Feature scaling starts before the model: inspect the displayed coordinate table first.

highlighted = computed this step

Start with raw coordinates

The displayed table has query row Q and two candidate rows A and B. The small feature runs from 0 to 4, while the large feature runs from 0 to 100.

Q=(0,90),A=(1,0),B=(4,100)Q=(0,90),\quad A=(1,0),\quad B=(4,100)
Feature Scaling ExactlyExact min-max fractions from one displayed table.min-max scaled feature tablerowsmall rawlarge rawsmall scaledlarge scaledQ09009/10A101/40B410011small: min 0, max 4, range 4large: min 0, max 100, range 100preprocessing changes coordinate scale onlydistance and gradient-style methods see the changed coordinatesNOT training; NOT learning; NOT generalizationNOT accuracy; NOT calibration; NOT a guarantee of model qualityNOT probability truth

Scaling is preprocessing

Nothing has been trained. The table is only being rewritten onto a new coordinate scale before a later method reads it.

same rows, new coordinate scale\text{same rows, new coordinate scale}
Feature Scaling ExactlyExact min-max fractions from one displayed table.min-max scaled feature tablerowsmall rawlarge rawsmall scaledlarge scaledQ09009/10A101/40B410011small: min 0, max 4, range 4large: min 0, max 100, range 100preprocessing changes coordinate scale onlydistance and gradient-style methods see the changed coordinatesNOT training; NOT learning; NOT generalizationNOT accuracy; NOT calibration; NOT a guarantee of model qualityNOT probability truth

Keep the claim narrow

This is exact preprocessing arithmetic. It does not claim accuracy, calibration, learning, or generalization.

preprocessing only\text{preprocessing only}
Feature Scaling ExactlyExact min-max fractions from one displayed table.min-max scaled feature tablerowsmall rawlarge rawsmall scaledlarge scaledQ09009/10A101/40B410011small: min 0, max 4, range 4large: min 0, max 100, range 100preprocessing changes coordinate scale onlydistance and gradient-style methods see the changed coordinatesNOT training; NOT learning; NOT generalizationNOT accuracy; NOT calibration; NOT a guarantee of model qualityNOT probability truth