy_ip_itermA000 (one-hot drop)B110C000 (one-hot drop)H=0exact one-hot selection plus named log boundary; one loss on one pinned probabilitydistribution; NOT learning